Documentation Of HeatPumpModel_v31




Quick Links All Variables Variable Link Detail Variable Types Views Groups Units Macros Feedback Loops Exogenous Variables Analysis Endogenous Variables Analysis Link Polarity View Summary View-Variable Profile

Model Assessment Results

Model Information Result
342|32,718
27 (7.9%)|525 (1.6%)
14 (4.1%)|466 (1.4%)
163 (47.7%)|747 (2.3%)
178 (52.0%)|31,971 (97.7%)
17 (7|10|0)
0 (0|0|0)
586 (432|87|67)|103,446 (80,357|19,037|4,052)
7
9/42
0 (0.0%)|0 (0.0%)
0 (0.0%)|0 (0.0%)
59 (17.3%)|4,177 (12.8%)
341 (99.7%)|32,718 (100.0%)
0 (0.0%)|0 (0.0%)
0 (0.0%)|0 (0.0%)
Time Unit
Year
Initial Time
2020
Final Time
2050
Reported Time Interval
TIME STEP
Time Step
0.03125
Model Is Fully Formulated
Yes
Model Defined Groups
Yes

Warnings Result
18 (5.3%)|18 (0.1%)
19 (5.6%)|413 (1.3%)
2 (0.6%)|2 (0.0%)
0 (0.0%)|0 (0.0%)
0 (0.0%)|0 (0.0%)
5 (1.5%)|5 (0.0%)
22 (6.4%)|3,089 (9.4%)
13 (3.8%)|2,677 (8.2%)
3 (0.9%)|3 (0.0%)
5 (1.5%)|15 (0.0%)

Potential Omissions Result
49 (14.3%)|704 (2.2%)
0 (0.0%)|0 (0.0%)
0 (0.0%)|0 (0.0%)
46 (13.5%)|11,644 (35.6%)
0 (0.0%)|0 (0.0%)


Variable Types

L: Level (14 / 466)* SM: Smooth (13 / 173)* DE: Delay (0 / 0)*† LI: Level Initial (7) I: Initial (1 / 38)
C: Constant (121 / 3,418) F: Flow (24 / 4,563) A: Auxiliary (202 / 28,829) Sub: Subscripts (19) D: Data (0 / 0)
G: Game (0 / 0) T: Lookup (5 / 5)*††      
* (State Variables/Total Stocks) † Total Stocks Do Not Include Fixed Delay Variables. †† (Lookup Tables).  

Views

View: Age (14 Variables)
View: Area (18 Variables)
View: Average Attributes (64 Variables)
View: Average and Peak Load (17 Variables)
View: Carbon Emissions (13 Variables)
View: Cumulative Subsidies (39 Variables)
View: Energy Use (28 Variables)
View: Housing Aging Chain & U Coflows (68 Variables)
View: Input Test (59 Variables)
View: Optimal U & Retrofit Costs (42 Variables)
View: Perceived Subsidies & Costs (64 Variables)
View: Retrofitting Decision Making (23 Variables)
View: Social Influence in Retrofitting Decisions (1 Variables)
View: Switching Systems (34 Variables)
View: U Value of Housing Starts (18 Variables)



Groups

. (1) .Control (4) .housingagingchain v15 (28) .housingagingchain v18 (5) .housingagingchain v4 testing (4)
.housingagingchain v5 testing (14) .housingagingchain v8 (51) .housingagingchain v9 (1) HeatPumpModel_v31 (234) 



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Top (All) Variables (342 Variables)
Group
Type
Variable Name And Description
.housingagingchain v8 #0
C
Active Cohort Indicator (dmnl)
Active Cohort Indicator[Cohort] = IF THEN ELSE(INTEGER((
Time- INITIAL TIME)/ Cohort Duration)+1= Cohort-ELMCOUNT( Preexisting Cohorts),1,0)
Active Cohort Indicator[Preexisting Cohorts] = 0
Description: The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
Present In 1 View: Used By
  • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #1
A
Actual EEHIC Subsidy for Retrofits (Dollar / House)
Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] = MIN(
Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]* Implemented EEHIC Subsidy Proportional Rate for Retrofits, Implemented EEHIC Maximum Subsidy for Retrofits)
Description: The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value.
Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #2
A
Actual HOMES Subsidy for Retrofits (Dollar/ Home)
Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] = IF THEN ELSE(
Energy Savings[ Cohort, Heating and Cooling System]< HOMES Cut Off for Savings, HOMES Implemented Lower Subsidy, HOMES Implemented High Subsidy)
Description: The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #3
A
Actual MassSave Subsidy for Retrofits (Dollar / House)
Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] = MIN(
Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]* Implemented MassSave Subsidy Proportional Rate for Retrofits, Implemented MassSave Maximum Subsidy for Retrofits)
Description: The actual subsidy offered for retrofits by MassSave, not the expected value.
Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
.housingagingchain v15 #4
A
Additional Cost of Building to U Value (Dollar / sf)
Additional Cost of Building to U Value[Cohort,Heating and Cooling System] = ((1-
Expected MassSave Proportional Subsidy Rate for Retrofits)* Expected Reference Marginal Cost/(1- Sensitivity of Marginal Cost to U Value))*((( Reference U Value/ Code U)^ Sensitivity of Marginal Cost to U Value)* Code U-(( Reference U Value/ Optimal U for New Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value))* Optimal U for New Homes[ Cohort, Heating and Cooling System])- Expected Lump Sum Subsidy Intensity[New Housing]
Description: Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
Present In 1 View: Used By
  • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #5
A
Affinity of Heating and Cooling Systems (dmnl)
Affinity of Heating and Cooling Systems[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = IF THEN ELSE(
Cost of Switching Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]>0,exp(- Sensitivity of Affinity to Cost* Cost of Switching Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Reference Lifetime Cost of Heating and Cooling Systems),0)
Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = IF THEN ELSE( Cost of Switching Heating and Cooling Systems[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]>0,exp(- Sensitivity of Affinity to Cost* Cost of Switching Heating and Cooling Systems[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]/ Reference Lifetime Cost of Heating and Cooling Systems),0)
Description: The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
Present In 1 View: Used By
  • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #6
A
Affinity of Not Retrofitting (dmnl)
Affinity of Not Retrofitting[Cohort,Heating and Cooling System] = exp(-
Sensitivity of Retrofits to Cost* Perceived Cost of Not Retrofitting[ Cohort, Heating and Cooling System]/ Reference Retrofit Cost)
Description: The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
Present In 1 View: Used By
  • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
.housingagingchain v4 testing #7
A
Affinity of Retrofitting (dmnl)
Affinity of Retrofitting[Cohort,Heating and Cooling System] = exp(-
Sensitivity of Retrofits to Cost* Perceived Cost of Retrofitting[ Cohort, Heating and Cooling System]/ Reference Retrofit Cost)
Description: Affinity of retrofitting, where utility value is equal to its NPV.
Present In 2 Views: Used By
  • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
.housingagingchain v8 #8
F,A
Age Removal (House * Year /Year)
Age Removal[Cohort,Retrofitting Status] = SUM(
Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])* Average Age[ Cohort, Retrofitting Status]
Description: Total age lost as houses are destroyed, scrapped, etc.
Present In 1 View: Used By
  • Total Age "Total" age for each cohort of housing.
Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
.housingagingchain v8 #10
F,A
Aging (House * Year / Year)
Aging[Cohort,Retrofitting Status] =
Aging per Year*SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
Description: Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
Present In 1 View: Used By
  • Total Age "Total" age for each cohort of housing.
Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
.housingagingchain v8 #9
C
Aging per Year (Year / Year)
= 1
Description: Number of years a house ages per year (which must be one), used to ensure dimensional consistency and make the model clearer
Present In 1 View:
Used By
  • Aging Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #11
C
Amoritization Period (Year )
= 20
Description: Time period over which incurred retrofit cost is amoritized; should be related to lifetime of a home.
Present In 1 View:
Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
.housingagingchain v15 #12
A
Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))
Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]/ Amoritization Period
Description: The incurred total retrofit cost amoritized over the specified amoritization period.
Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #13
F,A
Annual Federal Subsidies (Dollar / Year)
=
Federal Annual Heat Pump Subsidy+ Federal Annual Retrofit Subsidy
Description: The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year.
Present In 1 View: Used By
  • Cumulative Federal Subsidy The amount of money the federal government spends on subsidies for heat pumps and retrofits since the beginning of the model's run.
Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #14
F,A
Annual Heat Pump Subsidy (Dollar / Year)
=
Federal Annual Heat Pump Subsidy+ Massachusetts Annual Heat Pumps Subsidy
Description: The amount of money the government spends to subsidize heat pumps, including state and federal government.
Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #15
A
Annual Load from Heat Pumps (kBTU / Year)
= SUM(
Energy Use by Grouping[ Cohort!, Heat Pump Heating and Cooling!, Retrofitting Status!])
Description: The load on the electric grid from servicing heating and cooling demand from heat pumps, across the whole year.
Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #16
F,A
Annual MA Subsidies (Dollar / Year)
=
Massachusetts Annual Retrofit Subsidy+ Massachusetts Annual Heat Pumps Subsidy
Description: The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps.
Present In 1 View: Used By
  • Cumulative MA Subsidy The amount of subsidies that the Massachusetts state government has given out for heat pumps and retrofits since the beginning of the model's run.
Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #17
F,A
Annual Retrofit Subsidy (Dollar / Year)
=
Federal Annual Retrofit Subsidy+ Massachusetts Annual Retrofit Subsidy
Description: The subsidies for retrofits paid out every year.
Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
HeatPumpModel_v31 #18
A
Annual Subsidies (Dollar / Year)
=
Annual Heat Pump Subsidy+ Annual Retrofit Subsidy
Description: The amount of subsidies spent on heat pumps and retrofits every year.
Present In 1 View: Used By
    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
    .housingagingchain v8 #21
    L
    Area (sf)
    Area[Cohort,Not Open to Retrofitting] = (
    Area of New Homes[ Cohort]- Net Area Shift due to Retrofit Status Switching[ Cohort])- Area Removal[ Cohort,Not Open to Retrofitting] dt + Initial Area[ Cohort]*(1.0- Fraction Retrofitting by Cohort[ Cohort])
    Area[Preexisting Cohorts,Not Open to Retrofitting] = (- Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts])- Area Removal[ Preexisting Cohorts,Not Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]*(1.0- Fraction Retrofitting by Cohort[ Preexisting Cohorts])
    Area[Cohort,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Cohort]- Area Removal[ Cohort,Open to Retrofitting] dt + Initial Area[ Cohort]* Fraction Retrofitting by Cohort[ Cohort]
    Area[Preexisting Cohorts,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts]- Area Removal[ Preexisting Cohorts,Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]* Fraction Retrofitting by Cohort[ Preexisting Cohorts]
    Description: "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
    Present In 2 Views: Used By
    • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
    • Total Area The total area across all housing.
    Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
    .housingagingchain v8 #19
    F,A
    Area of New Homes (sf / Year)
    Area of New Homes[Cohort] =
    Average Area of Housing Starts*SUM( Housing Starts[ Cohort, Heating and Cooling System!])
    Description: The total Area added by the construction of new homes, by cohort.
    Present In 1 View: Used By
    • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
    .housingagingchain v8 #20
    F,A
    Area Removal (sf /Year)
    Area Removal[Cohort,Retrofitting Status] =
    Average Area[ Cohort, Retrofitting Status]*SUM( Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])
    Description: Total area lost as houses are destroyed, scrapped, etc.
    Present In 1 View: Used By
    • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
    .housingagingchain v8 #24
    L
    Autocorrelated Noise (Dimensionless)
    =
    Change in AC Noise dt + 0.0
    Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
    Present In 1 View: Used By
    • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
    .housingagingchain v8 #22
    L
    Autocorrelated Noise 0 (Dimensionless)
    =
    Change in AC Noise 0 dt + 0.0
    Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
    Present In 1 View: Used By
    • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
    HeatPumpModel_v31 #23
    L
    Autocorrelated Noise 1 (Dimensionless)
    =
    Change in AC Noise 1 dt + 0.0
    Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
    Present In 1 View: Used By
    • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
    • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
    .housingagingchain v8 #26
    A
    Average Age (Year)
    Average Age[Cohort,Retrofitting Status] = ZIDZ(
    Total Age[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
    Description: The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
    Present In 1 View: Used By
    • Age Removal Total age lost as houses are destroyed, scrapped, etc.
    • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
    Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
    .housingagingchain v8 #25
    A
    Average Age in All Housing (Year)
    = ZIDZ(SUM(
    Total Age[ Cohort!, Retrofitting Status!]), Total Housing Stock)
    Description: Average age of houses, regardless of cohort
    Present In 2 Views: Used By
      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
      HeatPumpModel_v31 #29
      A
      Average Area (sf / House)
      Average Area[Cohort,Retrofitting Status] = ZIDZ(
      Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
      Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
      Present In 7 Views: Used By
      • Area Removal Total area lost as houses are destroyed, scrapped, etc.
      • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
      • Average EUI by Grouping The average energy use intensity by grouping
      • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
      • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
      • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
      • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
      • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
      • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
      • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
      • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
      • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
      • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
      • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
      • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
      • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
      Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
      .housingagingchain v8 #27
      A
      Average Area in All Housing (sf/ House)
      = ZIDZ(
      Total Area, Total Housing Stock)
      Description: The average are of all houses, regardless of what group they're in.
      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
      HeatPumpModel_v31 #28
      A
      Average Area of Housing Starts (sf / House)
      =
      Increase in Area per Year*( Time- INITIAL TIME)+ Initial Average Area of Housing Starts
      Description: The average area of housing starts.
      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
      HeatPumpModel_v31 #31
      A
      Average Cooling Cost (Dollar / (Year * House))
      Average Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
      Expected Cooling Energy Price* Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
      Description: The average costs for keeping a home cool, by grouping.
      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
      HeatPumpModel_v31 #30
      A
      Average Cooling Cost Across All Homes (Dollar / House/ Year)
      =
      Total Cooling Cost/SUM( Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
      Description: The average cost to cool a home, for all cohorts and systems.
      Present In 1 View: Used By
        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
        HeatPumpModel_v31 #33
        C
        Average Cooling Energy Use (kBTU / (Year * House))
        Average Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
        U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
        Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
        Description: The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
        Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
        HeatPumpModel_v31 #32
        A
        Average Cooling Energy Use Across All Homes (kBTU / Year / House)
        = ZIDZ(
        Total Cooling Energy Use, Total Housing Stock)
        Description: The amount of energy an average home spends on cooling, regardless of cohort, retrofit status, etc.
        Present In 1 View: Used By
          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
          HeatPumpModel_v31 #34
          A
          Average Daily Load from Heat Pumps (kBTU / Day)
          =
          Annual Load from Heat Pumps/ Days per Year
          Description: The average load on the electric grid from heat pumps, per day.
          Present In 1 View: Used By
            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
            HeatPumpModel_v31 #39
            A
            Average Emissions (tCO2 / House / Year)
            = ZIDZ(
            Emissions, Total Housing Stock)
            Description: The average CO2 emissions for a household, not disaggregated into any grouping.
            Present In 1 View: Used By
              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
              HeatPumpModel_v31 #35
              A
              Average Emissions by Grouping (tCO2 / (Year * House))
              Average Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
              Average Emissions from Cooling by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Emissions from Heating by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
              Description: The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
              HeatPumpModel_v31 #36
              A
              Average Emissions by Heating and Cooling System (tCO2 / Year / House)
              Average Emissions by Heating and Cooling System[Heating and Cooling System] = ZIDZ(
              Emissions by Heating and Cooling System[ Heating and Cooling System], Housing by Heating and Cooling System[ Heating and Cooling System])
              Description: The average CO2 emissions for each house, by heating and cooling system.
              Present In 2 Views: Used By
                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                HeatPumpModel_v31 #37
                A
                Average Emissions from Cooling by Grouping (tCO2 / (House * Year))
                Average Emissions from Cooling by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Cooling Emissions Factor/ Pounds per Ton
                Description: The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status.
                Present In 1 View: Used By
                • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                HeatPumpModel_v31 #38
                A
                Average Emissions from Heating by Grouping (tCO2 / (House * Year))
                Average Emissions from Heating by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Heating Emissions Factors[ Heating and Cooling System]/ Pounds per Ton
                Description: Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc.
                Present In 1 View: Used By
                • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                HeatPumpModel_v31 #40
                A
                Average Energy Cost (Dollar / (Year * House))
                Average Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                Average Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                Description: The average cost of both heating and cooling a home, by grouping.
                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                .housingagingchain v15 #41
                A
                Average Energy Costs for Retrofitting Home (Dollar / Year / House)
                Average Energy Costs for Retrofitting Home[Cohort,Heating and Cooling System] =
                Average Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                Description: Heating costs for each home open to retrofitting, annually, if no further retrofit measures are undertaken.
                Present In 2 Views: Used By
                • Total Cost of Ownership of Average Home Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                .housingagingchain v8 #42
                A
                Average Energy Costs if Retrofitted (Dollar/(Year*House))
                Average Energy Costs if Retrofitted[Cohort,Heating and Cooling System] =
                Optimal Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                Description: Energy costs per year for each retrofitting house if homes retrofit to the optimal U value.
                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                HeatPumpModel_v31 #45
                A
                Average Energy Use (kBTU / (Year * House))
                Average Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                Description: Average energy use to both heat and cool a home.
                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                HeatPumpModel_v31 #43
                A
                Average Energy Use by Heating and Cooling System (kBTU / (House * Year))
                Average Energy Use by Heating and Cooling System[Heating and Cooling System] = ZIDZ(SUM(
                Energy Use by Grouping[ Cohort!, Heating and Cooling System, Retrofitting Status!]),SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!]))
                Description: The average energy use for each home by heating and cooling system.
                Present In 1 View: Used By
                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                  HeatPumpModel_v31 #44
                  A
                  Average Energy Use in All Housing (kBTU / Year / House)
                  =
                  Total Energy Use/ Total Housing Stock
                  Description: The average energy use across all stocks.
                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                  HeatPumpModel_v31 #46
                  A
                  Average EUI by Grouping (kBTU / (sf * Year))
                  Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = XIDZ(
                  Average Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status], Average Area[ Cohort, Retrofitting Status], NAREPLACEMENT)
                  Description: The average energy use intensity by grouping
                  Present In 1 View: Used By
                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                    HeatPumpModel_v31 #47
                    A
                    Average EUI in All Housing (kBTU / (sf * Year))
                    =
                    Average Energy Use in All Housing/ Average Area in All Housing
                    Description: The average energy use intensity across all housing.
                    Present In 1 View: Used By
                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                      .housingagingchain v5 testing #49
                      A
                      Average Heating Cost (Dollar / (Year * House))
                      Average Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                      Expected Heating Energy Price[ Heating and Cooling System]* Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                      Description: The costs per year to heat one house.
                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                      HeatPumpModel_v31 #48
                      A
                      Average Heating Cost Across All Homes (Dollar / Year / House)
                      = ZIDZ(
                      Total Heating Cost,SUM( Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!]))
                      Description: The average amount a home spends on heating, regardless of cohort or heating and cooling system.
                      Present In 1 View: Used By
                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                        HeatPumpModel_v31 #51
                        A
                        Average Heating Energy Use (kBTU / (Year * House))
                        Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                        U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                        Description: The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                        Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                        HeatPumpModel_v31 #50
                        A
                        Average Heating Energy Use Across All Homes (kBTU / (Year * House))
                        = ZIDZ(
                        Total Heating Energy Use, Total Housing Stock)
                        Description: The average heating energy use per home, regardless of cohort, system,etc.
                        Present In 1 View: Used By
                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                          HeatPumpModel_v31 #52
                          C
                          Average Income (Dollar / Hour / House )
                          = 55
                          Description: The average income of single family homeowners in Massachusetts. Calculated from 2020 EIA RECS data for MA SFH, where each individual was assigned the average income of their reported income bracket, other than those making more than $150K/year, who were assigned $175,000. Hourly wage calculated by assuming working 8 hours a day, 5 days a week, for 50 weeks in a year.
                          Present In 1 View:
                          Used By
                          • Soft Costs of Retrofitting The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                          HeatPumpModel_v31 #53
                          A
                          Average Indicated Fraction of Homes Retrofitting (dmnl)
                          = SUM(
                          Indicated Homes Retrofitting[ Cohort!, Heating and Cooling System!])/ Total Housing Stock
                          Description: The average fraction of homes that will retrofit retrofitting after decision delayacross all housing.
                          Present In 2 Views: Used By
                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                            HeatPumpModel_v31 #54
                            A
                            Average Lifetime of Cooling Technology (Years)
                            Average Lifetime of Cooling Technology[Heat Pump Heating and Cooling] = 12.5
                            Average Lifetime of Cooling Technology[Central AC Cooling] = 12.5
                            Average Lifetime of Cooling Technology[Window AC Cooling] = 9
                            Average Lifetime of Cooling Technology[No AC Cooling] =
                            NAREPLACEMENT
                            Description: The average lifetime of each cooling system.Central AC data from: https://www.energy.gov/energysaver/central-air-conditioningWindow AC data from: https://www.consumerreports.org/air-conditioner/is-it-time-to-get-a-new-window-air-conditioner-a1532530762/
                            Present In 1 View: Used By
                            • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                            • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                            HeatPumpModel_v31 #55
                            C
                            Average Lifetime of Heating Technology (Year)
                            Average Lifetime of Heating Technology[Heat Pump Heating and Cooling] = 12.5
                            Average Lifetime of Heating Technology[Gas Heating] = 20
                            Average Lifetime of Heating Technology[Oil Heating] = 20
                            Description: The average lifetime of each heating system.Heat pump data from: https://glascohvac.com/heating/heat-pumps/long-heat-pump-last/Gas data from: https://www.carrier.com/residential/en/us/products/furnaces/how-long-does-a-furnaces-last/Oil data from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                            Present In 1 View:
                            Used By
                            • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                            • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                            HeatPumpModel_v31 #56
                            A
                            Average Subsidized Retrofit Cost (Dollar / House)
                            = SUM(
                            Housing[ Cohort!, Heating and Cooling System!,Open to Retrofitting]* Subsidized Retrofit Cost[ Cohort!, Heating and Cooling System!])/SUM( Housing[ Cohort!, Heating and Cooling System!,Open to Retrofitting])
                            Description: The average subsidized retrofit cost across all houses.
                            Present In 1 View: Used By
                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                              HeatPumpModel_v31 #57
                              C
                              Average Time To Consider Switching (Year )
                              = 15
                              Description: The average time it takes for a house to consider switching their heating and cooling system.
                              Present In 2 Views:
                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                              HeatPumpModel_v31 #58
                              A
                              Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))
                              Average U Value by Heating and Cooling System[Heating and Cooling System] = ZIDZ(
                              Total U Value by Heating and Cooling System[ Heating and Cooling System], Housing by Heating and Cooling System[ Heating and Cooling System])
                              Description: The U value of the average house using each heating and cooling system.
                              Present In 1 View: Used By
                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                .housingagingchain v4 testing #59
                                A
                                Average U Value in All Housing (kBTU / (sf * F * Year))
                                = ZIDZ(
                                Total U Value Across All Groupings, Total Housing Stock)
                                Description: The average U Value over the entire housing stock, not disaggregated by any groupings.
                                Present In 1 View: Used By
                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                  HeatPumpModel_v31 #60
                                  A
                                  Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))
                                  Average U Value of Houses Switching Into Sources[Heating and Cooling System] = XIDZ(
                                  U Value Increase from Source Switching[ Heating and Cooling System], Houses Switching Into Sources[ Heating and Cooling System], NAREPLACEMENT)
                                  Description: The average U value of houses switching into each source, for each source.
                                  Present In 1 View: Used By
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #61
                                    C
                                    CDD on Coldest Day (F )
                                    = 17.1
                                    Description: The total CDD from hottest day.Data from https://www.degreedays.net/ for KOWD, weather station nearest to centre of population for MA, Natick. Calculated by finding CDDs from the past three years (February 2021 - January 2024), finding the highest CDD in each year, and averaging them. Following industry standard, used 65°F as set point.
                                    Present In 1 View:
                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    .housingagingchain v8 #64
                                    F,A
                                    Change in AC Noise (1/Year)
                                    = (
                                    White Noise- Autocorrelated Noise)/ Noise Correlation Time
                                    Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                    Present In 1 View: Used By
                                    • Autocorrelated Noise First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                    .housingagingchain v8 #62
                                    F,A
                                    Change in AC Noise 0 (1/Year)
                                    = (
                                    White Noise 0- Autocorrelated Noise 0)/ Noise Correlation Time 0
                                    Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                    Present In 1 View: Used By
                                    • Autocorrelated Noise 0 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                    HeatPumpModel_v31 #63
                                    F,A
                                    Change in AC Noise 1 (1/Year)
                                    = (
                                    White Noise 1- Autocorrelated Noise 1)/ Noise Correlation Time 1
                                    Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                    Present In 1 View: Used By
                                    • Autocorrelated Noise 1 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                    .housingagingchain v18 #65
                                    L
                                    Code U (kBTU / (sf * Year * F))
                                    = -
                                    Decrease in Code U dt + Initial Code U Value
                                    Description: U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                    Present In 2 Views: Used By
                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                    • Decrease in Code U The change in code U from policy.
                                    • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                    .housingagingchain v8 #66
                                    C
                                    Cohort Duration (Year )
                                    = 10
                                    Description: The width (duration) of each cohort.
                                    Present In 2 Views:
                                    Used By
                                    • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                    • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #67
                                    C
                                    Cooling Degree Days (F )
                                    = 1029
                                    Description: The difference between temperature setpoint (65 F) and outside temperature for heating. Typically called cooling degree days, but units are solely in terms of fahrenheit.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. Use set point of 65°F, in line with industry standard, as at that temperature little heating or cooling is necessary.
                                    Present In 3 Views:
                                    Used By
                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #68
                                    C
                                    Cooling Emissions Factor (lb CO2 / kBTU)
                                    = 614/3414.43
                                    Description: Amount of CO2 emitted from using one kBTU to cool a home. Emissions factor is common, and is for electricity.Taken from: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/download
                                    Present In 1 View:
                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #70
                                    A
                                    Cooling Energy Price (Dollar / kBTU)
                                    =
                                    Initial Cooling Energy Price* Input 1
                                    Description: Price of cooling a home (through air conditioning), subject to the test input.
                                    Present In 3 Views: Used By
                                    • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #69
                                    C
                                    Cooling Energy Price Step Height 1 (Dimensionless )
                                    = 0
                                    Description: Height of step input to customer orders, as fraction of initial value.
                                    Present In 1 View:
                                    Used By
                                    • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #71
                                    A
                                    Cooling Energy Use Under Alternatives (kBTU / (House * Year))
                                    Cooling Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Not Open to Retrofitting,Heating and Cooling System] =
                                    U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                    Cooling Energy Use Under Alternatives[Cohort,Traditional Cooling,Not Open to Retrofitting,Heating and Cooling System] = U Value by Grouping[ Cohort, Traditional Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                    Cooling Energy Use Under Alternatives[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] = 0
                                    Cooling Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                    Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Fossil Fuel Heating,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                    Description: The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                    Present In 1 View: Used By
                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #72
                                    A
                                    Cooling System Efficiency (dmnl)
                                    Cooling System Efficiency[Heat Pump Heating and Cooling] =
                                    Heat Pump Cooling COP TABLE( Time)
                                    Cooling System Efficiency[Central AC Cooling] = 2.93
                                    Cooling System Efficiency[Window AC Cooling] = 2.49* Effect of Air Leakage from Window AC on Efficiency
                                    Cooling System Efficiency[No AC Cooling] = NAREPLACEMENT
                                    Description: The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                    Present In 4 Views: Used By
                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #73
                                    C
                                    Cost of Bad Air Conditioning (Dollar / House )
                                    Cost of Bad Air Conditioning[Window AC Cooling] = 80000
                                    Cost of Bad Air Conditioning[No AC Cooling] = 100000
                                    Description: Willingness of Window AC users and those without AC to pay for central AC or heat pumps due to those technologies' inability to heat homes and their noisiness.Chosen to be sufficiently high that very few or no houses choose to keep window AC or no AC.
                                    Present In 1 View:
                                    Used By
                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #74
                                    C
                                    Cost of Cooling System Replacement (Dollar / House)
                                    Cost of Cooling System Replacement[Heat Pump Heating and Cooling] =
                                    Subsidized Cost of Heat Pumps
                                    Cost of Cooling System Replacement[Central AC Cooling] = 5800
                                    Cost of Cooling System Replacement[Window AC Cooling] = 1600
                                    Cost of Cooling System Replacement[No AC Cooling] = 0
                                    Description: The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                    Present In 1 View: Used By
                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #75
                                    C
                                    Cost of Heating System Replacement (Dollar / House )
                                    Cost of Heating System Replacement[Heat Pump Heating and Cooling] =
                                    Subsidized Cost of Heat Pumps
                                    Cost of Heating System Replacement[Gas Heating] = 10000
                                    Cost of Heating System Replacement[Oil Heating] = 7450
                                    Description: The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                    Present In 1 View: Used By
                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    .housingagingchain v15 #76
                                    A
                                    Cost of Switching Heating and Cooling Systems (Dollar / House)
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Heating and Cooling System] = 0
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Heat Pump Only] =
                                    Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Heat Pump Only]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]+ Cost of Heating System Replacement[Gas and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heating and Cooling System] = 0
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heat Pump and Gas] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Heat Pump and Gas]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heating and Cooling System] = 0
                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Heat Pump Only]+ Cost of Heating System Replacement[Heat Pump Only]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Heat Pump and Gas]+ Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Heat Pump and Gas]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Gas and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heating and Cooling System] = 0
                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Heat Pump Only]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Heat Pump and Gas]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Gas and Central AC] = Cost of Cooling System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Gas and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Heat Pump Only]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Oil and Central AC] = Cost of Heating System Replacement[Oil and Central AC]+ Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Oil and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heating and Cooling System] = 0
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Heat Pump Only]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Gas and Central AC] = Cost of Heating System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Gas and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heat Pump and Oil] = Cost of Heating System Replacement[Heat Pump and Oil]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Heat Pump and Oil]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Oil and Central AC] = Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Oil and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heating and Cooling System] = 0
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Heat Pump Only]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Gas and Central AC] = Cost of Heating System Replacement[Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Gas and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heat Pump and Oil] = Cost of Heating System Replacement[Heat Pump and Oil]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Heat Pump and Oil]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Oil and Central AC] = Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Oil and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heating and Cooling System] = 0
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Heat Pump Only]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Heat Pump and Gas]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Oil and Central AC] = Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Oil and Central AC]
                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Oil] = Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Heat Pump and Oil]
                                    Description: Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                    Present In 1 View: Used By
                                    • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                    HeatPumpModel_v31 #77
                                    L
                                    Cumulative Emissions (tCO2)
                                    =
                                    Emissions dt + 0.0
                                    Description: The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                    Present In 1 View: Used By
                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                      HeatPumpModel_v31 #78
                                      L
                                      Cumulative Federal Subsidy (Dollar)
                                      =
                                      Annual Federal Subsidies dt + 0.0
                                      Description: The amount of money the federal government spends on subsidies for heat pumps and retrofits since the beginning of the model's run.
                                      Present In 1 View: Used By
                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                        HeatPumpModel_v31 #79
                                        L
                                        Cumulative MA Subsidy (Dollar)
                                        =
                                        Annual MA Subsidies dt + 0.0
                                        Description: The amount of subsidies that the Massachusetts state government has given out for heat pumps and retrofits since the beginning of the model's run.
                                        Present In 1 View: Used By
                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                          HeatPumpModel_v31 #81
                                          A
                                          Cumulative Subsidies (Dollar)
                                          =
                                          Cumulative Subsidy for Retrofits+ Cumulative Subsidies for Heat Pumps
                                          Description: The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                          Present In 1 View: Used By
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #80
                                            L
                                            Cumulative Subsidies for Heat Pumps (Dollar)
                                            =
                                            Annual Heat Pump Subsidy dt + 0.0
                                            Description: The total amount of dollars spent on subsidizing heat pumps throughout the model's run.
                                            Present In 1 View: Used By
                                            • Cumulative Subsidies The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #82
                                            L
                                            Cumulative Subsidy for Retrofits (Dollar)
                                            =
                                            Annual Retrofit Subsidy dt + 0.0
                                            Description: The total amount spent on retrofits since the beginning of the model's run.
                                            Present In 1 View: Used By
                                            • Cumulative Subsidies The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #83
                                            C
                                            Days per Year (Day / Year )
                                            = 365
                                            Description: The number of days each year. Used to convert yearly measures to daily ones.
                                            Present In 1 View:
                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            .housingagingchain v18 #84
                                            F,A
                                            Decrease in Code U (kBTU / (sf * Year * F) / Year)
                                            =
                                            Code U* Fractional Decrease in Code U
                                            Description: The change in code U from policy.
                                            Present In 1 View: Used By
                                            • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                            .housingagingchain v15 #85
                                            C
                                            Delay in Changing Subsidy Expectations (Year )
                                            = 0.5
                                            Description: Delay in perceiving any changes to subsidies. Assumed to be the same for both subsidies.
                                            Present In 1 View:
                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            .housingagingchain v15 #86
                                            C
                                            Delay in Forming Expectations of Energy Price (Year )
                                            = 1
                                            Description: Delay in perceiving changes in energy price.
                                            Present In 1 View:
                                            Used By
                                            • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                            • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            .housingagingchain v15 #87
                                            C
                                            Delay in Forming Expectations of Retrofit Costs (Year )
                                            = 1.5
                                            Description: Delay in perceiving changes in fixed retrofit cost and reference marginal cost. Assumed to be the same for both types of costs.
                                            Present In 1 View:
                                            Used By
                                            • Expected Fixed Cost Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                            • Expected Reference Marginal Cost Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #88
                                            C
                                            Demolition Hazard Rate (1 / Year )
                                            = 0.01
                                            Description: Proportion of homes demolished every year. Value is assumed to be equal across both retrofitting and non-retrofitting homes. Heuristically chosen so total housing stock grows at net 1%/year.
                                            Present In 1 View:
                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #89
                                            F,A
                                            Demolitions (House / Year)
                                            Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] =
                                            Demolition Hazard Rate* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]*(1- No Turnover Switch)
                                            Description: Homes that are destroyed every year.
                                            Present In 3 Views: Used By
                                            • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                            • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                            • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                            • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                            HeatPumpModel_v31 #90
                                            C
                                            Discount Rate (1 / Year )
                                            = 0.05
                                            Description: Discount rate for discounting energy savings cash flows.Average and bounds from demand-side discount rate from MassDEP's analysis of pathways for net zero (pg. 103): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadhttps://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                            Present In 4 Views:
                                            Used By
                                            • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                            • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                            • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                            • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                            • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #91
                                            A
                                            EEHIC Expected Subsidy for Retrofits (Dollar / House)
                                            EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = MIN(
                                            Proportional Subsidy Switch for Retrofits* Expected EEHIC Proportional Subsidy Rate for Retrofits* Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status], Expected EEHIC Maximum Subsidy for Retrofits)
                                            Description: The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #92
                                            C
                                            EEHIC Maximum Subsidy for Retrofits (Dollar / House )
                                            = 1200
                                            Description: The maximum proportional subsidy that will be offered from Energy Efficient Home Improvement Credit, regardless of that subsidy's discount. Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                            Present In 1 View:
                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #93
                                            C
                                            EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
                                            = 0.3
                                            Description: Proportion of total retrofit cost that will be credited with the Energy Efficiency Home Improvement Credit.Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                            Present In 1 View:
                                            Used By
                                            • Implemented EEHIC Subsidy Proportional Rate for Retrofits The implemented proportional subsidy rate for retrofits from the IRA, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #94
                                            C
                                            EEHIC Subsidy for Retrofits Final Year (Year)
                                            = 2033
                                            Description: The year in which the EEHIC is phased out. If final time, then has no ending data.Source: https://www.irs.gov/credits-deductions/energy-efficient-home-improvement-credit
                                            Present In 2 Views:
                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #95
                                            C
                                            Effect of Air Leakage from Window AC on Efficiency (dmnl)
                                            = 0.9*10/11
                                            Description: A window air conditioner typically does not perfectly cover its intended cavity, leading to more air leakage and therefore reducing efficiency.Taken from: https://www.energy.gov/sites/prod/files/2014/08/f18/ba_innovations_1-2-5_window_ac.pdf
                                            Present In 1 View:
                                            Used By
                                            • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #98
                                            F,A
                                            Emissions (tCO2 / Year)
                                            = SUM(
                                            Emissions by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                            Description: The total amount of emissions across all housing groups.
                                            Present In 2 Views: Used By
                                            • Average Emissions The average CO2 emissions for a household, not disaggregated into any grouping.
                                            • Cumulative Emissions The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #96
                                            A
                                            Emissions by Grouping (tCO2 / Year)
                                            Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                            Housing[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Emissions by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
                                            Description: The total emissions for the most disaggregated grouping in the model.
                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #97
                                            A
                                            Emissions by Heating and Cooling System (tCO2 / Year)
                                            Emissions by Heating and Cooling System[Heating and Cooling System] = SUM(
                                            Emissions by Grouping[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                            Description: The total amount of emissions for houses by Heating and Cooling System.
                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            .housingagingchain v8 #100
                                            C
                                            Energy Price Exponential Growth Rate (1/Year )
                                            = 0
                                            Description: The exogenous growth fraction for the test input.
                                            Present In 1 View:
                                            Used By
                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #99
                                            C
                                            Energy Price Exponential Growth Rate 1 (1/Year )
                                            = 0
                                            Description: The exogenous growth fraction for the test input.
                                            Present In 1 View:
                                            Used By
                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            .housingagingchain v8 #102
                                            C
                                            Energy Price Pulse Quantity (Dimensionless*Year)
                                            = 0
                                            Description: The quantity to be injected to customer orders, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                            Present In 1 View:
                                            Used By
                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #101
                                            C
                                            Energy Price Pulse Quantity 1 (Dimensionless*Year)
                                            = 0
                                            Description: Pulse value, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                            Present In 1 View:
                                            Used By
                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            .housingagingchain v8 #104
                                            C
                                            Energy Price Ramp Slope (1/Year )
                                            = 0
                                            Description: Slope of the ramp input, as a fraction of the base value (per week).
                                            Present In 1 View:
                                            Used By
                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #103
                                            C
                                            Energy Price Ramp Slope 1 (1/Year )
                                            = 0
                                            Description: Slope of the ramp input, as a fraction of the base value (per week).
                                            Present In 1 View:
                                            Used By
                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            .housingagingchain v8 #105
                                            C
                                            Energy Price Step Height (Dimensionless )
                                            = 0
                                            Description: Height of step input to customer orders, as fraction of initial value.
                                            Present In 1 View:
                                            Used By
                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #106
                                            A
                                            Energy Savings (dmnl)
                                            Energy Savings[Cohort,Heating and Cooling System] = MAX(0,ABS(ZIDZ((
                                            Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]- U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]), U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting])))
                                            Description: The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                            HeatPumpModel_v31 #107
                                            A
                                            Energy Use by Gas Houses (kBTU/ Year)
                                            = SUM(
                                            Energy Use by Grouping[ Cohort!,Gas and Central AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Gas and Window AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Gas and No AC, Retrofitting Status!])
                                            Description: The total amount of energy for heating and cooling used by homes which primarily use gas to heat their homes.
                                            Present In 1 View: Used By
                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                              HeatPumpModel_v31 #108
                                              A
                                              Energy Use by Grouping (kBTU / Year)
                                              Energy Use by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                              Average Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]
                                              Description: The total amount of energy used for heating and cooling in each group.
                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                              HeatPumpModel_v31 #109
                                              A
                                              Energy Use by Heat Pump Houses (kBTU / Year)
                                              = SUM(
                                              Energy Use by Grouping[ Cohort!,Heat Pump Only, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Heat Pump and Gas, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Heat Pump and Oil, Retrofitting Status!])
                                              Description: The amount of energy used for heating and cooling by homes which primarily use heat pumps to heat their home.
                                              Present In 1 View: Used By
                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                HeatPumpModel_v31 #110
                                                A
                                                Energy Use by Oil Houses (kBTU / Year)
                                                = SUM(
                                                Energy Use by Grouping[ Cohort!,Oil and Central AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Oil and Window AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Oil and No AC, Retrofitting Status!])
                                                Description: The total amount of energy for heating and cooling used by homes primarily using oil to heat their home.
                                                Present In 1 View: Used By
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  HeatPumpModel_v31 #111
                                                  SM,A
                                                  Expected Cooling Energy Price (Dollar / kBTU)
                                                  = SMOOTH3(
                                                  Cooling Energy Price, Delay in Forming Expectations of Energy Price)
                                                  Description: Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                  Present In 4 Views: Used By
                                                  • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                  • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                  • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                  • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  HeatPumpModel_v31 #112
                                                  SM,A
                                                  Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                  = SMOOTH3(
                                                  Implemented EEHIC Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                  Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays.
                                                  Present In 2 Views: Used By
                                                  • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                  • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  HeatPumpModel_v31 #113
                                                  SM,A
                                                  Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                  = SMOOTH3(
                                                  Implemented EEHIC Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                  Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                  Present In 2 Views: Used By
                                                  • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                  • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                  • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  .housingagingchain v15 #114
                                                  SM,A
                                                  Expected Fixed Cost (Dollar / House)
                                                  = SMOOTH(
                                                  Fixed Cost, Delay in Forming Expectations of Retrofit Costs)
                                                  Description: Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                  Present In 2 Views: Used By
                                                  • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                  • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  .housingagingchain v15 #115
                                                  SM,A
                                                  Expected Heating Energy Price (Dollar / kBTU)
                                                  Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                  Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                  Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                  Present In 6 Views: Used By
                                                  • Average Heating Cost The costs per year to heat one house.
                                                  • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                  • Optimal Heating Cost Average heating cost if U value is optimal.
                                                  • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  HeatPumpModel_v31 #116
                                                  SM,A
                                                  Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
                                                  = SMOOTH3(
                                                  IRA Implemented Subsidy Proportional Rate for Heat Pumps, Delay in Changing Subsidy Expectations)* Proportional IRA Subsidy Switch for Heat Pumps
                                                  Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  .housingagingchain v15 #117
                                                  A
                                                  Expected Lump Sum Subsidy Intensity (Dollar / sf)
                                                  Expected Lump Sum Subsidy Intensity[Retrofit Cost] =
                                                  HOMES Expected Lower Lump Sum Subsidy/ Average Area of Housing Starts
                                                  Description: Lump sum subsidy for retrofits per square foot.
                                                  Present In 1 View: Used By
                                                  • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  .housingagingchain v15 #118
                                                  SM,A
                                                  Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                  = SMOOTH3(
                                                  Implemented MassSave Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                  Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  .housingagingchain v15 #119
                                                  SM,A
                                                  Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                  = SMOOTH3(
                                                  Implemented MassSave Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                  Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                  Present In 4 Views: Used By
                                                  • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                  • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                  • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                  • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                  • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  HeatPumpModel_v31 #120
                                                  SM,A
                                                  Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
                                                  = SMOOTH3(
                                                  Implemented IRA Maximum Proportional Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                  Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  .housingagingchain v15 #121
                                                  SM,A
                                                  Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                  = SMOOTH(
                                                  Reference Marginal Cost, Delay in Forming Expectations of Retrofit Costs)
                                                  Description: Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                  Present In 4 Views: Used By
                                                  • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                  • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                  • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                  • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                  • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                  • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                  • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  HeatPumpModel_v31 #122
                                                  A
                                                  Expected Subsidy for Heat Pumps (Dollar / House)
                                                  =
                                                  MassSave Expected Lump Sum Subsidy for Heat Pumps+ IRA Expected Proportional Subsidy for Heat Pumps
                                                  Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidies.
                                                  Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  .housingagingchain v15 #123
                                                  A
                                                  Expected Subsidy for Retrofits (Dollar / House)
                                                  Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                  Energy Savings[ Cohort, Heating and Cooling System]>= HOMES Cut Off for Savings, HOMES Expected Higher Subsidy, HOMES Expected Lower Lump Sum Subsidy)+ MassSave Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]+ EEHIC Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                  Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                  Present In 4 Views: Used By
                                                  • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  HeatPumpModel_v31 #124
                                                  A
                                                  Federal Annual Heat Pump Subsidy (Dollar / Year)
                                                  =
                                                  Total Heat Pump Sales* IRA Actual Subsidy for Heat Pumps
                                                  Description: The amount of subsidies the federal government spends on heat pumps through the Inflation Reduction Act every year.
                                                  Present In 1 View: Used By
                                                  • Annual Federal Subsidies The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year.
                                                  • Annual Heat Pump Subsidy The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  HeatPumpModel_v31 #125
                                                  A
                                                  Federal Annual Retrofit Subsidy (Dollar / Year)
                                                  = SUM((
                                                  Actual EEHIC Subsidy for Retrofits[ Cohort!, Heating and Cooling System!]+ Actual HOMES Subsidy for Retrofits[ Cohort!, Heating and Cooling System!])* Houses Retrofitting per Year[ Cohort!, Heating and Cooling System!])
                                                  Description: The amount of federal subsidies spent by the federal government, through the IRA.
                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  .housingagingchain v5 testing #128
                                                  C
                                                  Fixed Cost (Dollar / House )
                                                  = 0
                                                  Description: Fixed cost of retrofitting, due to permitting, finding contractors, etc. This is not taken into account in the marginal cost of retrofitting, and this model assumes that households have not yet paid a fixed cost when deciding to retrofit. This cost only applies to existing housing.Set this equal to 0, because almost all costs for retrofits seem to be variable (except for permitting, which isn't usually used), and there's no data to suggest otherwise.
                                                  Present In 2 Views:
                                                  Used By
                                                  • Expected Fixed Cost Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  .housingagingchain v5 testing #127
                                                  A
                                                  Fixed Cost per Unit Area (Dollar / sf)
                                                  Fixed Cost per Unit Area[Cohort] = ZIDZ(
                                                  Expected Fixed Cost, Average Area[ Cohort,Open to Retrofitting])
                                                  Description: The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                  Present In 2 Views: Used By
                                                  • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                  HeatPumpModel_v31 #129
                                                  A
                                                  Fraction of Houses in Each Heating and Cooling System (dmnl)
                                                  Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] = XIDZ(
                                                  Housing by Heating and Cooling System[ Heating and Cooling System], Total Housing Stock, NAREPLACEMENT)
                                                  Description: The fraction of houses using each heating and cooling system
                                                  Present In 1 View: Used By
                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                    .housingagingchain v5 testing #130
                                                    A
                                                    Fraction of Houses Switching (dmnl)
                                                    Fraction of Houses Switching[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                    Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System!])
                                                    Fraction of Houses Switching[Cohort,Gas Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System!])
                                                    Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System!])
                                                    Description: Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                    Present In 2 Views: Used By
                                                    • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                    HeatPumpModel_v31 #131
                                                    A
                                                    Fraction of Housing by Heating and Cooling System (dmnl)
                                                    Fraction of Housing by Heating and Cooling System[Heating and Cooling System] =
                                                    Housing by Heating and Cooling System[ Heating and Cooling System]/ Total Housing Stock
                                                    Description: The fraction of the total housing stock using each heating and cooling system.
                                                    Present In 1 View: Used By
                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                      HeatPumpModel_v31 #134
                                                      A
                                                      Fraction Retrofitting (dmnl)
                                                      =
                                                      Housing by Retrofitting Status[Open to Retrofitting]/( Housing by Retrofitting Status[Not Open to Retrofitting]+ Housing by Retrofitting Status[Open to Retrofitting])
                                                      Description: Proportion of housing that is open to retrofitting, across all cohorts and systems.
                                                      Present In 1 View: Used By
                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                        HeatPumpModel_v31 #132
                                                        LI,A
                                                        Fraction Retrofitting by Cohort (dmnl)
                                                        Fraction Retrofitting by Cohort[Cohort] = ZIDZ(SUM(
                                                        Housing[ Cohort, Heating and Cooling System!,Open to Retrofitting]),SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!]))
                                                        Description: Fraction that are retrofitting, only by cohort.
                                                        Present In 2 Views: Used By
                                                        • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                        HeatPumpModel_v31 #133
                                                        A
                                                        Fraction Retrofitting by System and Cohort (dmnl)
                                                        Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] = ZIDZ(
                                                        Housing[ Cohort, Heating and Cooling System,Open to Retrofitting],SUM( Housing[ Cohort, Heating and Cooling System, Retrofitting Status!]))
                                                        Description: The fraction of houses that are retrofitting, by heating/cooling system and cohort.
                                                        Present In 1 View: Used By
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #135
                                                          C
                                                          Fractional Decrease in Code U (1 / Year )
                                                          = 0
                                                          Description: Fractional decrease in code per year. Exogenous and set by policymakers in the real world. For initial paper, assume that code U is constant.
                                                          Present In 1 View:
                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #136
                                                          A,T
                                                          Gas COP TABLE (dmnl)
                                                          Gas COP TABLE([(2020,0)-(2050,1)],(2020,0.9),(2030,0.925),(2040,0.95),(2050,0.95))

                                                          Description: Efficiency of gas systems over time. Taken as the average of projected efficiency for reference gas boilers and gas furnaces, from MassDEP's Energy Pathways for Deep Decarbonization Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                          Present In 1 View:
                                                          Used By
                                                          • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #137
                                                          C
                                                          HDD on Coldest Day (F )
                                                          = 55.2333
                                                          Description: The total HDD from coldest day.Data from https://www.degreedays.net/ for KOWD, weather station nearest to centre of population for MA, Natick. Calculated by finding HDDs from the past three years (February 2021 - January 2024), finding the highest HDD in each year, and averaging them. Following industry standard, used set point of 65°F.
                                                          Present In 1 View:
                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #138
                                                          A,T
                                                          Heat Pump Cooling COP TABLE (dmnl)
                                                          Heat Pump Cooling COP TABLE([(2020,0)-(2050,10)],(2020,4.3),(2030,4.8),(2040,5.17),(2050,5.28))

                                                          Description: The COP of heat pumps when used for cooling. Calculated by assuming the ratio of heating and cooling COP is constant over time -- as heating COP improves the ability to cool improves proportionally-- finding cooling COP in 2020, finding the COP for cooling of heating in 2018, and then using the ratio between the two in 2020 to project future values. Data on this was difficult to find.Projected heating COP from pg. 97 of MassDEP's Energy Pathways for Deep Decarbonization: https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadCooling COP in 2020 here: https://www.raleighheatingandair.com/blog/is-a-heat-pump-more-effective-at-cooling-or-heating/
                                                          Present In 1 View:
                                                          Used By
                                                          • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #139
                                                          C
                                                          Heat Pump COP on Coldest Days (dmnl )
                                                          = 2.16438
                                                          Description: The heat pump COP on coolest day of the year.Taken from NYSERDA/MassCEC study on heat pump performance on 41 heat pumps: https://e4thefuture.org/wp-content/uploads/2022/06/Residential-ccASHP-Building-Electrification_060322.pdf (pg. 24). Regressed COP on temperature and its square. Using daily data on HDD (set point 65°F) for 2021-2023 from degreedays.net, calculated temperature of coldest day on average. Plugged that into regression model to find COP on coldest day.
                                                          Present In 1 View:
                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #140
                                                          A,T
                                                          Heat Pump Heating COP TABLE (dmnl)
                                                          Heat Pump Heating COP TABLE([(2020,0)-(2050,10)],(2020,2.485),(2030,2.785),(2040,2.99),(2050,3.05))

                                                          Description: The efficiency of heat pumps for heating, over time. Taken as the average of projected COP for reference ASHP and ductless mini-splits from MassDEP's Energy Pathways Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                          Present In 1 View:
                                                          Used By
                                                          • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #141
                                                          C
                                                          Heating Degree Days (F )
                                                          = 5026
                                                          Description: The difference between temperature setpoint (65 F) and outside temperature.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. In line with industry standard, use set point of 65°F, as thattemperature little heating or cooling is needed.
                                                          Present In 3 Views:
                                                          Used By
                                                          • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                          • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                          • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                          • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #142
                                                          C
                                                          Heating Emissions Factors (lb CO2 / kBTU)
                                                          Heating Emissions Factors[Heat Pump Heating and Cooling] = 684/3414.43
                                                          Heating Emissions Factors[Gas Heating] = 116.65/1000
                                                          Heating Emissions Factors[Oil Heating] = 163.45/1000
                                                          Description: The pounds of CO2 emitted per kBTU of heating energy provided, for each heating fuel.Data for heat pumps (electricity) is: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/downloadRest is from: https://www.eia.gov/environment/emissions/co2_vol_mass.phpIn line with that source, I assume that each heat pump will add to the grid and is not part of base demand, and so the marginal emissions from producing electricity from heat pumps will be constant at the value as it will come from natural gas generators (explanation of which is from here: https://willbrownsberger.com/how-green-will-the-power-be/
                                                          Present In 1 View:
                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          .housingagingchain v5 testing #143
                                                          A
                                                          Heating Energy Price (Dollar / (kBTU))
                                                          Heating Energy Price[Heating and Cooling System] =
                                                          Initial Heating Energy Price[ Heating and Cooling System]* Input 0
                                                          Description: The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                          Present In 6 Views: Used By
                                                          • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #144
                                                          A
                                                          Heating Energy Use Under Alternatives (kBTU / (House * Year))
                                                          Heating Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Not Open to Retrofitting,Heating and Cooling System] =
                                                          U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                          Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Not Open to Retrofitting,Heating and Cooling System] = U Value by Grouping[ Cohort, Fossil Fuel Heating,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                          Heating Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                          Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Fossil Fuel Heating,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                          Description: The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                          Present In 1 View: Used By
                                                          • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #145
                                                          A
                                                          Heating System Efficiency (dmnl)
                                                          Heating System Efficiency[Heat Pump Heating and Cooling] =
                                                          Heat Pump Heating COP TABLE( Time)
                                                          Heating System Efficiency[Gas Heating] = Gas COP TABLE( Time)
                                                          Heating System Efficiency[Oil Heating] = Oil COP TABLE( Time)
                                                          Description: The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                          Present In 3 Views: Used By
                                                          • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                          • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                          • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                          • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #146
                                                          C
                                                          Homeowner Hours Spent Retrofitting (Hour )
                                                          = 750
                                                          Description: The amount of hours a homeowners spends retrofitting their home themselves, i.e., the hours spent deciding to retrofit, supervising audits, moving out of the home as necessary, etc. No hard data on this, calibrated so that the initial fraction of homes willing to retrofit is 10%.
                                                          Present In 1 View:
                                                          Used By
                                                          • Soft Costs of Retrofitting The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #147
                                                          C
                                                          HOMES Cut Off for Savings (dmnl )
                                                          = 0.35
                                                          Description: The percent energy savings needed to get the higher subsidy amount from the Home Owner Managing Energy Savings rebate. Taken from: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                          Present In 2 Views:
                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #148
                                                          SM,A
                                                          HOMES Expected Higher Subsidy (Dollar / House)
                                                          = SMOOTH3(
                                                          HOMES Implemented High Subsidy, Delay in Changing Subsidy Expectations)
                                                          Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          .housingagingchain v15 #149
                                                          SM,A
                                                          HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                          = SMOOTH3(
                                                          HOMES Implemented Lower Subsidy, Delay in Changing Subsidy Expectations)
                                                          Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                          Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #150
                                                          C
                                                          HOMES High Subsidy Amount (Dollar / House )
                                                          = 4000
                                                          Description: The subsidy from the home owner managing energy savings rebate for retrofits saving more than 35% of energy.Source: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                          Present In 1 View:
                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #151
                                                          A
                                                          HOMES Implemented High Subsidy (Dollar / House)
                                                          = IF THEN ELSE(
                                                          Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES High Subsidy Amount,0)
                                                          Description: Implemented higher subsidy from the HOMES rebate program.
                                                          Present In 2 Views: Used By
                                                          • Actual HOMES Subsidy for Retrofits The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                          • HOMES Expected Higher Subsidy Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          .housingagingchain v15 #152
                                                          A
                                                          HOMES Implemented Lower Subsidy (Dollar / House)
                                                          = IF THEN ELSE(
                                                          Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES Lower Subsidy Amount,0)
                                                          Description: Lump sum subsidy that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          .housingagingchain v15 #153
                                                          C
                                                          HOMES Lower Subsidy Amount (Dollar / House )
                                                          = 2000
                                                          Description: The lump sum subsidy given for retrofits that save less than 35% of their energy from the Home Owner Managing Energy Savings tax credit.Source: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                          Present In 1 View:
                                                          Used By
                                                          • HOMES Implemented Lower Subsidy Lump sum subsidy that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #154
                                                          C
                                                          HOMES Subsidy Final Year (Year)
                                                          = 2032
                                                          Description: Final year of Home Owner Managing Energy Savings rebate, assumed to be the same as that of the EEHIC.
                                                          Present In 1 View:
                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          .housingagingchain v15 #155
                                                          C
                                                          HOMES Subsidy Implementation Year (Year )
                                                          = 2025
                                                          Description: The year in which the lump sum subsidy will activate.
                                                          Present In 1 View:
                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #156
                                                          A
                                                          Houses Considering Switching System (Houses / Year)
                                                          Houses Considering Switching System[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                          Housing[ Cohort, Heating and Cooling System, Retrofitting Status]/ Average Time To Consider Switching
                                                          Description: The number of houses per year considering switching their heating and cooling system.
                                                          Present In 1 View: Used By
                                                          • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                          Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                          HeatPumpModel_v31 #158
                                                          A
                                                          Houses Retrofitting (Houses)
                                                          Houses Retrofitting[Cohort,Heating and Cooling System] =
                                                          Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                          Description: Total amount of houses retrofitting in each cohort and heating and cooling system.
                                                          Present In 1 View: Used By
                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                            HeatPumpModel_v31 #157
                                                            A
                                                            Houses Retrofitting per Year (House / Year)
                                                            Houses Retrofitting per Year[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                            Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]< U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting], Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]/ Retrofit Delay,0)
                                                            Description: The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                            HeatPumpModel_v31 #159
                                                            A
                                                            Houses Switching Into Sources (Houses / Year)
                                                            Houses Switching Into Sources[Heating and Cooling System] = SUM(
                                                            Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!, Heating and Cooling System])
                                                            Description: The number of houses switching into each Heating and Cooling System, cohort, and retrofitting group due to system switching.
                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                            HeatPumpModel_v31 #160
                                                            F,A
                                                            Houses Switching Sources (House / Year)
                                                            Houses Switching Sources[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                            Fraction of Houses Switching[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* System Switching SWITCH
                                                            Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Fraction of Houses Switching[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Fossil Fuel Heating, Retrofitting Status]* System Switching SWITCH
                                                            Description: The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                            Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                            HeatPumpModel_v31 #174
                                                            L
                                                            Housing (House)
                                                            Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                            Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                            Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                            Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                            Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                            HeatPumpModel_v31 #163
                                                            A
                                                            Housing by Cohort (House)
                                                            Housing by Cohort[Cohort] = SUM(
                                                            Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!])
                                                            Description: Number of houses per cohort
                                                            Present In 1 View: Used By
                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                              HeatPumpModel_v31 #161
                                                              A
                                                              Housing by Cohort and Heating and Cooling System (Houses)
                                                              Housing by Cohort and Heating and Cooling System[Cohort,Heating and Cooling System] = SUM(
                                                              Housing[ Cohort, Heating and Cooling System, Retrofitting Status!])
                                                              Description: Housing by heating and cooling system and cohort, irrespective of retrofit status.
                                                              Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                              HeatPumpModel_v31 #162
                                                              A
                                                              Housing by Cohort and Retrofitting Status (House)
                                                              Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] = SUM(
                                                              Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                              Description: Amount of housing by retrofit status and cohort.
                                                              Present In 3 Views: Used By
                                                              • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                              • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                              • Housing by Retrofitting Status Amount of housing by retrofitting status, across all cohorts and systems.
                                                              • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                              HeatPumpModel_v31 #164
                                                              A
                                                              Housing by Heating and Cooling System (House)
                                                              Housing by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                              Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                              Description: Number of houses by energy source across all cohorts.
                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                              HeatPumpModel_v31 #165
                                                              A
                                                              Housing by Retrofitting Status (House)
                                                              Housing by Retrofitting Status[Retrofitting Status] = SUM(
                                                              Housing by Cohort and Retrofitting Status[ Cohort!, Retrofitting Status])
                                                              Description: Amount of housing by retrofitting status, across all cohorts and systems.
                                                              Present In 1 View: Used By
                                                              • Fraction Retrofitting Proportion of housing that is open to retrofitting, across all cohorts and systems.
                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                              HeatPumpModel_v31 #166
                                                              C
                                                              Housing Fractional Growth Rate (1 / Year )
                                                              = 0.02
                                                              Description: The annual growth rate in housing. Heuristically chosen so that total housing stock grows at net 1%/year.
                                                              Present In 1 View:
                                                              Used By
                                                              • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                              HeatPumpModel_v31 #173
                                                              F,A
                                                              Housing Starts (Houses / Year)
                                                              Housing Starts[Cohort,Heating and Cooling System] =
                                                              Housing Fractional Growth Rate*SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])* Active Cohort Indicator[ Cohort]*(1- No Turnover Switch)
                                                              Description: Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                              Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [2,2] (-) 0  [0,0]
                                                              HeatPumpModel_v31 #167
                                                              A
                                                              Housing Starts Across Cohorts ()
                                                              = SUM(
                                                              Housing Starts In Each Cohort[ Cohort!])
                                                              Description: Housing starts across all cohorts.
                                                              Present In 1 View: Used By
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v8 #168
                                                                C
                                                                Housing Starts Exponential Growth Rate (1/Year )
                                                                = 0
                                                                Description: The exogenous growth fraction for the test input.
                                                                Present In 1 View:
                                                                Used By
                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #169
                                                                A
                                                                Housing Starts In Each Cohort (House / Year)
                                                                Housing Starts In Each Cohort[Cohort] = SUM(
                                                                Housing Starts[ Cohort, Heating and Cooling System!])
                                                                Description: Housing starts across heating and cooling systems.
                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v8 #170
                                                                C
                                                                Housing Starts Pulse Quantity (Dimensionless*Year)
                                                                = 0
                                                                Description: The quantity to be injected to customer orders, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                Present In 1 View:
                                                                Used By
                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v8 #171
                                                                C
                                                                Housing Starts Ramp Slope (1/Year )
                                                                = 0
                                                                Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                Present In 1 View:
                                                                Used By
                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v8 #172
                                                                C
                                                                Housing Starts Step Height (Dimensionless )
                                                                = 0
                                                                Description: Height of step input to customer orders, as fraction of initial value.
                                                                Present In 1 View:
                                                                Used By
                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #175
                                                                A
                                                                Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                = IF THEN ELSE(
                                                                Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: Time<= EEHIC Subsidy for Retrofits Final Year, EEHIC Maximum Subsidy for Retrofits,0)
                                                                Description: Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #176
                                                                A
                                                                Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
                                                                = IF THEN ELSE(
                                                                Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: EEHIC Subsidy for Retrofits Final Year>= Time, EEHIC Proportional Subsidy Rate for Retrofits,0)
                                                                Description: The implemented proportional subsidy rate for retrofits from the IRA, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #177
                                                                A
                                                                Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                = IF THEN ELSE(
                                                                Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: Time<= IRA Lump Sum Subsidy for Heat Pumps Final Year, IRA Maximum Proportional Subsidy for Heat Pumps,0)
                                                                Description: Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v15 #178
                                                                A
                                                                Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                = IF THEN ELSE(
                                                                Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: Time<= MassSave Subsidy for Retrofits Final Year, MassSave Maximum Subsidy for Retrofits,0)
                                                                Description: Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v15 #179
                                                                A
                                                                Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
                                                                = IF THEN ELSE(
                                                                Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: MassSave Subsidy for Retrofits Final Year>= Time, Mass Save Proportional Subsidy Rate for Retrofits,0)
                                                                Description: The implemented proportional subsidy rate from the state, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #180
                                                                C
                                                                Increase in Area per Year (sf / Year / House )
                                                                = 10.76
                                                                Description: The exogenous increase in area per year, found by regressing area on year house was built in RECS 2020 data for MA SFG.
                                                                Present In 1 View:
                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v18 #181
                                                                F,A
                                                                Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)
                                                                Increase in U Value from Housing Starts[Cohort,Heating and Cooling System] =
                                                                Housing Starts[ Cohort, Heating and Cooling System]* U Value of Housing Starts[ Cohort, Heating and Cooling System]
                                                                Description: New U value from new homes being built.
                                                                Present In 1 View: Used By
                                                                • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #182
                                                                A
                                                                Indicated Fraction of Homes Retrofitting (dmnl)
                                                                Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                Affinity of Retrofitting[ Cohort, Heating and Cooling System]/( Affinity of Retrofitting[ Cohort, Heating and Cooling System]+ Affinity of Not Retrofitting[ Cohort, Heating and Cooling System])
                                                                Description: Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #183
                                                                A
                                                                Indicated Homes Retrofitting (House)
                                                                Indicated Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                Indicated Fraction of Homes Retrofitting[ Cohort, Heating and Cooling System]* Housing by Cohort and Heating and Cooling System[ Cohort, Heating and Cooling System]
                                                                Description: Number of homes that, once delays are taken into account, will be open to retrofitting.
                                                                Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                .housingagingchain v8 #184
                                                                LI,A
                                                                Initial Age (House * Year)
                                                                Initial Age[Cohort,Retrofitting Status] = INITIAL(0)
                                                                Initial Age[Preexisting Cohorts,Retrofitting Status] = (
                                                                Cohort Duration*(ELMCOUNT( Preexisting Cohorts)- Preexisting Cohorts+1))* Housing by Cohort and Retrofitting Status[ Preexisting Cohorts, Retrofitting Status]
                                                                Description: The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                Present In 1 View: Used By
                                                                • Total Age "Total" age for each cohort of housing.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #185
                                                                LI,C
                                                                Initial Area (sf)
                                                                Initial Area[Cohort] = 10
                                                                Description: Total initial area across all houses, by cohort (assuming that average area is the same across systems).
                                                                Present In 1 View:
                                                                Used By
                                                                • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #186
                                                                C
                                                                Initial Average Area of Housing Starts (sf / House )
                                                                = 2347
                                                                Description: Initial average area of housing starts. Taken from average area of MA SFH homes built from 2015 to 2020, from EIA RECS data.
                                                                Present In 1 View:
                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #187
                                                                C
                                                                Initial Average U Value (kBTU/(Year*sf*F))
                                                                Initial Average U Value[Cohort] = 0.19235
                                                                Description: The initial average U, equal to the average U value of MA SFH in 2022, from EIA RECS.
                                                                Present In 1 View:
                                                                Used By
                                                                • Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #188
                                                                LI,C
                                                                Initial Code U Value (kBTU / (sf * F * Year))
                                                                = 0.003
                                                                Description: The initial value of code U. For initial paper, assume that this is between initial optimal U (nearly 0) and average U (0.006).
                                                                Present In 1 View:
                                                                Used By
                                                                • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #189
                                                                C
                                                                Initial Cooling Energy Price (Dollar / kBTU)
                                                                = 0.062
                                                                Description: The price to cool a home per BTU. This is the price of electricity as all cooling systems, as air conditioning systems, use electricity.
                                                                Present In 1 View:
                                                                Used By
                                                                • Cooling Energy Price Price of cooling a home (through air conditioning), subject to the test input.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #190
                                                                C
                                                                Initial Fraction of Homes Retrofitting (dmnl )
                                                                = 0.1
                                                                Description: Initial fraction of homes open to retrofitting. Heuristically chosen to be 0.1 to match low level of retrofitting that current occurs.
                                                                Present In 1 View:
                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v5 testing #191
                                                                C
                                                                Initial Heating Energy Price (Dollar / (kBTU))
                                                                Initial Heating Energy Price[Heat Pump Heating and Cooling] = 0.062
                                                                Initial Heating Energy Price[Gas Heating] = 0.0142
                                                                Initial Heating Energy Price[Oil Heating] = 0.017
                                                                Description: Price of energy used in each technology: heat pump, central AC, window AC, no AC, gas, and oil. For heat pumps and air conditioners, this is electricity.Data from (using annual 2020 data for MA):electricity: https://www.eia.gov/electricity/data/browser/#/topic/7?agg=1,0&geo=vvvvvvvvvvvvo&endsec=8&freq=M&start=200101&ctype=linechart&ltype=pin&rtype=s&pin=&rse=0&maptype=0,natural gas:https://www.eia.gov/dnav/ng/ng_pri_sum_a_EPG0_PRS_DMcf_a.htmheating oil: https://www.eia.gov/petroleum/heatingoilpropane/
                                                                Present In 1 View:
                                                                Used By
                                                                • Heating Energy Price The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v5 testing #192
                                                                LI,A
                                                                Initial Homes Not Retrofitting (House)
                                                                Initial Homes Not Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                Initial Homes Not Retrofitting[Preexisting Cohorts,Heating and Cooling System] = (1-
                                                                Initial Fraction of Homes Retrofitting)* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                Description: Initial homes not open to retrofitting.
                                                                Present In 1 View: Used By
                                                                • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                .housingagingchain v5 testing #193
                                                                LI,A
                                                                Initial Homes Retrofitting (Houses)
                                                                Initial Homes Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                Initial Homes Retrofitting[Preexisting Cohorts,Heating and Cooling System] =
                                                                Initial Fraction of Homes Retrofitting* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                Description: Homes that are open to retrofitting initially.
                                                                Present In 1 View: Used By
                                                                • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                HeatPumpModel_v31 #195
                                                                C
                                                                Initial Housing (House)
                                                                Initial Housing[Cohort,Heating and Cooling System] = 2.2e+06
                                                                Description: The total number of houses that begin in each cohort and heating and cooling source. Taken from CIN file.
                                                                Present In 1 View:
                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                . #194
                                                                A
                                                                Initial Housing Starts (House/Year)
                                                                Initial Housing Starts[Heating and Cooling System] =
                                                                Total Initial Housing Starts/ELMCOUNT( Heating and Cooling System)
                                                                Description: Initial value of housing starts, initialized at 10 total houses.
                                                                Present In 1 View: Used By
                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                  .housingagingchain v15 #197
                                                                  LI,A
                                                                  Initial U Value (House * kBTU / (Year * F * sf))
                                                                  Initial U Value[Cohort,Heating and Cooling System,Retrofitting Status] = 0
                                                                  Initial U Value[Preexisting Cohorts,Heating and Cooling System,Retrofitting Status] =
                                                                  Initial Average U Value[ Preexisting Cohorts]* Housing[ Preexisting Cohorts, Heating and Cooling System, Retrofitting Status]
                                                                  Description: Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                  Present In 1 View: Used By
                                                                  • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                  .housingagingchain v8 #200
                                                                  A
                                                                  Input (Dimensionless)
                                                                  = 1+STEP(
                                                                  Housing Starts Step Height, INITIAL TIME+ Step Time)+( Housing Starts Pulse Quantity/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time, TIME STEP)+RAMP( Housing Starts Ramp Slope, INITIAL TIME+ Ramp Start Time, INITIAL TIME+ Ramp End Time)+(STEP(1, INITIAL TIME)*(exp( Housing Starts Exponential Growth Rate*( Time- INITIAL TIME))-1))+ Sine Amplitude*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period)+STEP(1, INITIAL TIME+ Noise Start Time)* Autocorrelated Noise
                                                                  Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                  Present In 1 View: Used By
                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    .housingagingchain v8 #198
                                                                    A
                                                                    Input 0 (Dimensionless)
                                                                    = 1+STEP(
                                                                    Energy Price Step Height, INITIAL TIME+ Step Time 0)+( Energy Price Pulse Quantity/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time 0, TIME STEP)+RAMP( Energy Price Ramp Slope, INITIAL TIME+ Ramp Start Time 0, INITIAL TIME+ Ramp End Time 0)+(STEP(1, INITIAL TIME)*(exp( Energy Price Exponential Growth Rate*( Time- INITIAL TIME))-1))+ Sine Amplitude 0*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period 0)+STEP(1, INITIAL TIME+ Noise Start Time 0)* Autocorrelated Noise 0
                                                                    Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                    Present In 1 View: Used By
                                                                    • Heating Energy Price The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #199
                                                                    A
                                                                    Input 1 (Dimensionless)
                                                                    = 1+STEP(
                                                                    Cooling Energy Price Step Height 1, INITIAL TIME+ Step Time 1)+( Energy Price Pulse Quantity 1/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time 1, TIME STEP)+RAMP( Energy Price Ramp Slope 1, INITIAL TIME+ Ramp Start Time 1, INITIAL TIME+ Ramp End Time 1)+(STEP(1, INITIAL TIME)*(exp( Energy Price Exponential Growth Rate 1*( Time- INITIAL TIME))-1))+ Sine Amplitude 1*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period 1)+STEP(1, INITIAL TIME+ Noise Start Time 1)* Autocorrelated Noise 1
                                                                    Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                    Present In 1 View: Used By
                                                                    • Cooling Energy Price Price of cooling a home (through air conditioning), subject to the test input.
                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #201
                                                                    A
                                                                    IRA Actual Subsidy for Heat Pumps (Dollar / House)
                                                                    = MIN(
                                                                    IRA Implemented Subsidy Proportional Rate for Heat Pumps* Unsubsidized Cost of Heat Pumps, Implemented IRA Maximum Proportional Subsidy for Heat Pumps)
                                                                    Description: The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value.
                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #202
                                                                    A
                                                                    IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                    = MIN(
                                                                    Proportional IRA Subsidy Switch for Heat Pumps* Expected IRA Proportional Subsidy Rate for Heat Pumps* Unsubsidized Cost of Heat Pumps, Expected Maximum IRA Proportional Subsidy for Heat Pumps)
                                                                    Description: The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect.
                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #203
                                                                    A
                                                                    IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
                                                                    = IF THEN ELSE(
                                                                    Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: IRA Lump Sum Subsidy for Heat Pumps Final Year>= Time, IRA Proportional Subsidy Rate for Heat Pumps,0)
                                                                    Description: The implemented proportional subsidy rate, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy rate afterwards.
                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #204
                                                                    C
                                                                    IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )
                                                                    = 2032
                                                                    Description: The year in which the subsidy is phased out. If final time, then has no ending date.
                                                                    Present In 1 View:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #205
                                                                    C
                                                                    IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )
                                                                    = 2000
                                                                    Description: The maximum proportional subsidy for heat pumps that will be offered, regardless of the subsidy rate. For instance, if the proportional subsidy is 50% but the maximum is $1000, then for a retrofit project that costs $3000 only a $1000 subsidy will be given.Taken from: https://www.energystar.gov/about/federal-tax-credits
                                                                    Present In 2 Views:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #206
                                                                    C
                                                                    IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )
                                                                    = 2023
                                                                    Description: Time at which the proportional subsidy will take effect from the Inflation Reduction Act, from https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                    Present In 1 View:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #207
                                                                    C
                                                                    IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
                                                                    = 0.3
                                                                    Description: Proportion of total heat pump cost that will be credited as part of a proportional subsidy.Taken from: https://www.energystar.gov/about/federal-tax-credits
                                                                    Present In 1 View:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #208
                                                                    C
                                                                    kBTU per kWH (kBTU / kWH )
                                                                    = 3.41214
                                                                    Present In 1 View:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #209
                                                                    A
                                                                    Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)
                                                                    Lifetime Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] =
                                                                    Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]/ Discount Rate
                                                                    Description: The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                    Present In 1 View: Used By
                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #210
                                                                    A
                                                                    Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))
                                                                    Marginal Cooling Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] =
                                                                    Expected Cooling Energy Price* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                    Description: The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #211
                                                                    A
                                                                    Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))
                                                                    Marginal Cost at Binding U Value without EEHIC[Cohort,Heating and Cooling System] =
                                                                    Expected Reference Marginal Cost*(ZIDZ( Reference U Value, U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]))^ Sensitivity of Marginal Cost to U Value
                                                                    Description: This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                    Present In 1 View: Used By
                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    .housingagingchain v15 #212
                                                                    A
                                                                    Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)
                                                                    Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] =
                                                                    Marginal Cooling Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]+ Marginal Heating Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]
                                                                    Description: Total cost reductions from retrofitting away one unit of U value for existing homes, including reductions in both heating and cooling costs.
                                                                    Present In 2 Views: Used By
                                                                    • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    .housingagingchain v5 testing #213
                                                                    A
                                                                    Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))
                                                                    Marginal Heating Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] =
                                                                    Expected Heating Energy Price[ Heating and Cooling System]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                    Description: The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    .housingagingchain v15 #214
                                                                    C
                                                                    Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
                                                                    = 0.75
                                                                    Description: Proportion of total retrofit cost that will be credited as part of a proportional subsidy. Theoretically, this can vary between current housing and housing under construction.Based off Mass Save data: https://www.masssave.com/en/residential/rebates-and-incentives/insulation-and-windows/insulation-and-air-sealing
                                                                    Present In 2 Views:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #215
                                                                    A
                                                                    Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)
                                                                    =
                                                                    Total Heat Pump Sales* MassSave Implemented Lump Sum Subsidy for Heat Pumps
                                                                    Description: The actual subsidy provided for purchase of heat pumps by Massachusetts, as opposed to what the subsidy expected by homeowners is.
                                                                    Present In 1 View: Used By
                                                                    • Annual Heat Pump Subsidy The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                    • Annual MA Subsidies The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps.
                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #216
                                                                    A
                                                                    Massachusetts Annual Retrofit Subsidy (Dollar / Year)
                                                                    = SUM(
                                                                    Houses Retrofitting per Year[ Cohort!, Heating and Cooling System!]* Actual MassSave Subsidy for Retrofits[ Cohort!, Heating and Cooling System!])
                                                                    Description: Amount of money Massachusetts spends on MassSave subsidies for retrofits, yearly.
                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #217
                                                                    SM,A
                                                                    MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                    = SMOOTH3(
                                                                    MassSave Implemented Lump Sum Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                                    Description: Expected lump sum subsidy that lowers subsidized retrofit costs from the state, taking into account information delays.
                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    .housingagingchain v15 #218
                                                                    A
                                                                    MassSave Expected Subsidy for Retrofits (Dollar / House)
                                                                    MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = MIN(
                                                                    Proportional Subsidy Switch for Retrofits* Expected MassSave Proportional Subsidy Rate for Retrofits* Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status], Expected MassSave Maximum Subsidy for Retrofits)
                                                                    Description: The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #219
                                                                    A
                                                                    MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                    = MIN(
                                                                    Unsubsidized Cost of Heat Pumps,IF THEN ELSE( Time>= MassSave Lump Sum Subsidy Implementation Year for Heat Pumps:AND: Time<= MassSave Lump Sum Subsidy for Heat Pumps Final Year, MassSave Lump Sum Subsidy Amount for Heat Pumps,0))
                                                                    Description: Lump sum subsidy from MassSave that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #220
                                                                    C
                                                                    MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )
                                                                    = 10000
                                                                    Description: The total amount of money offered by the lump sum subsidy.Taken from: https://www.masssave.com/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps.
                                                                    Present In 1 View:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #221
                                                                    C
                                                                    MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)
                                                                    = 2200
                                                                    Description: The year in which the state's subsidy for heat pumps is phased out.
                                                                    Present In 1 View:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #222
                                                                    C
                                                                    MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )
                                                                    = 2020
                                                                    Description: The year in which the state's lump sum subsidy for heat pumps will activate.
                                                                    Present In 1 View:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    .housingagingchain v15 #223
                                                                    C
                                                                    MassSave Maximum Subsidy for Retrofits (Dollar / House )
                                                                    = 1e+07
                                                                    Description: The maximum proportional subsidy that will be offered, regardless of that subsidy's discount. For instance, if the proportional subsidy is 50% but the maximum is $1000, then for a retrofit project that costs $3000 only a $1000 subsidy will be given.If very large, then no maximum subsidy given.
                                                                    Present In 1 View:
                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    HeatPumpModel_v31 #224
                                                                    A
                                                                    MassSave Subsidy for Retrofits Final Year (Year)
                                                                    =
                                                                    FINAL TIME
                                                                    Description: The year in which the subsidy is phased out. If final time, then has no ending data.
                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                    .housingagingchain v8 #225
                                                                    C
                                                                    Maximum Energy Price (Dollar / kBTU)
                                                                    = 10
                                                                    Description: Shifts x-axis for graph of optimal retrofit amount as a function of energy price.
                                                                    Present In 0 Views:
                                                                      Used By
                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                        HeatPumpModel_v31 #226
                                                                        A
                                                                        Monthly Total Heat Pump Sales (Houses/ Month)
                                                                        =
                                                                        Total Heat Pump Sales/ Months per Year
                                                                        Description: The number of homes buying heat pumps, every year.
                                                                        Present In 1 View: Used By
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #227
                                                                          C
                                                                          Months per Year (Month / Year )
                                                                          = 12
                                                                          Description: The number of months per year.
                                                                          Present In 1 View:
                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #229
                                                                          A
                                                                          Net Age Shift by System (Year * House / Year)
                                                                          Net Age Shift by System[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                          Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, Average Age[ Cohort,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], Average Age[ Cohort,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                          Description: The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                          Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #230
                                                                          F,A
                                                                          Net Age Shift from Retrofitting Status Shifting (House * Year / Year)
                                                                          Net Age Shift from Retrofitting Status Shifting[Cohort] = SUM(
                                                                          Net Age Shift by System[ Cohort, Heating and Cooling System!])
                                                                          Description: Shift in age within each cohort due to houses becoming open or closed to retrofitting.
                                                                          Present In 1 View: Used By
                                                                          • Total Age "Total" age for each cohort of housing.
                                                                          Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                          .housingagingchain v8 #231
                                                                          A
                                                                          Net Area Shift by System (sf / Year)
                                                                          Net Area Shift by System[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                          Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, Average Area[ Cohort,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], Average Area[ Cohort,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                          Description: The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                          Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #232
                                                                          F,A
                                                                          Net Area Shift due to Retrofit Status Switching (sf / Year)
                                                                          Net Area Shift due to Retrofit Status Switching[Cohort] = SUM(
                                                                          Net Area Shift by System[ Cohort, Heating and Cooling System!])
                                                                          Description: Shift in area between energy sources due to houses switching sources.
                                                                          Present In 1 View: Used By
                                                                          • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                          Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #233
                                                                          F,A
                                                                          Net Change in Homes Retrofitting (Houses / Year)
                                                                          Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] = (
                                                                          Indicated Homes Retrofitting[ Cohort, Heating and Cooling System]- Housing[ Cohort, Heating and Cooling System,Open to Retrofitting])/ Time to Decide to Retrofit
                                                                          Description: Homes that are in the process of deciding to retrofit.
                                                                          Present In 3 Views: Used By
                                                                          • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                          • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                          • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                          • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                          Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [2,2]
                                                                          HeatPumpModel_v31 #234
                                                                          F,A
                                                                          Net U Value Change from Retrofitting Home Shifts (House * kBTU / (Year * F * sf) / Year)
                                                                          Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                          Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, U Value by Grouping[ Cohort, Heating and Cooling System,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                          Description: Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                          Present In 1 View: Used By
                                                                          • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                          Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #235
                                                                          C
                                                                          No Turnover Switch (dmnl )
                                                                          = 0
                                                                          Description: Switch for having no turnover in housing stock-- i.e., no housing demolitions or constructions.
                                                                          Present In 1 View:
                                                                          Used By
                                                                          • Demolitions Homes that are destroyed every year.
                                                                          • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          .housingagingchain v8 #238
                                                                          C
                                                                          Noise Correlation Time (Year)
                                                                          = 4
                                                                          Description: The correlation time constant for Pink Noise.
                                                                          Present In 1 View:
                                                                          Used By
                                                                          • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                          • White Noise White noise input to the pink noise process.
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          .housingagingchain v8 #236
                                                                          C
                                                                          Noise Correlation Time 0 (Year)
                                                                          = 4
                                                                          Description: The correlation time constant for Pink Noise.
                                                                          Present In 1 View:
                                                                          Used By
                                                                          • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                          • White Noise 0 White noise input to the pink noise process.
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #237
                                                                          C
                                                                          Noise Correlation Time 1 (Year)
                                                                          = 4
                                                                          Description: The correlation time constant for Pink Noise.
                                                                          Present In 1 View:
                                                                          Used By
                                                                          • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                          • White Noise 1 White noise input to the pink noise process.
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          .housingagingchain v8 #241
                                                                          C
                                                                          Noise Standard Deviation (Dimensionless)
                                                                          = 0
                                                                          Description: The standard deviation of the pink noise process.
                                                                          Present In 1 View:
                                                                          Used By
                                                                          • White Noise White noise input to the pink noise process.
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          .housingagingchain v8 #239
                                                                          C
                                                                          Noise Standard Deviation 0 (Dimensionless)
                                                                          = 0
                                                                          Description: The standard deviation of the pink noise process.
                                                                          Present In 1 View:
                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #240
                                                                          C
                                                                          Noise Standard Deviation 1 (Dimensionless)
                                                                          = 0
                                                                          Description: The standard deviation of the pink noise process.
                                                                          Present In 1 View:
                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          .housingagingchain v8 #244
                                                                          C
                                                                          Noise Start Time (Year)
                                                                          = 5
                                                                          Description: Start time for the random input.
                                                                          Present In 1 View:
                                                                          Used By
                                                                          • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          .housingagingchain v8 #242
                                                                          C
                                                                          Noise Start Time 0 (Year)
                                                                          = 5
                                                                          Description: Start time for the random input.
                                                                          Present In 1 View:
                                                                          Used By
                                                                          • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #243
                                                                          C
                                                                          Noise Start Time 1 (Year)
                                                                          = 5
                                                                          Description: Start time for the random input.
                                                                          Present In 1 View:
                                                                          Used By
                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #245
                                                                          A,T
                                                                          Oil COP TABLE (dmnl)
                                                                          Oil COP TABLE([(2020,0)-(2050,1)],(2020,0.835),(2030,0.84),(2050,0.84))

                                                                          Description: Efficiency of oil systems over time. Taken as the average of projected efficiency for reference distillate boilers and furnaces, from MassDEP's Energy Pathways for Deep Decarbonization Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                          Present In 1 View:
                                                                          Used By
                                                                          • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #246
                                                                          A
                                                                          Optimal Cooling Cost (Dollar / (Year * House))
                                                                          Optimal Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                          Expected Cooling Energy Price* Optimal Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                          Description: The average cost of cooling, if homes have the optimal U value.
                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #247
                                                                          C
                                                                          Optimal Cooling Energy Use (kBTU / (Year * House))
                                                                          Optimal Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                          Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                          Optimal Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                          Description: The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #248
                                                                          A
                                                                          Optimal Energy Cost (Dollar / (Year * House))
                                                                          Optimal Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                          Optimal Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Optimal Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                          Description: Total energy cost if optimal U value is achieved.
                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                          HeatPumpModel_v31 #249
                                                                          A
                                                                          Optimal Energy Use (kBTU / (House * Year))
                                                                          Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                          Optimal Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]+ Optimal Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                          Description: Average energy use to heat and cool per house if U is optimal.
                                                                          Present In 1 View: Used By
                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                            HeatPumpModel_v31 #250
                                                                            A
                                                                            Optimal Heating Cost (Dollar / (Year * House))
                                                                            Optimal Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                            Expected Heating Energy Price[ Heating and Cooling System]* Optimal Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                            Description: Average heating cost if U value is optimal.
                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                            HeatPumpModel_v31 #251
                                                                            A
                                                                            Optimal Heating Energy Use (kBTU / (House * Year))
                                                                            Optimal Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                            Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                            Description: The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                            HeatPumpModel_v31 #252
                                                                            A
                                                                            Optimal U Across All Housing (kBTU / (sf * F * Year))
                                                                            = SUM(
                                                                            Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort!, Heating and Cooling System!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!]/ Total Housing Stock)
                                                                            Description: The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                            Present In 1 View: Used By
                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                              .housingagingchain v18 #253
                                                                              A
                                                                              Optimal U for New Homes (kBTU / (sf * Year * F))
                                                                              Optimal U for New Homes[Cohort,Heating and Cooling System] = ((
                                                                              Expected Reference Marginal Cost/( Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]/ Discount Rate))^(1/ Sensitivity of Marginal Cost to U Value))* Reference U Value*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)
                                                                              Description: The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                              Present In 2 Views: Used By
                                                                              • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                              • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                              HeatPumpModel_v31 #255
                                                                              A
                                                                              Optimal U Value for Existing Homes (kBTU / (sf * F * Year))
                                                                              Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                              U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]< Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System],IF THEN ELSE( Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]> Marginal Cost at Binding U Value without EEHIC[ Cohort, Heating and Cooling System], Optimal U Value with No EEHIC Proportional Subsidy[ Cohort, Heating and Cooling System], U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]))
                                                                              Description: This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                              Present In 1 View: Used By
                                                                              • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                              .housingagingchain v4 testing #254
                                                                              A
                                                                              Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                              Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                              Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                              Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                              Present In 8 Views: Used By
                                                                              • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                              • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                              • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                              • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                              • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                              • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                              • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                              • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                              • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                              HeatPumpModel_v31 #256
                                                                              A
                                                                              Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))
                                                                              Optimal U Value with No EEHIC Proportional Subsidy[Cohort,Heating and Cooling System] =
                                                                              Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                              Description: Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                              Present In 1 View: Used By
                                                                              • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                              HeatPumpModel_v31 #257
                                                                              A
                                                                              Peak Cooling Load on Grid (kWH / Day)
                                                                              = SUM(
                                                                              Peak Load from Heat Pumps on Hottest Days per Group[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                              Description: Annual load from heat pumps providing heating on the coldest day, across all groups.
                                                                              Present In 1 View: Used By
                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                HeatPumpModel_v31 #258
                                                                                A
                                                                                Peak Heating Load on Grid (kWH / Day)
                                                                                = SUM(
                                                                                Peak Load from Heat Pumps on Coldest Days per Group[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                Description: Annual load from heat pumps providing heating on the coldest days, across all groups.
                                                                                Present In 1 View: Used By
                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                  HeatPumpModel_v31 #259
                                                                                  C
                                                                                  Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)
                                                                                  Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Heat Pump Heating and Cooling,Retrofitting Status] =
                                                                                  Housing[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* HDD on Coldest Day/ Heat Pump COP on Coldest Days/( kBTU per kWH* Days per Year)
                                                                                  Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Fossil Fuel Heating,Retrofitting Status] = 0
                                                                                  Description: The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                  HeatPumpModel_v31 #260
                                                                                  C
                                                                                  Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)
                                                                                  Peak Load from Heat Pumps on Hottest Days per Group[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                  Housing[ Cohort, Heating and Cooling System, Retrofitting Status]* U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* CDD on Coldest Day/ Cooling System Efficiency[ Heating and Cooling System]/( kBTU per kWH* Days per Year)
                                                                                  Peak Load from Heat Pumps on Hottest Days per Group[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                  Description: The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                  HeatPumpModel_v31 #261
                                                                                  C
                                                                                  Peak Load from Non Heating or Cooling Sources (kWH / Day )
                                                                                  = 18344.8*1000*0.461799
                                                                                  Description: The peak load coming from non-heating sources, like other household uses, commercial uses, industrial uses, etc. Approximated as the average peak load in September, October, April, and May of 2022 and 2023 from New England ISO data, since there is little heating or cooling demand in those swing months. We multiply by 0.46 as Massachusetts has 46% of New England's population and we assume demand is proportional to population.Data source: https://www.iso-ne.com/isoexpress/web/reports/load-and-demand/-/tree/net-ener-peak-load
                                                                                  Present In 1 View:
                                                                                  Used By
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #262
                                                                                    A
                                                                                    Perceived Cost of Not Retrofitting (Dollar / (House * Year))
                                                                                    Perceived Cost of Not Retrofitting[Cohort,Heating and Cooling System] = (1-
                                                                                    Weight on Upfront Cost)* Total Cost of Ownership of Average Home[ Cohort, Heating and Cooling System]
                                                                                    Description: Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                    Present In 1 View: Used By
                                                                                    • Affinity of Not Retrofitting The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #263
                                                                                    A
                                                                                    Perceived Cost of Retrofitting (Dollar / (House * Year))
                                                                                    Perceived Cost of Retrofitting[Cohort,Heating and Cooling System] = (1-
                                                                                    Weight on Upfront Cost)* Total Cost of Ownership of Retrofitted Homes[ Cohort, Heating and Cooling System]+ Weight on Upfront Cost* Amoritized Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]
                                                                                    Description: Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #264
                                                                                    C
                                                                                    Pounds per Ton (lb CO2 / tCO2)
                                                                                    = 2204.6
                                                                                    Description: The number of pounds in a metric ton.
                                                                                    Present In 1 View:
                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v5 testing #265
                                                                                    C
                                                                                    Present Value of Cooling Operating Costs (Dollars / (House))
                                                                                    Present Value of Cooling Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = (
                                                                                    Expected Cooling Energy Price* Cooling Energy Use Under Alternatives[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Cooling Technology[ Heating and Cooling System]))
                                                                                    Present Value of Cooling Operating Costs[Cohort,Traditional Cooling,Retrofitting Status,Heating and Cooling System] = ( Expected Cooling Energy Price* Cooling Energy Use Under Alternatives[ Cohort, Traditional Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Cooling Technology[ Heating and Cooling System]))
                                                                                    Present Value of Cooling Operating Costs[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] = 0
                                                                                    Description: The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                    Present In 1 View: Used By
                                                                                    • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v5 testing #266
                                                                                    A
                                                                                    Present Value of Heating Operating Costs (Dollar / (House))
                                                                                    Present Value of Heating Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = (
                                                                                    Expected Heating Energy Price[ Heating and Cooling System]* Heating Energy Use Under Alternatives[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Heating Technology[ Heating and Cooling System]))
                                                                                    Present Value of Heating Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = ( Expected Heating Energy Price[ Heating and Cooling System]* Heating Energy Use Under Alternatives[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Heating Technology[ Heating and Cooling System]))
                                                                                    Description: The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                    Present In 1 View: Used By
                                                                                    • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #267
                                                                                    A
                                                                                    Present Value of Operating Costs (Dollar / (House) )
                                                                                    Present Value of Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                    Present Value of Cooling Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]+ Present Value of Heating Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]
                                                                                    Present Value of Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Present Value of Cooling Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]+ Present Value of Heating Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]
                                                                                    Description: Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                    Present In 1 View: Used By
                                                                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #268
                                                                                    C
                                                                                    Present Value Replacement Cost (Dollar / House)
                                                                                    Present Value Replacement Cost[Heating and Cooling System] =
                                                                                    Cost of Cooling System Replacement[ Heating and Cooling System]/( Average Lifetime of Cooling Technology[ Heating and Cooling System]* Discount Rate)+ Cost of Heating System Replacement[ Heating and Cooling System]/( Average Lifetime of Heating Technology[ Heating and Cooling System]* Discount Rate)
                                                                                    Present Value Replacement Cost[Heat Pump Heating and Cooling] = Cost of Cooling System Replacement[ Heat Pump Heating and Cooling]/( Average Lifetime of Cooling Technology[ Heat Pump Heating and Cooling]* Discount Rate)
                                                                                    Present Value Replacement Cost[No AC Cooling] = 0
                                                                                    Description: Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                    Present In 1 View: Used By
                                                                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #269
                                                                                    C
                                                                                    Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )
                                                                                    = 2023
                                                                                    Description: Time at which the proportional subsidy will take effect from the Energy Efficiency Home Improvement Credit.Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                    Present In 2 Views:
                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #270
                                                                                    C
                                                                                    Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
                                                                                    = 1
                                                                                    Description: Turns proportional subsidy's effect on retrofit cost on/off.
                                                                                    Present In 2 Views:
                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v15 #271
                                                                                    C
                                                                                    Proportional MassSave Subsidy Implementation Year for Retrofits (Year )
                                                                                    = 2020
                                                                                    Description: Time at which the proportional subsidy will take effect.
                                                                                    Present In 2 Views:
                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v15 #272
                                                                                    C
                                                                                    Proportional Subsidy Switch for Retrofits (dmnl )
                                                                                    = 1
                                                                                    Description: Turns proportional subsidy's effect on retrofit cost on/off.
                                                                                    Present In 1 View:
                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v8 #275
                                                                                    C
                                                                                    Pulse Time (Year)
                                                                                    = 5
                                                                                    Description: Time at which the pulse in Input occurs.
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v8 #273
                                                                                    C
                                                                                    Pulse Time 0 (Year)
                                                                                    = 5
                                                                                    Description: Time at which the pulse in Input occurs.
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #274
                                                                                    C
                                                                                    Pulse Time 1 (Year)
                                                                                    = 5
                                                                                    Description: Time at which the pulse in Input occurs.
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v8 #278
                                                                                    C
                                                                                    Ramp End Time (Year)
                                                                                    = 1e+09
                                                                                    Description: End time for the ramp input.
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v8 #276
                                                                                    C
                                                                                    Ramp End Time 0 (Year)
                                                                                    = 1e+09
                                                                                    Description: End time for the ramp input.
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #277
                                                                                    C
                                                                                    Ramp End Time 1 (Year)
                                                                                    = 1e+09
                                                                                    Description: End time for the ramp input.
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v8 #281
                                                                                    C
                                                                                    Ramp Start Time (Year)
                                                                                    = 5
                                                                                    Description: Start time for the ramp input.
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v8 #279
                                                                                    C
                                                                                    Ramp Start Time 0 (Year)
                                                                                    = 5
                                                                                    Description: Start time for the ramp input.
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #280
                                                                                    C
                                                                                    Ramp Start Time 1 (Year)
                                                                                    = 5
                                                                                    Description: Start time for the ramp input.
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #282
                                                                                    C
                                                                                    Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )
                                                                                    = 30000
                                                                                    Description: The reference value of lifetime heating and cooling combinations when people calculate affinity of each combo. Hand calibrated to roughly match heat pump sales in https://www.masssave.com/en/about/news-and-events/news/mass-save-sponsors-announce-record-number-of-heat-pump-installations-across-massachusetts
                                                                                    Present In 1 View:
                                                                                    Used By
                                                                                    • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v5 testing #283
                                                                                    C
                                                                                    Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )
                                                                                    = 12.88
                                                                                    Description: The marginal cost of retrofitting at the reference EUI. In particular, the marginal cost of retrofitting at some EUI is Reference U *( (Reference U / U) ^ Sensitivity )This was calculated by setting sensitivity of marginal cost equal to 1.25, and finding the MC where a 31% reduction in U value from the reference costs a total of 4.95 / (1 - 0.21) dollars per square foot. The sensitivity value is explained in the sensitivity variable. Less et al. (2021, pg. 17-18) note that in their project database, the median cost per square foot for retrofits after subsidies was $4.95, while subsidies accounted for 21% of the total project cost for the median project. The median cost reduced energy use by 28% - 33% (of which I took the average), and I use the lower bound value to account for the fact that energy savings may occur not only due to increase in U value.Obviously all of this is extraordinarily rough.Less et al. (2021): https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
                                                                                    Present In 2 Views:
                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #284
                                                                                    C
                                                                                    Reference Retrofit Cost (Dollar / (House * Year) )
                                                                                    = 8740
                                                                                    Description: Perceived cost of home heating to which households compare the perceived cost of retrofitting to when deciding to retrofit.Taken from average retrofit cost in Less et al. (2021)'s dataset, shown on page 17: https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
                                                                                    Present In 2 Views:
                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    .housingagingchain v9 #285
                                                                                    C
                                                                                    Reference U Value (kBTU / (sf * Year * F) )
                                                                                    = 0.006
                                                                                    Description: Reference U Value to ensure base of exponent in marginally optimal U value is dimensionless. This must be equal to or greater than code U value.Value taken as the average of U values of single family homes in MA in 2020 for our sample.
                                                                                    Present In 3 Views:
                                                                                    Used By
                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #286
                                                                                    C
                                                                                    Retrofit Delay (Year )
                                                                                    = 2
                                                                                    Description: Time to retrofit. Assumed to be on average six months.
                                                                                    Present In 2 Views:
                                                                                    Used By
                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                    HeatPumpModel_v31 #288
                                                                                    F,A
                                                                                    Retrofitting (House * kBTU / (sf * F* Year) / Year)
                                                                                    Retrofitting[Cohort,Heating and Cooling System] = MAX(0,
                                                                                    Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]*( U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]- Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])/ Retrofit Delay)
                                                                                    Description: Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                    Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                    HeatPumpModel_v31 #287
                                                                                    A
                                                                                    Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
                                                                                    = SUM(
                                                                                    Retrofitting[ Cohort!, Heating and Cooling System!])
                                                                                    Description: The total amount of retrofits across all cohorts and heating/cooling systems.
                                                                                    Present In 1 View: Used By
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #290
                                                                                      C
                                                                                      Sensitivity of Affinity to Cost (dmnl )
                                                                                      = 10
                                                                                      Description: Sensitivity of affinity to each heating and cooling combination having higher cost. The higher this, the fewer houses will convert to more expensive combinations.Calculated by hand calibration-- value ensures that amount of heat pumps sold 2020 - 2024 begins at about 10K and goes to about 20K in 2024, in accordance with MassSave data from https://www.masssave.com/en/about/news-and-events/news/mass-save-sponsors-announce-record-number-of-heat-pump-installations-across-massachusetts
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      .housingagingchain v5 testing #291
                                                                                      C
                                                                                      Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                      = 3.25
                                                                                      Description: Measures the sensitivity of marginal retrofit costs as a function of optimal U value. In particular, marginal Retrofit Cost is equal to Constant * (U Value retrofitted away ^ Convexity). This must be greater than 1.This is taken from pg. 69 of Caswell (2022), where she calculates the total retrofit cost curve as a function of percent savings as having an exponent of 2.25. Because this is the total retrofit cost curve, the exponent for the marginal cost is -2.25 - 1. Because percent savings is inversely proportional to U, the exponent in the total cost curve will be the negation of 2.25, which is ensured in the marginal cost curve formulation in other variables.
                                                                                      Present In 4 Views:
                                                                                      Used By
                                                                                      • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                      • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                      • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                      • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                      • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                      • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                      • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #292
                                                                                      C
                                                                                      Sensitivity of Retrofits to Cost (dmnl )
                                                                                      = 10
                                                                                      Description: Sensitivity of affinity (and fraction of houses retrofitting) to NPV of retrofitting.
                                                                                      Present In 2 Views:
                                                                                      Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      .housingagingchain v8 #295
                                                                                      C
                                                                                      Sine Amplitude (Dimensionless)
                                                                                      = 0
                                                                                      Description: Amplitude of sine wave in customer orders (fraction of mean).
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      .housingagingchain v8 #293
                                                                                      C
                                                                                      Sine Amplitude 0 (Dimensionless)
                                                                                      = 0
                                                                                      Description: Amplitude of sine wave in customer orders (fraction of mean).
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #294
                                                                                      C
                                                                                      Sine Amplitude 1 (Dimensionless)
                                                                                      = 0
                                                                                      Description: Amplitude of sine wave in customer orders (fraction of mean).
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      .housingagingchain v8 #298
                                                                                      C
                                                                                      Sine Period (Year)
                                                                                      = 50
                                                                                      Description: Period of sine wave in customer demand. Set initially to 50 weeks (1 year).
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      .housingagingchain v8 #296
                                                                                      C
                                                                                      Sine Period 0 (Year)
                                                                                      = 50
                                                                                      Description: Period of sine wave in customer demand. Set initially to 50 weeks (1 year).
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #297
                                                                                      C
                                                                                      Sine Period 1 (Year)
                                                                                      = 50
                                                                                      Description: Period of sine wave. Set initially to 50 weeks (1 year).
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #299
                                                                                      A
                                                                                      Soft Costs of Retrofitting (Dollar / Home)
                                                                                      =
                                                                                      Average Income* Homeowner Hours Spent Retrofitting
                                                                                      Description: The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                      Present In 1 View: Used By
                                                                                      • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      .housingagingchain v8 #302
                                                                                      C
                                                                                      Step Time (Year)
                                                                                      = 5
                                                                                      Description: Time for the step input.
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      .housingagingchain v8 #300
                                                                                      C
                                                                                      Step Time 0 (Year)
                                                                                      = 5
                                                                                      Description: Time for the step input.
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #301
                                                                                      C
                                                                                      Step Time 1 (Year)
                                                                                      = 5
                                                                                      Description: Time for the step input.
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #303
                                                                                      A
                                                                                      Subsidized Cost of Heat Pumps (Dollar / House)
                                                                                      = MAX(0,
                                                                                      Unsubsidized Cost of Heat Pumps- Expected Subsidy for Heat Pumps)
                                                                                      Description: The upfront cost of heat pump once subsidies are taken into account.
                                                                                      Present In 1 View: Used By
                                                                                      • Cost of Cooling System Replacement The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                      • Cost of Heating System Replacement The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      .housingagingchain v15 #304
                                                                                      A
                                                                                      Subsidized Retrofit Cost (Dollar /House)
                                                                                      Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                      Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]- Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System,Open to Retrofitting]+ Soft Costs of Retrofitting
                                                                                      Description: The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #305
                                                                                      C
                                                                                      System Switching SWITCH (dmnl )
                                                                                      = 1
                                                                                      Description: Switch for allowing houses to switch heating and cooling systems. If 1, they can switch.
                                                                                      Present In 1 View:
                                                                                      Used By
                                                                                      • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #307
                                                                                      C
                                                                                      Time to Decide to Retrofit (Year )
                                                                                      = 3
                                                                                      Description: Time to decide to retrofit.
                                                                                      Present In 1 View:
                                                                                      Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      .housingagingchain v8 #309
                                                                                      L
                                                                                      Total Age (House * Year)
                                                                                      Total Age[Cohort,Not Open to Retrofitting] = (
                                                                                      Aging[ Cohort,Not Open to Retrofitting]- Net Age Shift from Retrofitting Status Shifting[ Cohort])- Age Removal[ Cohort,Not Open to Retrofitting] dt + Initial Age[ Cohort,Not Open to Retrofitting]
                                                                                      Total Age[Cohort,Open to Retrofitting] = ( Net Age Shift from Retrofitting Status Shifting[ Cohort]+ Aging[ Cohort,Open to Retrofitting])- Age Removal[ Cohort,Open to Retrofitting] dt + Initial Age[ Cohort,Open to Retrofitting]
                                                                                      Description: "Total" age for each cohort of housing.
                                                                                      Present In 2 Views: Used By
                                                                                      • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                      • Average Age in All Housing Average age of houses, regardless of cohort
                                                                                      Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                      HeatPumpModel_v31 #310
                                                                                      A
                                                                                      Total Area (sf)
                                                                                      = SUM(
                                                                                      Area[ Cohort!, Retrofitting Status!])
                                                                                      Description: The total area across all housing.
                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #311
                                                                                      A
                                                                                      Total Cooling Cost (Dollar / Year)
                                                                                      = SUM(
                                                                                      Average Cooling Cost[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                      Description: The total amount of money spent on cooling homes, per year.
                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #312
                                                                                      A
                                                                                      Total Cooling Energy Use (kBTU/ Year)
                                                                                      = SUM(
                                                                                      Average Cooling Energy Use[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                      Description: The total amount of energy spent on cooling homes.
                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #313
                                                                                      A
                                                                                      Total Cost of Ownership of Average Home (Dollar / (Year * House))
                                                                                      Total Cost of Ownership of Average Home[Cohort,Heating and Cooling System] =
                                                                                      Average Energy Costs for Retrofitting Home[ Cohort, Heating and Cooling System]
                                                                                      Description: Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                      Present In 2 Views: Used By
                                                                                      • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #314
                                                                                      A
                                                                                      Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))
                                                                                      Total Cost of Ownership of Retrofitted Homes[Cohort,Heating and Cooling System] =
                                                                                      Amoritized Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]+ Average Energy Costs if Retrofitted[ Cohort, Heating and Cooling System]
                                                                                      Description: The total cost of ownership of owning a home that has been retrofitted to the optimal U.
                                                                                      Present In 1 View: Used By
                                                                                      • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #315
                                                                                      A
                                                                                      Total Energy Use (kBTU / Year)
                                                                                      = SUM(
                                                                                      Energy Use by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                      Description: The total energy use for all homes in the model.
                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #316
                                                                                      A
                                                                                      Total Heat Pump Sales (House / Year)
                                                                                      = SUM(
                                                                                      Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump Only]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Gas]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Oil])
                                                                                      Description: Number of houses buying heat pumps every year.
                                                                                      Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #317
                                                                                      A
                                                                                      Total Heating Cost (Dollar / Year)
                                                                                      = SUM(
                                                                                      Average Heating Cost[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                      Description: The total amount of money spent on heating homes.
                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #318
                                                                                      A
                                                                                      Total Heating Energy Use (kBTU/ Year)
                                                                                      = SUM(
                                                                                      Average Heating Energy Use[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                      Description: The total amount of energy spent on heating per year.
                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                      HeatPumpModel_v31 #319
                                                                                      A
                                                                                      Total Housing Starts (House/ Year)
                                                                                      = SUM(
                                                                                      Housing Starts[ Cohort!, Heating and Cooling System!])
                                                                                      Description: The total housing starts across all cohorts and sources.
                                                                                      Present In 1 View: Used By
                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                        .housingagingchain v4 testing #320
                                                                                        A
                                                                                        Total Housing Stock (House)
                                                                                        = SUM(
                                                                                        Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                        Description: Total number of houses across all cohorts, heating/cooling systems, and retrofitting status.
                                                                                        Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                        HeatPumpModel_v31 #321
                                                                                        C
                                                                                        Total Initial Homes (Houses )
                                                                                        = 20
                                                                                        Description: Total number of houses, including those retrofitting or not. Number taken from Census's list of households in MA in 2022: https://www.census.gov/quickfacts/fact/table/MA/PST045222
                                                                                        Present In 1 View:
                                                                                        Used By
                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #322
                                                                                          C
                                                                                          Total Initial Housing Starts (Houses / Year )
                                                                                          = 0.5
                                                                                          Description: Total number of houses that are built per year, across all systems.
                                                                                          Present In 1 View:
                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #323
                                                                                          A
                                                                                          Total Present Value of Cost (Dollar / House)
                                                                                          Total Present Value of Cost[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                          Present Value of Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]+ Present Value Replacement Cost[ Heating and Cooling System]+ Cost of Bad Air Conditioning[ Heating and Cooling System]
                                                                                          Total Present Value of Cost[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Present Value of Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]+ Present Value Replacement Cost[ Heating and Cooling System]+ Cost of Bad Air Conditioning[ Heating and Cooling System]
                                                                                          Description: Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                          Present In 1 View: Used By
                                                                                          • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #327
                                                                                          L
                                                                                          Total U Value (House * kBTU / (Year * F * sf) )
                                                                                          Total U Value[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                          Increase in U Value from Housing Starts[ Cohort, Heating and Cooling System]- Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System])- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Not Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Not Open to Retrofitting])) dt + Initial U Value[ Cohort, Heating and Cooling System,Not Open to Retrofitting]
                                                                                          Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] = ((( Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System]- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Open to Retrofitting])))- Retrofitting[ Cohort, Heating and Cooling Systemdt + Initial U Value[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                          Description: Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                          Present In 2 Views: Used By Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                          HeatPumpModel_v31 #324
                                                                                          A
                                                                                          Total U Value Across All Groupings (House * kBTU / (sf * F * Year))
                                                                                          = SUM(
                                                                                          Total U Value by Cohort[ Cohort!])
                                                                                          Description: Total U value across all groupings of households.
                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #325
                                                                                          A
                                                                                          Total U Value by Cohort (House * kBTU / (sf * F * Year))
                                                                                          Total U Value by Cohort[Cohort] = SUM(
                                                                                          Total U Value[ Cohort, Heating and Cooling System!, Retrofitting Status!])
                                                                                          Description: Total U Value within each cohort.
                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #326
                                                                                          A
                                                                                          Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))
                                                                                          Total U Value by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                          Total U Value[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                          Description: The total U value by heating and cooling system
                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #328
                                                                                          A
                                                                                          U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))
                                                                                          U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                          U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06:AND: Expected EEHIC Proportional Subsidy Rate for Retrofits>1e-06, Reference U Value*(( Sensitivity of Marginal Cost to U Value-1)*((( Expected EEHIC Maximum Subsidy for Retrofits- Expected EEHIC Proportional Subsidy Rate for Retrofits* Expected Fixed Cost)/( U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]* Expected EEHIC Proportional Subsidy Rate for Retrofits* Expected Reference Marginal Cost* Average Area[ Cohort,Open to Retrofitting]))-(1/(- Sensitivity of Marginal Cost to U Value+1))*(( U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]/ Reference U Value)^(- Sensitivity of Marginal Cost to U Value+1)))^(1/(- Sensitivity of Marginal Cost to U Value+1))),0)
                                                                                          Description: This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                          Present In 1 View: Used By
                                                                                          • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                          • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #329
                                                                                          A
                                                                                          U Value by Grouping (kBTU / (sf * F * Year))
                                                                                          U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                          Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                          Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                          Present In 8 Views: Used By
                                                                                          • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                          • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                          • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                          • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                          • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                          • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                          • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                          • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                          • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                          • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                          • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                          • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                          • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                          Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                          HeatPumpModel_v31 #330
                                                                                          A
                                                                                          U Value Increase from Source Switching (kBTU*House/(Year*Year*sf*F))
                                                                                          U Value Increase from Source Switching[Heating and Cooling System] = SUM(
                                                                                          U Value Shift from Source Switching[ Cohort!, Heating and Cooling System!, Heating and Cooling System, Retrofitting Status!])
                                                                                          Description: The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #331
                                                                                          F,A
                                                                                          U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)
                                                                                          U Value Loss from Demolition[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                          U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Demolitions[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                          Description: Homes' total energy use decrease from those homes being demolished.
                                                                                          Present In 1 View: Used By
                                                                                          • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                          Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                          .housingagingchain v18 #332
                                                                                          A
                                                                                          U Value of Housing Starts (kBTU / (Year * F * sf))
                                                                                          U Value of Housing Starts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                          Additional Cost of Building to U Value[ Cohort, Heating and Cooling System]<0:AND: Optimal U for New Homes[ Cohort, Heating and Cooling System]< Code U, Optimal U for New Homes[ Cohort, Heating and Cooling System], Code U)
                                                                                          Description: Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #333
                                                                                          A
                                                                                          U Value of Retrofitting Homes (kBTU / (sf * Year * F))
                                                                                          U Value of Retrofitting Homes[Cohort,Heating and Cooling System] =
                                                                                          U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                          Description: The Average U Value of each home that is open to retrofitting.
                                                                                          Present In 1 View: Used By
                                                                                          • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                          • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                          HeatPumpModel_v31 #334
                                                                                          L
                                                                                          U Value Retrofitted Away (House * kBTU / (Year * F * sf))
                                                                                          = SUM(
                                                                                          Retrofitting[ Cohort!, Heating and Cooling System!]) dt + 0.0
                                                                                          Description: Total amount of U value that has been retrofitted away.
                                                                                          Present In 1 View: Used By
                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            HeatPumpModel_v31 #335
                                                                                            F,A
                                                                                            U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)
                                                                                            U Value Shift from Source Switching[Cohort,Heat Pump Heating and Cooling,Heating and Cooling System,Retrofitting Status] =
                                                                                            Houses Switching Sources[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]
                                                                                            U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] = Houses Switching Sources[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Fossil Fuel Heating, Retrofitting Status]
                                                                                            Description: The shift in total U value coming from switching sources.
                                                                                            Present In 2 Views: Used By
                                                                                            • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                            • U Value Increase from Source Switching The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                            Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                            HeatPumpModel_v31 #336
                                                                                            A,T
                                                                                            Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)
                                                                                            Unsubsidized Cost of Heat Pump Over Time TABLE([(2020,5000)-(2050,10000)],(2020,22000),(2030,20483.7 ),(2040,18967.3),(2050,17448.6))

                                                                                            Description: The cost of installing and buying a heat pump over time. Initial value taken from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then assume that ratio of future prices to initial is the same as average of reference and ductless heat pumps in MassDEP's Energy Pathways Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download. (That is, I took the ratio of the initial price to the initial price in that report, then I multiplied that ratio times all projections of future heat pump prices). I was unable to use the MassDEP report's prices directly, because they are based on national estimates from NREL, and MA is typically a more expensive state. In particular, the MassDEP projections say that heat pumps cost only $9K, but MassSave subsidy is $10K!Assumes rates of change are linear between projected points.
                                                                                            Present In 1 View:
                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            HeatPumpModel_v31 #337
                                                                                            A
                                                                                            Unsubsidized Cost of Heat Pumps (Dollar / House)
                                                                                            =
                                                                                            Unsubsidized Cost of Heat Pump Over Time TABLE( Time)
                                                                                            Description: The unsubsidized cost of heat pumps, instantiated at each time.
                                                                                            Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            .housingagingchain v8 #339
                                                                                            A
                                                                                            Unsubsidized Retrofit Cost (Dollar / House)
                                                                                            Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                            Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort,Open to Retrofitting]
                                                                                            Description: Total retrofit cost without taking into account subsidies.
                                                                                            Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            .housingagingchain v5 testing #338
                                                                                            A
                                                                                            Unsubsidized Retrofit Cost Intensity (Dollar / sf)
                                                                                            Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] = MAX(IF THEN ELSE(
                                                                                            U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06,( Expected Reference Marginal Cost* Reference U Value/(- Sensitivity of Marginal Cost to U Value+1))*((( Reference U Value/ U Value of Retrofitting Homes[ Cohort, Heating and Cooling System])^ Sensitivity of Marginal Cost to U Value-1)-(( Reference U Value/ Optimal U Value for Existing Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value-1)))+ Fixed Cost per Unit Area[ Cohort],0),0)
                                                                                            Description: Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                            Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            HeatPumpModel_v31 #340
                                                                                            C
                                                                                            Weight on Upfront Cost (dmnl )
                                                                                            = 0.5
                                                                                            Description: How much homeowners weigh upfront (amoritized) costs of retrofits as opposed to the total cost of ownership due to being more perceptive of short-term costs.
                                                                                            Present In 2 Views:
                                                                                            Used By
                                                                                            • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                            • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            .housingagingchain v8 #343
                                                                                            A
                                                                                            White Noise (Dimensionless)
                                                                                            =
                                                                                            Noise Standard Deviation*((24* Noise Correlation Time/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                            Description: White noise input to the pink noise process.
                                                                                            Present In 1 View: Used By
                                                                                            • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            .housingagingchain v8 #341
                                                                                            A
                                                                                            White Noise 0 (Dimensionless)
                                                                                            =
                                                                                            Noise Standard Deviation 0*((24* Noise Correlation Time 0/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                            Description: White noise input to the pink noise process.
                                                                                            Present In 1 View: Used By
                                                                                            • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            HeatPumpModel_v31 #342
                                                                                            A
                                                                                            White Noise 1 (Dimensionless)
                                                                                            =
                                                                                            Noise Standard Deviation 1*((24* Noise Correlation Time 1/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                            Description: White noise input to the pink noise process.
                                                                                            Present In 1 View: Used By
                                                                                            • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            .Control #126
                                                                                            C
                                                                                            FINAL TIME (Year)
                                                                                            = 2050
                                                                                            Description: The final time for the simulation.
                                                                                            Present In 1 View:
                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            .Control #196
                                                                                            C
                                                                                            INITIAL TIME (Year)
                                                                                            = 2020
                                                                                            Description: The initial time for the simulation.
                                                                                            Present In 3 Views:
                                                                                            Used By
                                                                                            • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                            • Average Area of Housing Starts The average area of housing starts.
                                                                                            • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                            .Control #289
                                                                                            A
                                                                                            SAVEPER (Year )
                                                                                            =
                                                                                            TIME STEP
                                                                                            Description: The frequency with which output is stored.
                                                                                            Present In 0 Views:
                                                                                              Used By
                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                .Control #306
                                                                                                C
                                                                                                TIME STEP (Year )
                                                                                                = 0.03125
                                                                                                Description: The time step for the simulation.
                                                                                                Present In 1 View:
                                                                                                Used By
                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                • SAVEPER The frequency with which output is stored.
                                                                                                • White Noise White noise input to the pink noise process.
                                                                                                • White Noise 0 White noise input to the pink noise process.
                                                                                                • White Noise 1 White noise input to the pink noise process.
                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                (View) Not in View (2 Variables)
                                                                                                Top (View) Not in View (2 Variables)
                                                                                                Group
                                                                                                Type
                                                                                                Variable Name And Description
                                                                                                .housingagingchain v8 #225
                                                                                                C
                                                                                                Maximum Energy Price (Dollar / kBTU)
                                                                                                = 10
                                                                                                Description: Shifts x-axis for graph of optimal retrofit amount as a function of energy price.
                                                                                                Present In 0 Views:
                                                                                                  Used By
                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                    .Control #289
                                                                                                    A
                                                                                                    SAVEPER (Year )
                                                                                                    =
                                                                                                    TIME STEP
                                                                                                    Description: The frequency with which output is stored.
                                                                                                    Present In 0 Views:
                                                                                                      Used By
                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                        (View) Age (14 Variables)
                                                                                                        Top (View) Age (14 Variables)
                                                                                                        Group
                                                                                                        Type
                                                                                                        Variable Name And Description
                                                                                                        .housingagingchain v8 #8
                                                                                                        F,A
                                                                                                        Age Removal (House * Year /Year)
                                                                                                        Age Removal[Cohort,Retrofitting Status] = SUM(
                                                                                                        Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])* Average Age[ Cohort, Retrofitting Status]
                                                                                                        Description: Total age lost as houses are destroyed, scrapped, etc.
                                                                                                        Present In 1 View: Used By
                                                                                                        • Total Age "Total" age for each cohort of housing.
                                                                                                        Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                        .housingagingchain v8 #10
                                                                                                        F,A
                                                                                                        Aging (House * Year / Year)
                                                                                                        Aging[Cohort,Retrofitting Status] =
                                                                                                        Aging per Year*SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                        Description: Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
                                                                                                        Present In 1 View: Used By
                                                                                                        • Total Age "Total" age for each cohort of housing.
                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                        .housingagingchain v8 #9
                                                                                                        C
                                                                                                        Aging per Year (Year / Year)
                                                                                                        = 1
                                                                                                        Description: Number of years a house ages per year (which must be one), used to ensure dimensional consistency and make the model clearer
                                                                                                        Present In 1 View:
                                                                                                        Used By
                                                                                                        • Aging Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                        .housingagingchain v8 #26
                                                                                                        A
                                                                                                        Average Age (Year)
                                                                                                        Average Age[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                        Total Age[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                        Description: The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                        Present In 1 View: Used By
                                                                                                        • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                        • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                        Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                        .housingagingchain v8 #66
                                                                                                        C
                                                                                                        Cohort Duration (Year )
                                                                                                        = 10
                                                                                                        Description: The width (duration) of each cohort.
                                                                                                        Present In 2 Views:
                                                                                                        Used By
                                                                                                        • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                        • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                        HeatPumpModel_v31 #89
                                                                                                        F,A
                                                                                                        Demolitions (House / Year)
                                                                                                        Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                        Demolition Hazard Rate* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]*(1- No Turnover Switch)
                                                                                                        Description: Homes that are destroyed every year.
                                                                                                        Present In 3 Views: Used By
                                                                                                        • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                        • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                        • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                        • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                        Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                        HeatPumpModel_v31 #160
                                                                                                        F,A
                                                                                                        Houses Switching Sources (House / Year)
                                                                                                        Houses Switching Sources[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                        Fraction of Houses Switching[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* System Switching SWITCH
                                                                                                        Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Fraction of Houses Switching[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Fossil Fuel Heating, Retrofitting Status]* System Switching SWITCH
                                                                                                        Description: The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                        Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                        HeatPumpModel_v31 #174
                                                                                                        L
                                                                                                        Housing (House)
                                                                                                        Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                        Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                        Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                        Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                        Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                                                                        HeatPumpModel_v31 #162
                                                                                                        A
                                                                                                        Housing by Cohort and Retrofitting Status (House)
                                                                                                        Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] = SUM(
                                                                                                        Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                        Description: Amount of housing by retrofit status and cohort.
                                                                                                        Present In 3 Views: Used By
                                                                                                        • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                        • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                        • Housing by Retrofitting Status Amount of housing by retrofitting status, across all cohorts and systems.
                                                                                                        • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                        .housingagingchain v8 #184
                                                                                                        LI,A
                                                                                                        Initial Age (House * Year)
                                                                                                        Initial Age[Cohort,Retrofitting Status] = INITIAL(0)
                                                                                                        Initial Age[Preexisting Cohorts,Retrofitting Status] = (
                                                                                                        Cohort Duration*(ELMCOUNT( Preexisting Cohorts)- Preexisting Cohorts+1))* Housing by Cohort and Retrofitting Status[ Preexisting Cohorts, Retrofitting Status]
                                                                                                        Description: The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                        Present In 1 View: Used By
                                                                                                        • Total Age "Total" age for each cohort of housing.
                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                        HeatPumpModel_v31 #229
                                                                                                        A
                                                                                                        Net Age Shift by System (Year * House / Year)
                                                                                                        Net Age Shift by System[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                        Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, Average Age[ Cohort,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], Average Age[ Cohort,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                        Description: The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                        Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                        HeatPumpModel_v31 #230
                                                                                                        F,A
                                                                                                        Net Age Shift from Retrofitting Status Shifting (House * Year / Year)
                                                                                                        Net Age Shift from Retrofitting Status Shifting[Cohort] = SUM(
                                                                                                        Net Age Shift by System[ Cohort, Heating and Cooling System!])
                                                                                                        Description: Shift in age within each cohort due to houses becoming open or closed to retrofitting.
                                                                                                        Present In 1 View: Used By
                                                                                                        • Total Age "Total" age for each cohort of housing.
                                                                                                        Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                        HeatPumpModel_v31 #233
                                                                                                        F,A
                                                                                                        Net Change in Homes Retrofitting (Houses / Year)
                                                                                                        Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] = (
                                                                                                        Indicated Homes Retrofitting[ Cohort, Heating and Cooling System]- Housing[ Cohort, Heating and Cooling System,Open to Retrofitting])/ Time to Decide to Retrofit
                                                                                                        Description: Homes that are in the process of deciding to retrofit.
                                                                                                        Present In 3 Views: Used By
                                                                                                        • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                        • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                        • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                        • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                        Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [2,2]
                                                                                                        .housingagingchain v8 #309
                                                                                                        L
                                                                                                        Total Age (House * Year)
                                                                                                        Total Age[Cohort,Not Open to Retrofitting] = (
                                                                                                        Aging[ Cohort,Not Open to Retrofitting]- Net Age Shift from Retrofitting Status Shifting[ Cohort])- Age Removal[ Cohort,Not Open to Retrofitting] dt + Initial Age[ Cohort,Not Open to Retrofitting]
                                                                                                        Total Age[Cohort,Open to Retrofitting] = ( Net Age Shift from Retrofitting Status Shifting[ Cohort]+ Aging[ Cohort,Open to Retrofitting])- Age Removal[ Cohort,Open to Retrofitting] dt + Initial Age[ Cohort,Open to Retrofitting]
                                                                                                        Description: "Total" age for each cohort of housing.
                                                                                                        Present In 2 Views: Used By
                                                                                                        • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                        • Average Age in All Housing Average age of houses, regardless of cohort
                                                                                                        Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                        (View) Area (18 Variables)
                                                                                                        Top (View) Area (18 Variables)
                                                                                                        Group
                                                                                                        Type
                                                                                                        Variable Name And Description
                                                                                                        .housingagingchain v8 #21
                                                                                                        L
                                                                                                        Area (sf)
                                                                                                        Area[Cohort,Not Open to Retrofitting] = (
                                                                                                        Area of New Homes[ Cohort]- Net Area Shift due to Retrofit Status Switching[ Cohort])- Area Removal[ Cohort,Not Open to Retrofitting] dt + Initial Area[ Cohort]*(1.0- Fraction Retrofitting by Cohort[ Cohort])
                                                                                                        Area[Preexisting Cohorts,Not Open to Retrofitting] = (- Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts])- Area Removal[ Preexisting Cohorts,Not Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]*(1.0- Fraction Retrofitting by Cohort[ Preexisting Cohorts])
                                                                                                        Area[Cohort,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Cohort]- Area Removal[ Cohort,Open to Retrofitting] dt + Initial Area[ Cohort]* Fraction Retrofitting by Cohort[ Cohort]
                                                                                                        Area[Preexisting Cohorts,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts]- Area Removal[ Preexisting Cohorts,Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]* Fraction Retrofitting by Cohort[ Preexisting Cohorts]
                                                                                                        Description: "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                        Present In 2 Views: Used By
                                                                                                        • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                        • Total Area The total area across all housing.
                                                                                                        Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                        .housingagingchain v8 #19
                                                                                                        F,A
                                                                                                        Area of New Homes (sf / Year)
                                                                                                        Area of New Homes[Cohort] =
                                                                                                        Average Area of Housing Starts*SUM( Housing Starts[ Cohort, Heating and Cooling System!])
                                                                                                        Description: The total Area added by the construction of new homes, by cohort.
                                                                                                        Present In 1 View: Used By
                                                                                                        • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                        .housingagingchain v8 #20
                                                                                                        F,A
                                                                                                        Area Removal (sf /Year)
                                                                                                        Area Removal[Cohort,Retrofitting Status] =
                                                                                                        Average Area[ Cohort, Retrofitting Status]*SUM( Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                        Description: Total area lost as houses are destroyed, scrapped, etc.
                                                                                                        Present In 1 View: Used By
                                                                                                        • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                        Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                        .housingagingchain v8 #25
                                                                                                        A
                                                                                                        Average Age in All Housing (Year)
                                                                                                        = ZIDZ(SUM(
                                                                                                        Total Age[ Cohort!, Retrofitting Status!]), Total Housing Stock)
                                                                                                        Description: Average age of houses, regardless of cohort
                                                                                                        Present In 2 Views: Used By
                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #29
                                                                                                          A
                                                                                                          Average Area (sf / House)
                                                                                                          Average Area[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                          Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                          Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                          Present In 7 Views: Used By
                                                                                                          • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                          • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                          • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                          • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                          • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                          • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                          • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                          • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                          • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                          • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                          • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                          • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                          • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                          • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                          • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                          • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                          Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                          .housingagingchain v8 #27
                                                                                                          A
                                                                                                          Average Area in All Housing (sf/ House)
                                                                                                          = ZIDZ(
                                                                                                          Total Area, Total Housing Stock)
                                                                                                          Description: The average are of all houses, regardless of what group they're in.
                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #28
                                                                                                          A
                                                                                                          Average Area of Housing Starts (sf / House)
                                                                                                          =
                                                                                                          Increase in Area per Year*( Time- INITIAL TIME)+ Initial Average Area of Housing Starts
                                                                                                          Description: The average area of housing starts.
                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #89
                                                                                                          F,A
                                                                                                          Demolitions (House / Year)
                                                                                                          Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                          Demolition Hazard Rate* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]*(1- No Turnover Switch)
                                                                                                          Description: Homes that are destroyed every year.
                                                                                                          Present In 3 Views: Used By
                                                                                                          • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                          • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                          • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                          • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                          Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                          HeatPumpModel_v31 #132
                                                                                                          LI,A
                                                                                                          Fraction Retrofitting by Cohort (dmnl)
                                                                                                          Fraction Retrofitting by Cohort[Cohort] = ZIDZ(SUM(
                                                                                                          Housing[ Cohort, Heating and Cooling System!,Open to Retrofitting]),SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!]))
                                                                                                          Description: Fraction that are retrofitting, only by cohort.
                                                                                                          Present In 2 Views: Used By
                                                                                                          • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #162
                                                                                                          A
                                                                                                          Housing by Cohort and Retrofitting Status (House)
                                                                                                          Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] = SUM(
                                                                                                          Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                          Description: Amount of housing by retrofit status and cohort.
                                                                                                          Present In 3 Views: Used By
                                                                                                          • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                          • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                          • Housing by Retrofitting Status Amount of housing by retrofitting status, across all cohorts and systems.
                                                                                                          • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #173
                                                                                                          F,A
                                                                                                          Housing Starts (Houses / Year)
                                                                                                          Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                          Housing Fractional Growth Rate*SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])* Active Cohort Indicator[ Cohort]*(1- No Turnover Switch)
                                                                                                          Description: Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                          Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [2,2] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #180
                                                                                                          C
                                                                                                          Increase in Area per Year (sf / Year / House )
                                                                                                          = 10.76
                                                                                                          Description: The exogenous increase in area per year, found by regressing area on year house was built in RECS 2020 data for MA SFG.
                                                                                                          Present In 1 View:
                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #185
                                                                                                          LI,C
                                                                                                          Initial Area (sf)
                                                                                                          Initial Area[Cohort] = 10
                                                                                                          Description: Total initial area across all houses, by cohort (assuming that average area is the same across systems).
                                                                                                          Present In 1 View:
                                                                                                          Used By
                                                                                                          • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #186
                                                                                                          C
                                                                                                          Initial Average Area of Housing Starts (sf / House )
                                                                                                          = 2347
                                                                                                          Description: Initial average area of housing starts. Taken from average area of MA SFH homes built from 2015 to 2020, from EIA RECS data.
                                                                                                          Present In 1 View:
                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          .housingagingchain v8 #231
                                                                                                          A
                                                                                                          Net Area Shift by System (sf / Year)
                                                                                                          Net Area Shift by System[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                          Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, Average Area[ Cohort,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], Average Area[ Cohort,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                          Description: The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                          Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #232
                                                                                                          F,A
                                                                                                          Net Area Shift due to Retrofit Status Switching (sf / Year)
                                                                                                          Net Area Shift due to Retrofit Status Switching[Cohort] = SUM(
                                                                                                          Net Area Shift by System[ Cohort, Heating and Cooling System!])
                                                                                                          Description: Shift in area between energy sources due to houses switching sources.
                                                                                                          Present In 1 View: Used By
                                                                                                          • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                          Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                          HeatPumpModel_v31 #233
                                                                                                          F,A
                                                                                                          Net Change in Homes Retrofitting (Houses / Year)
                                                                                                          Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] = (
                                                                                                          Indicated Homes Retrofitting[ Cohort, Heating and Cooling System]- Housing[ Cohort, Heating and Cooling System,Open to Retrofitting])/ Time to Decide to Retrofit
                                                                                                          Description: Homes that are in the process of deciding to retrofit.
                                                                                                          Present In 3 Views: Used By
                                                                                                          • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                          • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                          • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                          • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                          Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [2,2]
                                                                                                          .Control #196
                                                                                                          C
                                                                                                          INITIAL TIME (Year)
                                                                                                          = 2020
                                                                                                          Description: The initial time for the simulation.
                                                                                                          Present In 3 Views:
                                                                                                          Used By
                                                                                                          • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                          • Average Area of Housing Starts The average area of housing starts.
                                                                                                          • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                          • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          (View) Average Attributes (64 Variables)
                                                                                                          Top (View) Average Attributes (64 Variables)
                                                                                                          Group
                                                                                                          Type
                                                                                                          Variable Name And Description
                                                                                                          .housingagingchain v4 testing #7
                                                                                                          A
                                                                                                          Affinity of Retrofitting (dmnl)
                                                                                                          Affinity of Retrofitting[Cohort,Heating and Cooling System] = exp(-
                                                                                                          Sensitivity of Retrofits to Cost* Perceived Cost of Retrofitting[ Cohort, Heating and Cooling System]/ Reference Retrofit Cost)
                                                                                                          Description: Affinity of retrofitting, where utility value is equal to its NPV.
                                                                                                          Present In 2 Views: Used By
                                                                                                          • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                          .housingagingchain v8 #21
                                                                                                          L
                                                                                                          Area (sf)
                                                                                                          Area[Cohort,Not Open to Retrofitting] = (
                                                                                                          Area of New Homes[ Cohort]- Net Area Shift due to Retrofit Status Switching[ Cohort])- Area Removal[ Cohort,Not Open to Retrofitting] dt + Initial Area[ Cohort]*(1.0- Fraction Retrofitting by Cohort[ Cohort])
                                                                                                          Area[Preexisting Cohorts,Not Open to Retrofitting] = (- Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts])- Area Removal[ Preexisting Cohorts,Not Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]*(1.0- Fraction Retrofitting by Cohort[ Preexisting Cohorts])
                                                                                                          Area[Cohort,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Cohort]- Area Removal[ Cohort,Open to Retrofitting] dt + Initial Area[ Cohort]* Fraction Retrofitting by Cohort[ Cohort]
                                                                                                          Area[Preexisting Cohorts,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts]- Area Removal[ Preexisting Cohorts,Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]* Fraction Retrofitting by Cohort[ Preexisting Cohorts]
                                                                                                          Description: "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                          Present In 2 Views: Used By
                                                                                                          • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                          • Total Area The total area across all housing.
                                                                                                          Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                          .housingagingchain v8 #25
                                                                                                          A
                                                                                                          Average Age in All Housing (Year)
                                                                                                          = ZIDZ(SUM(
                                                                                                          Total Age[ Cohort!, Retrofitting Status!]), Total Housing Stock)
                                                                                                          Description: Average age of houses, regardless of cohort
                                                                                                          Present In 2 Views: Used By
                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                            HeatPumpModel_v31 #29
                                                                                                            A
                                                                                                            Average Area (sf / House)
                                                                                                            Average Area[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                            Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                            Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                            Present In 7 Views: Used By
                                                                                                            • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                            • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                            • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                            • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                            • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                            • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                            • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                            • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                            • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                            • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                            • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                            • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                            • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                            • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                            • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                            • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                            Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                            .housingagingchain v8 #27
                                                                                                            A
                                                                                                            Average Area in All Housing (sf/ House)
                                                                                                            = ZIDZ(
                                                                                                            Total Area, Total Housing Stock)
                                                                                                            Description: The average are of all houses, regardless of what group they're in.
                                                                                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                            HeatPumpModel_v31 #31
                                                                                                            A
                                                                                                            Average Cooling Cost (Dollar / (Year * House))
                                                                                                            Average Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                            Expected Cooling Energy Price* Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                            Description: The average costs for keeping a home cool, by grouping.
                                                                                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                            HeatPumpModel_v31 #30
                                                                                                            A
                                                                                                            Average Cooling Cost Across All Homes (Dollar / House/ Year)
                                                                                                            =
                                                                                                            Total Cooling Cost/SUM( Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                            Description: The average cost to cool a home, for all cohorts and systems.
                                                                                                            Present In 1 View: Used By
                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                              HeatPumpModel_v31 #33
                                                                                                              C
                                                                                                              Average Cooling Energy Use (kBTU / (Year * House))
                                                                                                              Average Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                              U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                              Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                              Description: The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                              Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                              HeatPumpModel_v31 #32
                                                                                                              A
                                                                                                              Average Cooling Energy Use Across All Homes (kBTU / Year / House)
                                                                                                              = ZIDZ(
                                                                                                              Total Cooling Energy Use, Total Housing Stock)
                                                                                                              Description: The amount of energy an average home spends on cooling, regardless of cohort, retrofit status, etc.
                                                                                                              Present In 1 View: Used By
                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                HeatPumpModel_v31 #39
                                                                                                                A
                                                                                                                Average Emissions (tCO2 / House / Year)
                                                                                                                = ZIDZ(
                                                                                                                Emissions, Total Housing Stock)
                                                                                                                Description: The average CO2 emissions for a household, not disaggregated into any grouping.
                                                                                                                Present In 1 View: Used By
                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                  HeatPumpModel_v31 #35
                                                                                                                  A
                                                                                                                  Average Emissions by Grouping (tCO2 / (Year * House))
                                                                                                                  Average Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                  Average Emissions from Cooling by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Emissions from Heating by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                  Description: The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                  Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                  HeatPumpModel_v31 #36
                                                                                                                  A
                                                                                                                  Average Emissions by Heating and Cooling System (tCO2 / Year / House)
                                                                                                                  Average Emissions by Heating and Cooling System[Heating and Cooling System] = ZIDZ(
                                                                                                                  Emissions by Heating and Cooling System[ Heating and Cooling System], Housing by Heating and Cooling System[ Heating and Cooling System])
                                                                                                                  Description: The average CO2 emissions for each house, by heating and cooling system.
                                                                                                                  Present In 2 Views: Used By
                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                    HeatPumpModel_v31 #45
                                                                                                                    A
                                                                                                                    Average Energy Use (kBTU / (Year * House))
                                                                                                                    Average Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                    Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                    Description: Average energy use to both heat and cool a home.
                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                    HeatPumpModel_v31 #43
                                                                                                                    A
                                                                                                                    Average Energy Use by Heating and Cooling System (kBTU / (House * Year))
                                                                                                                    Average Energy Use by Heating and Cooling System[Heating and Cooling System] = ZIDZ(SUM(
                                                                                                                    Energy Use by Grouping[ Cohort!, Heating and Cooling System, Retrofitting Status!]),SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!]))
                                                                                                                    Description: The average energy use for each home by heating and cooling system.
                                                                                                                    Present In 1 View: Used By
                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                      HeatPumpModel_v31 #44
                                                                                                                      A
                                                                                                                      Average Energy Use in All Housing (kBTU / Year / House)
                                                                                                                      =
                                                                                                                      Total Energy Use/ Total Housing Stock
                                                                                                                      Description: The average energy use across all stocks.
                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                      HeatPumpModel_v31 #46
                                                                                                                      A
                                                                                                                      Average EUI by Grouping (kBTU / (sf * Year))
                                                                                                                      Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = XIDZ(
                                                                                                                      Average Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status], Average Area[ Cohort, Retrofitting Status], NAREPLACEMENT)
                                                                                                                      Description: The average energy use intensity by grouping
                                                                                                                      Present In 1 View: Used By
                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                        HeatPumpModel_v31 #47
                                                                                                                        A
                                                                                                                        Average EUI in All Housing (kBTU / (sf * Year))
                                                                                                                        =
                                                                                                                        Average Energy Use in All Housing/ Average Area in All Housing
                                                                                                                        Description: The average energy use intensity across all housing.
                                                                                                                        Present In 1 View: Used By
                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                          .housingagingchain v5 testing #49
                                                                                                                          A
                                                                                                                          Average Heating Cost (Dollar / (Year * House))
                                                                                                                          Average Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                          Expected Heating Energy Price[ Heating and Cooling System]* Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                          Description: The costs per year to heat one house.
                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                          HeatPumpModel_v31 #48
                                                                                                                          A
                                                                                                                          Average Heating Cost Across All Homes (Dollar / Year / House)
                                                                                                                          = ZIDZ(
                                                                                                                          Total Heating Cost,SUM( Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!]))
                                                                                                                          Description: The average amount a home spends on heating, regardless of cohort or heating and cooling system.
                                                                                                                          Present In 1 View: Used By
                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                            HeatPumpModel_v31 #51
                                                                                                                            A
                                                                                                                            Average Heating Energy Use (kBTU / (Year * House))
                                                                                                                            Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                            U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                            Description: The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                            Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                            HeatPumpModel_v31 #50
                                                                                                                            A
                                                                                                                            Average Heating Energy Use Across All Homes (kBTU / (Year * House))
                                                                                                                            = ZIDZ(
                                                                                                                            Total Heating Energy Use, Total Housing Stock)
                                                                                                                            Description: The average heating energy use per home, regardless of cohort, system,etc.
                                                                                                                            Present In 1 View: Used By
                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                              HeatPumpModel_v31 #53
                                                                                                                              A
                                                                                                                              Average Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                              = SUM(
                                                                                                                              Indicated Homes Retrofitting[ Cohort!, Heating and Cooling System!])/ Total Housing Stock
                                                                                                                              Description: The average fraction of homes that will retrofit retrofitting after decision delayacross all housing.
                                                                                                                              Present In 2 Views: Used By
                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                HeatPumpModel_v31 #58
                                                                                                                                A
                                                                                                                                Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))
                                                                                                                                Average U Value by Heating and Cooling System[Heating and Cooling System] = ZIDZ(
                                                                                                                                Total U Value by Heating and Cooling System[ Heating and Cooling System], Housing by Heating and Cooling System[ Heating and Cooling System])
                                                                                                                                Description: The U value of the average house using each heating and cooling system.
                                                                                                                                Present In 1 View: Used By
                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                  .housingagingchain v4 testing #59
                                                                                                                                  A
                                                                                                                                  Average U Value in All Housing (kBTU / (sf * F * Year))
                                                                                                                                  = ZIDZ(
                                                                                                                                  Total U Value Across All Groupings, Total Housing Stock)
                                                                                                                                  Description: The average U Value over the entire housing stock, not disaggregated by any groupings.
                                                                                                                                  Present In 1 View: Used By
                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                    HeatPumpModel_v31 #60
                                                                                                                                    A
                                                                                                                                    Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))
                                                                                                                                    Average U Value of Houses Switching Into Sources[Heating and Cooling System] = XIDZ(
                                                                                                                                    U Value Increase from Source Switching[ Heating and Cooling System], Houses Switching Into Sources[ Heating and Cooling System], NAREPLACEMENT)
                                                                                                                                    Description: The average U value of houses switching into each source, for each source.
                                                                                                                                    Present In 1 View: Used By
                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                      HeatPumpModel_v31 #98
                                                                                                                                      F,A
                                                                                                                                      Emissions (tCO2 / Year)
                                                                                                                                      = SUM(
                                                                                                                                      Emissions by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                      Description: The total amount of emissions across all housing groups.
                                                                                                                                      Present In 2 Views: Used By
                                                                                                                                      • Average Emissions The average CO2 emissions for a household, not disaggregated into any grouping.
                                                                                                                                      • Cumulative Emissions The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                      HeatPumpModel_v31 #96
                                                                                                                                      A
                                                                                                                                      Emissions by Grouping (tCO2 / Year)
                                                                                                                                      Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                      Housing[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Emissions by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                      Description: The total emissions for the most disaggregated grouping in the model.
                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                      HeatPumpModel_v31 #97
                                                                                                                                      A
                                                                                                                                      Emissions by Heating and Cooling System (tCO2 / Year)
                                                                                                                                      Emissions by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                                                                      Emissions by Grouping[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                      Description: The total amount of emissions for houses by Heating and Cooling System.
                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                      HeatPumpModel_v31 #107
                                                                                                                                      A
                                                                                                                                      Energy Use by Gas Houses (kBTU/ Year)
                                                                                                                                      = SUM(
                                                                                                                                      Energy Use by Grouping[ Cohort!,Gas and Central AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Gas and Window AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Gas and No AC, Retrofitting Status!])
                                                                                                                                      Description: The total amount of energy for heating and cooling used by homes which primarily use gas to heat their homes.
                                                                                                                                      Present In 1 View: Used By
                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                        HeatPumpModel_v31 #108
                                                                                                                                        A
                                                                                                                                        Energy Use by Grouping (kBTU / Year)
                                                                                                                                        Energy Use by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                        Average Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                        Description: The total amount of energy used for heating and cooling in each group.
                                                                                                                                        Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                        HeatPumpModel_v31 #109
                                                                                                                                        A
                                                                                                                                        Energy Use by Heat Pump Houses (kBTU / Year)
                                                                                                                                        = SUM(
                                                                                                                                        Energy Use by Grouping[ Cohort!,Heat Pump Only, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Heat Pump and Gas, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Heat Pump and Oil, Retrofitting Status!])
                                                                                                                                        Description: The amount of energy used for heating and cooling by homes which primarily use heat pumps to heat their home.
                                                                                                                                        Present In 1 View: Used By
                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                          HeatPumpModel_v31 #110
                                                                                                                                          A
                                                                                                                                          Energy Use by Oil Houses (kBTU / Year)
                                                                                                                                          = SUM(
                                                                                                                                          Energy Use by Grouping[ Cohort!,Oil and Central AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Oil and Window AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Oil and No AC, Retrofitting Status!])
                                                                                                                                          Description: The total amount of energy for heating and cooling used by homes primarily using oil to heat their home.
                                                                                                                                          Present In 1 View: Used By
                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                            HeatPumpModel_v31 #129
                                                                                                                                            A
                                                                                                                                            Fraction of Houses in Each Heating and Cooling System (dmnl)
                                                                                                                                            Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] = XIDZ(
                                                                                                                                            Housing by Heating and Cooling System[ Heating and Cooling System], Total Housing Stock, NAREPLACEMENT)
                                                                                                                                            Description: The fraction of houses using each heating and cooling system
                                                                                                                                            Present In 1 View: Used By
                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                              HeatPumpModel_v31 #131
                                                                                                                                              A
                                                                                                                                              Fraction of Housing by Heating and Cooling System (dmnl)
                                                                                                                                              Fraction of Housing by Heating and Cooling System[Heating and Cooling System] =
                                                                                                                                              Housing by Heating and Cooling System[ Heating and Cooling System]/ Total Housing Stock
                                                                                                                                              Description: The fraction of the total housing stock using each heating and cooling system.
                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                HeatPumpModel_v31 #134
                                                                                                                                                A
                                                                                                                                                Fraction Retrofitting (dmnl)
                                                                                                                                                =
                                                                                                                                                Housing by Retrofitting Status[Open to Retrofitting]/( Housing by Retrofitting Status[Not Open to Retrofitting]+ Housing by Retrofitting Status[Open to Retrofitting])
                                                                                                                                                Description: Proportion of housing that is open to retrofitting, across all cohorts and systems.
                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                  HeatPumpModel_v31 #132
                                                                                                                                                  LI,A
                                                                                                                                                  Fraction Retrofitting by Cohort (dmnl)
                                                                                                                                                  Fraction Retrofitting by Cohort[Cohort] = ZIDZ(SUM(
                                                                                                                                                  Housing[ Cohort, Heating and Cooling System!,Open to Retrofitting]),SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!]))
                                                                                                                                                  Description: Fraction that are retrofitting, only by cohort.
                                                                                                                                                  Present In 2 Views: Used By
                                                                                                                                                  • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                  HeatPumpModel_v31 #133
                                                                                                                                                  A
                                                                                                                                                  Fraction Retrofitting by System and Cohort (dmnl)
                                                                                                                                                  Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] = ZIDZ(
                                                                                                                                                  Housing[ Cohort, Heating and Cooling System,Open to Retrofitting],SUM( Housing[ Cohort, Heating and Cooling System, Retrofitting Status!]))
                                                                                                                                                  Description: The fraction of houses that are retrofitting, by heating/cooling system and cohort.
                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                    HeatPumpModel_v31 #159
                                                                                                                                                    A
                                                                                                                                                    Houses Switching Into Sources (Houses / Year)
                                                                                                                                                    Houses Switching Into Sources[Heating and Cooling System] = SUM(
                                                                                                                                                    Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!, Heating and Cooling System])
                                                                                                                                                    Description: The number of houses switching into each Heating and Cooling System, cohort, and retrofitting group due to system switching.
                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                    HeatPumpModel_v31 #160
                                                                                                                                                    F,A
                                                                                                                                                    Houses Switching Sources (House / Year)
                                                                                                                                                    Houses Switching Sources[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                    Fraction of Houses Switching[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                    Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Fraction of Houses Switching[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Fossil Fuel Heating, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                    Description: The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                    Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                    HeatPumpModel_v31 #174
                                                                                                                                                    L
                                                                                                                                                    Housing (House)
                                                                                                                                                    Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                    Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                    Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                    Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                    Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                                                                                                                    HeatPumpModel_v31 #163
                                                                                                                                                    A
                                                                                                                                                    Housing by Cohort (House)
                                                                                                                                                    Housing by Cohort[Cohort] = SUM(
                                                                                                                                                    Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                    Description: Number of houses per cohort
                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                      HeatPumpModel_v31 #161
                                                                                                                                                      A
                                                                                                                                                      Housing by Cohort and Heating and Cooling System (Houses)
                                                                                                                                                      Housing by Cohort and Heating and Cooling System[Cohort,Heating and Cooling System] = SUM(
                                                                                                                                                      Housing[ Cohort, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                      Description: Housing by heating and cooling system and cohort, irrespective of retrofit status.
                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                      HeatPumpModel_v31 #162
                                                                                                                                                      A
                                                                                                                                                      Housing by Cohort and Retrofitting Status (House)
                                                                                                                                                      Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] = SUM(
                                                                                                                                                      Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                                                                      Description: Amount of housing by retrofit status and cohort.
                                                                                                                                                      Present In 3 Views: Used By
                                                                                                                                                      • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                      • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                      • Housing by Retrofitting Status Amount of housing by retrofitting status, across all cohorts and systems.
                                                                                                                                                      • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                      HeatPumpModel_v31 #164
                                                                                                                                                      A
                                                                                                                                                      Housing by Heating and Cooling System (House)
                                                                                                                                                      Housing by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                                                                                      Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                      Description: Number of houses by energy source across all cohorts.
                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                      HeatPumpModel_v31 #165
                                                                                                                                                      A
                                                                                                                                                      Housing by Retrofitting Status (House)
                                                                                                                                                      Housing by Retrofitting Status[Retrofitting Status] = SUM(
                                                                                                                                                      Housing by Cohort and Retrofitting Status[ Cohort!, Retrofitting Status])
                                                                                                                                                      Description: Amount of housing by retrofitting status, across all cohorts and systems.
                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                      • Fraction Retrofitting Proportion of housing that is open to retrofitting, across all cohorts and systems.
                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                      HeatPumpModel_v31 #173
                                                                                                                                                      F,A
                                                                                                                                                      Housing Starts (Houses / Year)
                                                                                                                                                      Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                                                                      Housing Fractional Growth Rate*SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])* Active Cohort Indicator[ Cohort]*(1- No Turnover Switch)
                                                                                                                                                      Description: Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                      Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [2,2] (-) 0  [0,0]
                                                                                                                                                      HeatPumpModel_v31 #183
                                                                                                                                                      A
                                                                                                                                                      Indicated Homes Retrofitting (House)
                                                                                                                                                      Indicated Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                      Indicated Fraction of Homes Retrofitting[ Cohort, Heating and Cooling System]* Housing by Cohort and Heating and Cooling System[ Cohort, Heating and Cooling System]
                                                                                                                                                      Description: Number of homes that, once delays are taken into account, will be open to retrofitting.
                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                      HeatPumpModel_v31 #252
                                                                                                                                                      A
                                                                                                                                                      Optimal U Across All Housing (kBTU / (sf * F * Year))
                                                                                                                                                      = SUM(
                                                                                                                                                      Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort!, Heating and Cooling System!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!]/ Total Housing Stock)
                                                                                                                                                      Description: The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                        .housingagingchain v4 testing #254
                                                                                                                                                        A
                                                                                                                                                        Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                        Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                        Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                        Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                        Present In 8 Views: Used By
                                                                                                                                                        • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                        • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                        • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                        • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                        • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                        • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                        • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                        • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                        • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                        .housingagingchain v8 #309
                                                                                                                                                        L
                                                                                                                                                        Total Age (House * Year)
                                                                                                                                                        Total Age[Cohort,Not Open to Retrofitting] = (
                                                                                                                                                        Aging[ Cohort,Not Open to Retrofitting]- Net Age Shift from Retrofitting Status Shifting[ Cohort])- Age Removal[ Cohort,Not Open to Retrofitting] dt + Initial Age[ Cohort,Not Open to Retrofitting]
                                                                                                                                                        Total Age[Cohort,Open to Retrofitting] = ( Net Age Shift from Retrofitting Status Shifting[ Cohort]+ Aging[ Cohort,Open to Retrofitting])- Age Removal[ Cohort,Open to Retrofitting] dt + Initial Age[ Cohort,Open to Retrofitting]
                                                                                                                                                        Description: "Total" age for each cohort of housing.
                                                                                                                                                        Present In 2 Views: Used By
                                                                                                                                                        • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                        • Average Age in All Housing Average age of houses, regardless of cohort
                                                                                                                                                        Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                        HeatPumpModel_v31 #310
                                                                                                                                                        A
                                                                                                                                                        Total Area (sf)
                                                                                                                                                        = SUM(
                                                                                                                                                        Area[ Cohort!, Retrofitting Status!])
                                                                                                                                                        Description: The total area across all housing.
                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                        HeatPumpModel_v31 #311
                                                                                                                                                        A
                                                                                                                                                        Total Cooling Cost (Dollar / Year)
                                                                                                                                                        = SUM(
                                                                                                                                                        Average Cooling Cost[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                        Description: The total amount of money spent on cooling homes, per year.
                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                        HeatPumpModel_v31 #312
                                                                                                                                                        A
                                                                                                                                                        Total Cooling Energy Use (kBTU/ Year)
                                                                                                                                                        = SUM(
                                                                                                                                                        Average Cooling Energy Use[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                        Description: The total amount of energy spent on cooling homes.
                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                        HeatPumpModel_v31 #315
                                                                                                                                                        A
                                                                                                                                                        Total Energy Use (kBTU / Year)
                                                                                                                                                        = SUM(
                                                                                                                                                        Energy Use by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                        Description: The total energy use for all homes in the model.
                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                        HeatPumpModel_v31 #317
                                                                                                                                                        A
                                                                                                                                                        Total Heating Cost (Dollar / Year)
                                                                                                                                                        = SUM(
                                                                                                                                                        Average Heating Cost[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                        Description: The total amount of money spent on heating homes.
                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                        HeatPumpModel_v31 #318
                                                                                                                                                        A
                                                                                                                                                        Total Heating Energy Use (kBTU/ Year)
                                                                                                                                                        = SUM(
                                                                                                                                                        Average Heating Energy Use[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                        Description: The total amount of energy spent on heating per year.
                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                        HeatPumpModel_v31 #319
                                                                                                                                                        A
                                                                                                                                                        Total Housing Starts (House/ Year)
                                                                                                                                                        = SUM(
                                                                                                                                                        Housing Starts[ Cohort!, Heating and Cooling System!])
                                                                                                                                                        Description: The total housing starts across all cohorts and sources.
                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                          .housingagingchain v4 testing #320
                                                                                                                                                          A
                                                                                                                                                          Total Housing Stock (House)
                                                                                                                                                          = SUM(
                                                                                                                                                          Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                          Description: Total number of houses across all cohorts, heating/cooling systems, and retrofitting status.
                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                          HeatPumpModel_v31 #327
                                                                                                                                                          L
                                                                                                                                                          Total U Value (House * kBTU / (Year * F * sf) )
                                                                                                                                                          Total U Value[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                          Increase in U Value from Housing Starts[ Cohort, Heating and Cooling System]- Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System])- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Not Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Not Open to Retrofitting])) dt + Initial U Value[ Cohort, Heating and Cooling System,Not Open to Retrofitting]
                                                                                                                                                          Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] = ((( Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System]- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Open to Retrofitting])))- Retrofitting[ Cohort, Heating and Cooling Systemdt + Initial U Value[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                          Description: Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                          HeatPumpModel_v31 #324
                                                                                                                                                          A
                                                                                                                                                          Total U Value Across All Groupings (House * kBTU / (sf * F * Year))
                                                                                                                                                          = SUM(
                                                                                                                                                          Total U Value by Cohort[ Cohort!])
                                                                                                                                                          Description: Total U value across all groupings of households.
                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                          HeatPumpModel_v31 #325
                                                                                                                                                          A
                                                                                                                                                          Total U Value by Cohort (House * kBTU / (sf * F * Year))
                                                                                                                                                          Total U Value by Cohort[Cohort] = SUM(
                                                                                                                                                          Total U Value[ Cohort, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                          Description: Total U Value within each cohort.
                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                          HeatPumpModel_v31 #326
                                                                                                                                                          A
                                                                                                                                                          Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))
                                                                                                                                                          Total U Value by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                                                                                          Total U Value[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                          Description: The total U value by heating and cooling system
                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                          HeatPumpModel_v31 #330
                                                                                                                                                          A
                                                                                                                                                          U Value Increase from Source Switching (kBTU*House/(Year*Year*sf*F))
                                                                                                                                                          U Value Increase from Source Switching[Heating and Cooling System] = SUM(
                                                                                                                                                          U Value Shift from Source Switching[ Cohort!, Heating and Cooling System!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                          Description: The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                          HeatPumpModel_v31 #335
                                                                                                                                                          F,A
                                                                                                                                                          U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                          U Value Shift from Source Switching[Cohort,Heat Pump Heating and Cooling,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                          Houses Switching Sources[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]
                                                                                                                                                          U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] = Houses Switching Sources[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Fossil Fuel Heating, Retrofitting Status]
                                                                                                                                                          Description: The shift in total U value coming from switching sources.
                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                          • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                          • U Value Increase from Source Switching The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                                                                                          Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                          (View) Average and Peak Load (17 Variables)
                                                                                                                                                          Top (View) Average and Peak Load (17 Variables)
                                                                                                                                                          Group
                                                                                                                                                          Type
                                                                                                                                                          Variable Name And Description
                                                                                                                                                          HeatPumpModel_v31 #15
                                                                                                                                                          A
                                                                                                                                                          Annual Load from Heat Pumps (kBTU / Year)
                                                                                                                                                          = SUM(
                                                                                                                                                          Energy Use by Grouping[ Cohort!, Heat Pump Heating and Cooling!, Retrofitting Status!])
                                                                                                                                                          Description: The load on the electric grid from servicing heating and cooling demand from heat pumps, across the whole year.
                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                          HeatPumpModel_v31 #29
                                                                                                                                                          A
                                                                                                                                                          Average Area (sf / House)
                                                                                                                                                          Average Area[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                                                                          Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                                                                          Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                          Present In 7 Views: Used By
                                                                                                                                                          • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                          • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                          • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                          • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                          • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                          • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                          • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                          • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                          • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                          • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                          • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                          • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                          • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                          • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                          • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                          • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                                                                          Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                          HeatPumpModel_v31 #34
                                                                                                                                                          A
                                                                                                                                                          Average Daily Load from Heat Pumps (kBTU / Day)
                                                                                                                                                          =
                                                                                                                                                          Annual Load from Heat Pumps/ Days per Year
                                                                                                                                                          Description: The average load on the electric grid from heat pumps, per day.
                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                            HeatPumpModel_v31 #61
                                                                                                                                                            C
                                                                                                                                                            CDD on Coldest Day (F )
                                                                                                                                                            = 17.1
                                                                                                                                                            Description: The total CDD from hottest day.Data from https://www.degreedays.net/ for KOWD, weather station nearest to centre of population for MA, Natick. Calculated by finding CDDs from the past three years (February 2021 - January 2024), finding the highest CDD in each year, and averaging them. Following industry standard, used 65°F as set point.
                                                                                                                                                            Present In 1 View:
                                                                                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                            HeatPumpModel_v31 #72
                                                                                                                                                            A
                                                                                                                                                            Cooling System Efficiency (dmnl)
                                                                                                                                                            Cooling System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                            Heat Pump Cooling COP TABLE( Time)
                                                                                                                                                            Cooling System Efficiency[Central AC Cooling] = 2.93
                                                                                                                                                            Cooling System Efficiency[Window AC Cooling] = 2.49* Effect of Air Leakage from Window AC on Efficiency
                                                                                                                                                            Cooling System Efficiency[No AC Cooling] = NAREPLACEMENT
                                                                                                                                                            Description: The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                            Present In 4 Views: Used By
                                                                                                                                                            • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                            • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                            • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                            • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                            • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                            HeatPumpModel_v31 #83
                                                                                                                                                            C
                                                                                                                                                            Days per Year (Day / Year )
                                                                                                                                                            = 365
                                                                                                                                                            Description: The number of days each year. Used to convert yearly measures to daily ones.
                                                                                                                                                            Present In 1 View:
                                                                                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                            HeatPumpModel_v31 #108
                                                                                                                                                            A
                                                                                                                                                            Energy Use by Grouping (kBTU / Year)
                                                                                                                                                            Energy Use by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                            Average Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                            Description: The total amount of energy used for heating and cooling in each group.
                                                                                                                                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                            HeatPumpModel_v31 #137
                                                                                                                                                            C
                                                                                                                                                            HDD on Coldest Day (F )
                                                                                                                                                            = 55.2333
                                                                                                                                                            Description: The total HDD from coldest day.Data from https://www.degreedays.net/ for KOWD, weather station nearest to centre of population for MA, Natick. Calculated by finding HDDs from the past three years (February 2021 - January 2024), finding the highest HDD in each year, and averaging them. Following industry standard, used set point of 65°F.
                                                                                                                                                            Present In 1 View:
                                                                                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                            HeatPumpModel_v31 #139
                                                                                                                                                            C
                                                                                                                                                            Heat Pump COP on Coldest Days (dmnl )
                                                                                                                                                            = 2.16438
                                                                                                                                                            Description: The heat pump COP on coolest day of the year.Taken from NYSERDA/MassCEC study on heat pump performance on 41 heat pumps: https://e4thefuture.org/wp-content/uploads/2022/06/Residential-ccASHP-Building-Electrification_060322.pdf (pg. 24). Regressed COP on temperature and its square. Using daily data on HDD (set point 65°F) for 2021-2023 from degreedays.net, calculated temperature of coldest day on average. Plugged that into regression model to find COP on coldest day.
                                                                                                                                                            Present In 1 View:
                                                                                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                            HeatPumpModel_v31 #174
                                                                                                                                                            L
                                                                                                                                                            Housing (House)
                                                                                                                                                            Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                            Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                            Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                            Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                            Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                                                                                                                            HeatPumpModel_v31 #208
                                                                                                                                                            C
                                                                                                                                                            kBTU per kWH (kBTU / kWH )
                                                                                                                                                            = 3.41214
                                                                                                                                                            Present In 1 View:
                                                                                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                            HeatPumpModel_v31 #257
                                                                                                                                                            A
                                                                                                                                                            Peak Cooling Load on Grid (kWH / Day)
                                                                                                                                                            = SUM(
                                                                                                                                                            Peak Load from Heat Pumps on Hottest Days per Group[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                            Description: Annual load from heat pumps providing heating on the coldest day, across all groups.
                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                              HeatPumpModel_v31 #258
                                                                                                                                                              A
                                                                                                                                                              Peak Heating Load on Grid (kWH / Day)
                                                                                                                                                              = SUM(
                                                                                                                                                              Peak Load from Heat Pumps on Coldest Days per Group[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                              Description: Annual load from heat pumps providing heating on the coldest days, across all groups.
                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                HeatPumpModel_v31 #259
                                                                                                                                                                C
                                                                                                                                                                Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)
                                                                                                                                                                Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Heat Pump Heating and Cooling,Retrofitting Status] =
                                                                                                                                                                Housing[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* HDD on Coldest Day/ Heat Pump COP on Coldest Days/( kBTU per kWH* Days per Year)
                                                                                                                                                                Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Fossil Fuel Heating,Retrofitting Status] = 0
                                                                                                                                                                Description: The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                HeatPumpModel_v31 #260
                                                                                                                                                                C
                                                                                                                                                                Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)
                                                                                                                                                                Peak Load from Heat Pumps on Hottest Days per Group[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                Housing[ Cohort, Heating and Cooling System, Retrofitting Status]* U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* CDD on Coldest Day/ Cooling System Efficiency[ Heating and Cooling System]/( kBTU per kWH* Days per Year)
                                                                                                                                                                Peak Load from Heat Pumps on Hottest Days per Group[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                Description: The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                HeatPumpModel_v31 #261
                                                                                                                                                                C
                                                                                                                                                                Peak Load from Non Heating or Cooling Sources (kWH / Day )
                                                                                                                                                                = 18344.8*1000*0.461799
                                                                                                                                                                Description: The peak load coming from non-heating sources, like other household uses, commercial uses, industrial uses, etc. Approximated as the average peak load in September, October, April, and May of 2022 and 2023 from New England ISO data, since there is little heating or cooling demand in those swing months. We multiply by 0.46 as Massachusetts has 46% of New England's population and we assume demand is proportional to population.Data source: https://www.iso-ne.com/isoexpress/web/reports/load-and-demand/-/tree/net-ener-peak-load
                                                                                                                                                                Present In 1 View:
                                                                                                                                                                Used By
                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                  HeatPumpModel_v31 #329
                                                                                                                                                                  A
                                                                                                                                                                  U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                  U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                  Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                  Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                  Present In 8 Views: Used By
                                                                                                                                                                  • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                  • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                  • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                  • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                  • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                  • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                  • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                  • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                  • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                  • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                  • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                  • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                  • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                  Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                  (View) Carbon Emissions (13 Variables)
                                                                                                                                                                  Top (View) Carbon Emissions (13 Variables)
                                                                                                                                                                  Group
                                                                                                                                                                  Type
                                                                                                                                                                  Variable Name And Description
                                                                                                                                                                  HeatPumpModel_v31 #33
                                                                                                                                                                  C
                                                                                                                                                                  Average Cooling Energy Use (kBTU / (Year * House))
                                                                                                                                                                  Average Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                  U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                  Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                  Description: The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                  Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                  HeatPumpModel_v31 #35
                                                                                                                                                                  A
                                                                                                                                                                  Average Emissions by Grouping (tCO2 / (Year * House))
                                                                                                                                                                  Average Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                  Average Emissions from Cooling by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Emissions from Heating by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                  Description: The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                  Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                  HeatPumpModel_v31 #36
                                                                                                                                                                  A
                                                                                                                                                                  Average Emissions by Heating and Cooling System (tCO2 / Year / House)
                                                                                                                                                                  Average Emissions by Heating and Cooling System[Heating and Cooling System] = ZIDZ(
                                                                                                                                                                  Emissions by Heating and Cooling System[ Heating and Cooling System], Housing by Heating and Cooling System[ Heating and Cooling System])
                                                                                                                                                                  Description: The average CO2 emissions for each house, by heating and cooling system.
                                                                                                                                                                  Present In 2 Views: Used By
                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                    HeatPumpModel_v31 #37
                                                                                                                                                                    A
                                                                                                                                                                    Average Emissions from Cooling by Grouping (tCO2 / (House * Year))
                                                                                                                                                                    Average Emissions from Cooling by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                    Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Cooling Emissions Factor/ Pounds per Ton
                                                                                                                                                                    Description: The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status.
                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                    • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                    HeatPumpModel_v31 #38
                                                                                                                                                                    A
                                                                                                                                                                    Average Emissions from Heating by Grouping (tCO2 / (House * Year))
                                                                                                                                                                    Average Emissions from Heating by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                    Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Heating Emissions Factors[ Heating and Cooling System]/ Pounds per Ton
                                                                                                                                                                    Description: Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc.
                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                    • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                    HeatPumpModel_v31 #51
                                                                                                                                                                    A
                                                                                                                                                                    Average Heating Energy Use (kBTU / (Year * House))
                                                                                                                                                                    Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                    U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                    Description: The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                    Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                    HeatPumpModel_v31 #68
                                                                                                                                                                    C
                                                                                                                                                                    Cooling Emissions Factor (lb CO2 / kBTU)
                                                                                                                                                                    = 614/3414.43
                                                                                                                                                                    Description: Amount of CO2 emitted from using one kBTU to cool a home. Emissions factor is common, and is for electricity.Taken from: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/download
                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                    HeatPumpModel_v31 #77
                                                                                                                                                                    L
                                                                                                                                                                    Cumulative Emissions (tCO2)
                                                                                                                                                                    =
                                                                                                                                                                    Emissions dt + 0.0
                                                                                                                                                                    Description: The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #98
                                                                                                                                                                      F,A
                                                                                                                                                                      Emissions (tCO2 / Year)
                                                                                                                                                                      = SUM(
                                                                                                                                                                      Emissions by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                      Description: The total amount of emissions across all housing groups.
                                                                                                                                                                      Present In 2 Views: Used By
                                                                                                                                                                      • Average Emissions The average CO2 emissions for a household, not disaggregated into any grouping.
                                                                                                                                                                      • Cumulative Emissions The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #96
                                                                                                                                                                      A
                                                                                                                                                                      Emissions by Grouping (tCO2 / Year)
                                                                                                                                                                      Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                      Housing[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Emissions by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                      Description: The total emissions for the most disaggregated grouping in the model.
                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #142
                                                                                                                                                                      C
                                                                                                                                                                      Heating Emissions Factors (lb CO2 / kBTU)
                                                                                                                                                                      Heating Emissions Factors[Heat Pump Heating and Cooling] = 684/3414.43
                                                                                                                                                                      Heating Emissions Factors[Gas Heating] = 116.65/1000
                                                                                                                                                                      Heating Emissions Factors[Oil Heating] = 163.45/1000
                                                                                                                                                                      Description: The pounds of CO2 emitted per kBTU of heating energy provided, for each heating fuel.Data for heat pumps (electricity) is: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/downloadRest is from: https://www.eia.gov/environment/emissions/co2_vol_mass.phpIn line with that source, I assume that each heat pump will add to the grid and is not part of base demand, and so the marginal emissions from producing electricity from heat pumps will be constant at the value as it will come from natural gas generators (explanation of which is from here: https://willbrownsberger.com/how-green-will-the-power-be/
                                                                                                                                                                      Present In 1 View:
                                                                                                                                                                      Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #174
                                                                                                                                                                      L
                                                                                                                                                                      Housing (House)
                                                                                                                                                                      Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                                      Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                      Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                      Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                      Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                                                                                                                                      HeatPumpModel_v31 #264
                                                                                                                                                                      C
                                                                                                                                                                      Pounds per Ton (lb CO2 / tCO2)
                                                                                                                                                                      = 2204.6
                                                                                                                                                                      Description: The number of pounds in a metric ton.
                                                                                                                                                                      Present In 1 View:
                                                                                                                                                                      Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      (View) Cumulative Subsidies (39 Variables)
                                                                                                                                                                      Top (View) Cumulative Subsidies (39 Variables)
                                                                                                                                                                      Group
                                                                                                                                                                      Type
                                                                                                                                                                      Variable Name And Description
                                                                                                                                                                      HeatPumpModel_v31 #1
                                                                                                                                                                      A
                                                                                                                                                                      Actual EEHIC Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                      Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] = MIN(
                                                                                                                                                                      Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]* Implemented EEHIC Subsidy Proportional Rate for Retrofits, Implemented EEHIC Maximum Subsidy for Retrofits)
                                                                                                                                                                      Description: The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value.
                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #2
                                                                                                                                                                      A
                                                                                                                                                                      Actual HOMES Subsidy for Retrofits (Dollar/ Home)
                                                                                                                                                                      Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                      Energy Savings[ Cohort, Heating and Cooling System]< HOMES Cut Off for Savings, HOMES Implemented Lower Subsidy, HOMES Implemented High Subsidy)
                                                                                                                                                                      Description: The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #3
                                                                                                                                                                      A
                                                                                                                                                                      Actual MassSave Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                      Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] = MIN(
                                                                                                                                                                      Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]* Implemented MassSave Subsidy Proportional Rate for Retrofits, Implemented MassSave Maximum Subsidy for Retrofits)
                                                                                                                                                                      Description: The actual subsidy offered for retrofits by MassSave, not the expected value.
                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #13
                                                                                                                                                                      F,A
                                                                                                                                                                      Annual Federal Subsidies (Dollar / Year)
                                                                                                                                                                      =
                                                                                                                                                                      Federal Annual Heat Pump Subsidy+ Federal Annual Retrofit Subsidy
                                                                                                                                                                      Description: The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year.
                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                      • Cumulative Federal Subsidy The amount of money the federal government spends on subsidies for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #14
                                                                                                                                                                      F,A
                                                                                                                                                                      Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                      =
                                                                                                                                                                      Federal Annual Heat Pump Subsidy+ Massachusetts Annual Heat Pumps Subsidy
                                                                                                                                                                      Description: The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #16
                                                                                                                                                                      F,A
                                                                                                                                                                      Annual MA Subsidies (Dollar / Year)
                                                                                                                                                                      =
                                                                                                                                                                      Massachusetts Annual Retrofit Subsidy+ Massachusetts Annual Heat Pumps Subsidy
                                                                                                                                                                      Description: The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps.
                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                      • Cumulative MA Subsidy The amount of subsidies that the Massachusetts state government has given out for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #17
                                                                                                                                                                      F,A
                                                                                                                                                                      Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                      =
                                                                                                                                                                      Federal Annual Retrofit Subsidy+ Massachusetts Annual Retrofit Subsidy
                                                                                                                                                                      Description: The subsidies for retrofits paid out every year.
                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                      HeatPumpModel_v31 #18
                                                                                                                                                                      A
                                                                                                                                                                      Annual Subsidies (Dollar / Year)
                                                                                                                                                                      =
                                                                                                                                                                      Annual Heat Pump Subsidy+ Annual Retrofit Subsidy
                                                                                                                                                                      Description: The amount of subsidies spent on heat pumps and retrofits every year.
                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                        HeatPumpModel_v31 #78
                                                                                                                                                                        L
                                                                                                                                                                        Cumulative Federal Subsidy (Dollar)
                                                                                                                                                                        =
                                                                                                                                                                        Annual Federal Subsidies dt + 0.0
                                                                                                                                                                        Description: The amount of money the federal government spends on subsidies for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                          HeatPumpModel_v31 #79
                                                                                                                                                                          L
                                                                                                                                                                          Cumulative MA Subsidy (Dollar)
                                                                                                                                                                          =
                                                                                                                                                                          Annual MA Subsidies dt + 0.0
                                                                                                                                                                          Description: The amount of subsidies that the Massachusetts state government has given out for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                            HeatPumpModel_v31 #81
                                                                                                                                                                            A
                                                                                                                                                                            Cumulative Subsidies (Dollar)
                                                                                                                                                                            =
                                                                                                                                                                            Cumulative Subsidy for Retrofits+ Cumulative Subsidies for Heat Pumps
                                                                                                                                                                            Description: The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #80
                                                                                                                                                                              L
                                                                                                                                                                              Cumulative Subsidies for Heat Pumps (Dollar)
                                                                                                                                                                              =
                                                                                                                                                                              Annual Heat Pump Subsidy dt + 0.0
                                                                                                                                                                              Description: The total amount of dollars spent on subsidizing heat pumps throughout the model's run.
                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                              • Cumulative Subsidies The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #82
                                                                                                                                                                              L
                                                                                                                                                                              Cumulative Subsidy for Retrofits (Dollar)
                                                                                                                                                                              =
                                                                                                                                                                              Annual Retrofit Subsidy dt + 0.0
                                                                                                                                                                              Description: The total amount spent on retrofits since the beginning of the model's run.
                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                              • Cumulative Subsidies The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #106
                                                                                                                                                                              A
                                                                                                                                                                              Energy Savings (dmnl)
                                                                                                                                                                              Energy Savings[Cohort,Heating and Cooling System] = MAX(0,ABS(ZIDZ((
                                                                                                                                                                              Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]- U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]), U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting])))
                                                                                                                                                                              Description: The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #124
                                                                                                                                                                              A
                                                                                                                                                                              Federal Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                              =
                                                                                                                                                                              Total Heat Pump Sales* IRA Actual Subsidy for Heat Pumps
                                                                                                                                                                              Description: The amount of subsidies the federal government spends on heat pumps through the Inflation Reduction Act every year.
                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                              • Annual Federal Subsidies The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year.
                                                                                                                                                                              • Annual Heat Pump Subsidy The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #125
                                                                                                                                                                              A
                                                                                                                                                                              Federal Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                              = SUM((
                                                                                                                                                                              Actual EEHIC Subsidy for Retrofits[ Cohort!, Heating and Cooling System!]+ Actual HOMES Subsidy for Retrofits[ Cohort!, Heating and Cooling System!])* Houses Retrofitting per Year[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                              Description: The amount of federal subsidies spent by the federal government, through the IRA.
                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #147
                                                                                                                                                                              C
                                                                                                                                                                              HOMES Cut Off for Savings (dmnl )
                                                                                                                                                                              = 0.35
                                                                                                                                                                              Description: The percent energy savings needed to get the higher subsidy amount from the Home Owner Managing Energy Savings rebate. Taken from: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                              Present In 2 Views:
                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #151
                                                                                                                                                                              A
                                                                                                                                                                              HOMES Implemented High Subsidy (Dollar / House)
                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                              Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES High Subsidy Amount,0)
                                                                                                                                                                              Description: Implemented higher subsidy from the HOMES rebate program.
                                                                                                                                                                              Present In 2 Views: Used By
                                                                                                                                                                              • Actual HOMES Subsidy for Retrofits The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                                                                                                                                              • HOMES Expected Higher Subsidy Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              .housingagingchain v15 #152
                                                                                                                                                                              A
                                                                                                                                                                              HOMES Implemented Lower Subsidy (Dollar / House)
                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                              Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES Lower Subsidy Amount,0)
                                                                                                                                                                              Description: Lump sum subsidy that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #157
                                                                                                                                                                              A
                                                                                                                                                                              Houses Retrofitting per Year (House / Year)
                                                                                                                                                                              Houses Retrofitting per Year[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                              Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]< U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting], Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]/ Retrofit Delay,0)
                                                                                                                                                                              Description: The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #174
                                                                                                                                                                              L
                                                                                                                                                                              Housing (House)
                                                                                                                                                                              Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                                              Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                              Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                              Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                              Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                                                                                                                                              HeatPumpModel_v31 #175
                                                                                                                                                                              A
                                                                                                                                                                              Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                              Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: Time<= EEHIC Subsidy for Retrofits Final Year, EEHIC Maximum Subsidy for Retrofits,0)
                                                                                                                                                                              Description: Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #176
                                                                                                                                                                              A
                                                                                                                                                                              Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                              Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: EEHIC Subsidy for Retrofits Final Year>= Time, EEHIC Proportional Subsidy Rate for Retrofits,0)
                                                                                                                                                                              Description: The implemented proportional subsidy rate for retrofits from the IRA, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #177
                                                                                                                                                                              A
                                                                                                                                                                              Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                              Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: Time<= IRA Lump Sum Subsidy for Heat Pumps Final Year, IRA Maximum Proportional Subsidy for Heat Pumps,0)
                                                                                                                                                                              Description: Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              .housingagingchain v15 #178
                                                                                                                                                                              A
                                                                                                                                                                              Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                              Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: Time<= MassSave Subsidy for Retrofits Final Year, MassSave Maximum Subsidy for Retrofits,0)
                                                                                                                                                                              Description: Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              .housingagingchain v15 #179
                                                                                                                                                                              A
                                                                                                                                                                              Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                              Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: MassSave Subsidy for Retrofits Final Year>= Time, Mass Save Proportional Subsidy Rate for Retrofits,0)
                                                                                                                                                                              Description: The implemented proportional subsidy rate from the state, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #201
                                                                                                                                                                              A
                                                                                                                                                                              IRA Actual Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                              = MIN(
                                                                                                                                                                              IRA Implemented Subsidy Proportional Rate for Heat Pumps* Unsubsidized Cost of Heat Pumps, Implemented IRA Maximum Proportional Subsidy for Heat Pumps)
                                                                                                                                                                              Description: The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value.
                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #203
                                                                                                                                                                              A
                                                                                                                                                                              IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                              Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: IRA Lump Sum Subsidy for Heat Pumps Final Year>= Time, IRA Proportional Subsidy Rate for Heat Pumps,0)
                                                                                                                                                                              Description: The implemented proportional subsidy rate, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy rate afterwards.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #205
                                                                                                                                                                              C
                                                                                                                                                                              IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )
                                                                                                                                                                              = 2000
                                                                                                                                                                              Description: The maximum proportional subsidy for heat pumps that will be offered, regardless of the subsidy rate. For instance, if the proportional subsidy is 50% but the maximum is $1000, then for a retrofit project that costs $3000 only a $1000 subsidy will be given.Taken from: https://www.energystar.gov/about/federal-tax-credits
                                                                                                                                                                              Present In 2 Views:
                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #215
                                                                                                                                                                              A
                                                                                                                                                                              Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)
                                                                                                                                                                              =
                                                                                                                                                                              Total Heat Pump Sales* MassSave Implemented Lump Sum Subsidy for Heat Pumps
                                                                                                                                                                              Description: The actual subsidy provided for purchase of heat pumps by Massachusetts, as opposed to what the subsidy expected by homeowners is.
                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                              • Annual Heat Pump Subsidy The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                              • Annual MA Subsidies The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #216
                                                                                                                                                                              A
                                                                                                                                                                              Massachusetts Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                              = SUM(
                                                                                                                                                                              Houses Retrofitting per Year[ Cohort!, Heating and Cooling System!]* Actual MassSave Subsidy for Retrofits[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                              Description: Amount of money Massachusetts spends on MassSave subsidies for retrofits, yearly.
                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #219
                                                                                                                                                                              A
                                                                                                                                                                              MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                              = MIN(
                                                                                                                                                                              Unsubsidized Cost of Heat Pumps,IF THEN ELSE( Time>= MassSave Lump Sum Subsidy Implementation Year for Heat Pumps:AND: Time<= MassSave Lump Sum Subsidy for Heat Pumps Final Year, MassSave Lump Sum Subsidy Amount for Heat Pumps,0))
                                                                                                                                                                              Description: Lump sum subsidy from MassSave that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              .housingagingchain v4 testing #254
                                                                                                                                                                              A
                                                                                                                                                                              Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                                              Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                                              Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                              Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                              Present In 8 Views: Used By
                                                                                                                                                                              • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                              • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                              • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                              • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                              • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                              • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                              • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                              • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                              • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #270
                                                                                                                                                                              C
                                                                                                                                                                              Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
                                                                                                                                                                              = 1
                                                                                                                                                                              Description: Turns proportional subsidy's effect on retrofit cost on/off.
                                                                                                                                                                              Present In 2 Views:
                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #286
                                                                                                                                                                              C
                                                                                                                                                                              Retrofit Delay (Year )
                                                                                                                                                                              = 2
                                                                                                                                                                              Description: Time to retrofit. Assumed to be on average six months.
                                                                                                                                                                              Present In 2 Views:
                                                                                                                                                                              Used By
                                                                                                                                                                              • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                              • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #316
                                                                                                                                                                              A
                                                                                                                                                                              Total Heat Pump Sales (House / Year)
                                                                                                                                                                              = SUM(
                                                                                                                                                                              Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump Only]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Gas]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Oil])
                                                                                                                                                                              Description: Number of houses buying heat pumps every year.
                                                                                                                                                                              Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #329
                                                                                                                                                                              A
                                                                                                                                                                              U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                              U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                              Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                              Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                              Present In 8 Views: Used By
                                                                                                                                                                              • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                              • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                              • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                              • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                              • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                              • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                              • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                              • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                              • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                              • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                              • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                              • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                              • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                              Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                              HeatPumpModel_v31 #337
                                                                                                                                                                              A
                                                                                                                                                                              Unsubsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                              =
                                                                                                                                                                              Unsubsidized Cost of Heat Pump Over Time TABLE( Time)
                                                                                                                                                                              Description: The unsubsidized cost of heat pumps, instantiated at each time.
                                                                                                                                                                              Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              .housingagingchain v8 #339
                                                                                                                                                                              A
                                                                                                                                                                              Unsubsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                              Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                              Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort,Open to Retrofitting]
                                                                                                                                                                              Description: Total retrofit cost without taking into account subsidies.
                                                                                                                                                                              Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              (View) Energy Use (28 Variables)
                                                                                                                                                                              Top (View) Energy Use (28 Variables)
                                                                                                                                                                              Group
                                                                                                                                                                              Type
                                                                                                                                                                              Variable Name And Description
                                                                                                                                                                              HeatPumpModel_v31 #29
                                                                                                                                                                              A
                                                                                                                                                                              Average Area (sf / House)
                                                                                                                                                                              Average Area[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                                                                                              Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                                                                                              Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                              Present In 7 Views: Used By
                                                                                                                                                                              • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                              • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                              • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                                              • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                              • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                              • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                              • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                              • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                              • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                              • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                              • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                              • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                              • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                              • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                              • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                              • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                                                                                              Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                              HeatPumpModel_v31 #31
                                                                                                                                                                              A
                                                                                                                                                                              Average Cooling Cost (Dollar / (Year * House))
                                                                                                                                                                              Average Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              Expected Cooling Energy Price* Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                              Description: The average costs for keeping a home cool, by grouping.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #33
                                                                                                                                                                              C
                                                                                                                                                                              Average Cooling Energy Use (kBTU / (Year * House))
                                                                                                                                                                              Average Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                              Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                              Description: The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                              Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #40
                                                                                                                                                                              A
                                                                                                                                                                              Average Energy Cost (Dollar / (Year * House))
                                                                                                                                                                              Average Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              Average Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                              Description: The average cost of both heating and cooling a home, by grouping.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #45
                                                                                                                                                                              A
                                                                                                                                                                              Average Energy Use (kBTU / (Year * House))
                                                                                                                                                                              Average Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                              Description: Average energy use to both heat and cool a home.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              .housingagingchain v5 testing #49
                                                                                                                                                                              A
                                                                                                                                                                              Average Heating Cost (Dollar / (Year * House))
                                                                                                                                                                              Average Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              Expected Heating Energy Price[ Heating and Cooling System]* Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                              Description: The costs per year to heat one house.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #51
                                                                                                                                                                              A
                                                                                                                                                                              Average Heating Energy Use (kBTU / (Year * House))
                                                                                                                                                                              Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                              Description: The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                              Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #67
                                                                                                                                                                              C
                                                                                                                                                                              Cooling Degree Days (F )
                                                                                                                                                                              = 1029
                                                                                                                                                                              Description: The difference between temperature setpoint (65 F) and outside temperature for heating. Typically called cooling degree days, but units are solely in terms of fahrenheit.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. Use set point of 65°F, in line with industry standard, as at that temperature little heating or cooling is necessary.
                                                                                                                                                                              Present In 3 Views:
                                                                                                                                                                              Used By
                                                                                                                                                                              • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                              • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                              • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                              • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #70
                                                                                                                                                                              A
                                                                                                                                                                              Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                              =
                                                                                                                                                                              Initial Cooling Energy Price* Input 1
                                                                                                                                                                              Description: Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                              Present In 3 Views: Used By
                                                                                                                                                                              • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #72
                                                                                                                                                                              A
                                                                                                                                                                              Cooling System Efficiency (dmnl)
                                                                                                                                                                              Cooling System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                              Heat Pump Cooling COP TABLE( Time)
                                                                                                                                                                              Cooling System Efficiency[Central AC Cooling] = 2.93
                                                                                                                                                                              Cooling System Efficiency[Window AC Cooling] = 2.49* Effect of Air Leakage from Window AC on Efficiency
                                                                                                                                                                              Cooling System Efficiency[No AC Cooling] = NAREPLACEMENT
                                                                                                                                                                              Description: The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                              Present In 4 Views: Used By
                                                                                                                                                                              • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                              • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                              • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                              • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                              • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #95
                                                                                                                                                                              C
                                                                                                                                                                              Effect of Air Leakage from Window AC on Efficiency (dmnl)
                                                                                                                                                                              = 0.9*10/11
                                                                                                                                                                              Description: A window air conditioner typically does not perfectly cover its intended cavity, leading to more air leakage and therefore reducing efficiency.Taken from: https://www.energy.gov/sites/prod/files/2014/08/f18/ba_innovations_1-2-5_window_ac.pdf
                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                              Used By
                                                                                                                                                                              • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #111
                                                                                                                                                                              SM,A
                                                                                                                                                                              Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                              = SMOOTH3(
                                                                                                                                                                              Cooling Energy Price, Delay in Forming Expectations of Energy Price)
                                                                                                                                                                              Description: Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                              Present In 4 Views: Used By
                                                                                                                                                                              • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                              • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                              • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                              • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              .housingagingchain v15 #115
                                                                                                                                                                              SM,A
                                                                                                                                                                              Expected Heating Energy Price (Dollar / kBTU)
                                                                                                                                                                              Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                                                                                                                                              Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                                                                                                                                              Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                              Present In 6 Views: Used By
                                                                                                                                                                              • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                              • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                              • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                              • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #136
                                                                                                                                                                              A,T
                                                                                                                                                                              Gas COP TABLE (dmnl)
                                                                                                                                                                              Gas COP TABLE([(2020,0)-(2050,1)],(2020,0.9),(2030,0.925),(2040,0.95),(2050,0.95))

                                                                                                                                                                              Description: Efficiency of gas systems over time. Taken as the average of projected efficiency for reference gas boilers and gas furnaces, from MassDEP's Energy Pathways for Deep Decarbonization Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                              Used By
                                                                                                                                                                              • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #138
                                                                                                                                                                              A,T
                                                                                                                                                                              Heat Pump Cooling COP TABLE (dmnl)
                                                                                                                                                                              Heat Pump Cooling COP TABLE([(2020,0)-(2050,10)],(2020,4.3),(2030,4.8),(2040,5.17),(2050,5.28))

                                                                                                                                                                              Description: The COP of heat pumps when used for cooling. Calculated by assuming the ratio of heating and cooling COP is constant over time -- as heating COP improves the ability to cool improves proportionally-- finding cooling COP in 2020, finding the COP for cooling of heating in 2018, and then using the ratio between the two in 2020 to project future values. Data on this was difficult to find.Projected heating COP from pg. 97 of MassDEP's Energy Pathways for Deep Decarbonization: https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadCooling COP in 2020 here: https://www.raleighheatingandair.com/blog/is-a-heat-pump-more-effective-at-cooling-or-heating/
                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                              Used By
                                                                                                                                                                              • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #140
                                                                                                                                                                              A,T
                                                                                                                                                                              Heat Pump Heating COP TABLE (dmnl)
                                                                                                                                                                              Heat Pump Heating COP TABLE([(2020,0)-(2050,10)],(2020,2.485),(2030,2.785),(2040,2.99),(2050,3.05))

                                                                                                                                                                              Description: The efficiency of heat pumps for heating, over time. Taken as the average of projected COP for reference ASHP and ductless mini-splits from MassDEP's Energy Pathways Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                              Used By
                                                                                                                                                                              • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #141
                                                                                                                                                                              C
                                                                                                                                                                              Heating Degree Days (F )
                                                                                                                                                                              = 5026
                                                                                                                                                                              Description: The difference between temperature setpoint (65 F) and outside temperature.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. In line with industry standard, use set point of 65°F, as thattemperature little heating or cooling is needed.
                                                                                                                                                                              Present In 3 Views:
                                                                                                                                                                              Used By
                                                                                                                                                                              • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                              • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                              • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                              • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              .housingagingchain v5 testing #143
                                                                                                                                                                              A
                                                                                                                                                                              Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                              Heating Energy Price[Heating and Cooling System] =
                                                                                                                                                                              Initial Heating Energy Price[ Heating and Cooling System]* Input 0
                                                                                                                                                                              Description: The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                              Present In 6 Views: Used By
                                                                                                                                                                              • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #145
                                                                                                                                                                              A
                                                                                                                                                                              Heating System Efficiency (dmnl)
                                                                                                                                                                              Heating System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                              Heat Pump Heating COP TABLE( Time)
                                                                                                                                                                              Heating System Efficiency[Gas Heating] = Gas COP TABLE( Time)
                                                                                                                                                                              Heating System Efficiency[Oil Heating] = Oil COP TABLE( Time)
                                                                                                                                                                              Description: The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                              Present In 3 Views: Used By
                                                                                                                                                                              • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                              • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                              • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                              • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #245
                                                                                                                                                                              A,T
                                                                                                                                                                              Oil COP TABLE (dmnl)
                                                                                                                                                                              Oil COP TABLE([(2020,0)-(2050,1)],(2020,0.835),(2030,0.84),(2050,0.84))

                                                                                                                                                                              Description: Efficiency of oil systems over time. Taken as the average of projected efficiency for reference distillate boilers and furnaces, from MassDEP's Energy Pathways for Deep Decarbonization Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                              Used By
                                                                                                                                                                              • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #246
                                                                                                                                                                              A
                                                                                                                                                                              Optimal Cooling Cost (Dollar / (Year * House))
                                                                                                                                                                              Optimal Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              Expected Cooling Energy Price* Optimal Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                              Description: The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #247
                                                                                                                                                                              C
                                                                                                                                                                              Optimal Cooling Energy Use (kBTU / (Year * House))
                                                                                                                                                                              Optimal Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                              Optimal Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                              Description: The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #248
                                                                                                                                                                              A
                                                                                                                                                                              Optimal Energy Cost (Dollar / (Year * House))
                                                                                                                                                                              Optimal Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              Optimal Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Optimal Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                              Description: Total energy cost if optimal U value is achieved.
                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                              HeatPumpModel_v31 #249
                                                                                                                                                                              A
                                                                                                                                                                              Optimal Energy Use (kBTU / (House * Year))
                                                                                                                                                                              Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                              Optimal Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]+ Optimal Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                              Description: Average energy use to heat and cool per house if U is optimal.
                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                HeatPumpModel_v31 #250
                                                                                                                                                                                A
                                                                                                                                                                                Optimal Heating Cost (Dollar / (Year * House))
                                                                                                                                                                                Optimal Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                Expected Heating Energy Price[ Heating and Cooling System]* Optimal Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                Description: Average heating cost if U value is optimal.
                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                HeatPumpModel_v31 #251
                                                                                                                                                                                A
                                                                                                                                                                                Optimal Heating Energy Use (kBTU / (House * Year))
                                                                                                                                                                                Optimal Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                Description: The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v4 testing #254
                                                                                                                                                                                A
                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                                                Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                Present In 8 Views: Used By
                                                                                                                                                                                • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                HeatPumpModel_v31 #329
                                                                                                                                                                                A
                                                                                                                                                                                U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                                U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                                Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                Present In 8 Views: Used By
                                                                                                                                                                                • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                (View) Housing Aging Chain & U Coflows (68 Variables)
                                                                                                                                                                                Top (View) Housing Aging Chain & U Coflows (68 Variables)
                                                                                                                                                                                Group
                                                                                                                                                                                Type
                                                                                                                                                                                Variable Name And Description
                                                                                                                                                                                .housingagingchain v8 #0
                                                                                                                                                                                C
                                                                                                                                                                                Active Cohort Indicator (dmnl)
                                                                                                                                                                                Active Cohort Indicator[Cohort] = IF THEN ELSE(INTEGER((
                                                                                                                                                                                Time- INITIAL TIME)/ Cohort Duration)+1= Cohort-ELMCOUNT( Preexisting Cohorts),1,0)
                                                                                                                                                                                Active Cohort Indicator[Preexisting Cohorts] = 0
                                                                                                                                                                                Description: The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v15 #12
                                                                                                                                                                                A
                                                                                                                                                                                Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))
                                                                                                                                                                                Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]/ Amoritization Period
                                                                                                                                                                                Description: The incurred total retrofit cost amoritized over the specified amoritization period.
                                                                                                                                                                                Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v15 #41
                                                                                                                                                                                A
                                                                                                                                                                                Average Energy Costs for Retrofitting Home (Dollar / Year / House)
                                                                                                                                                                                Average Energy Costs for Retrofitting Home[Cohort,Heating and Cooling System] =
                                                                                                                                                                                Average Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                Description: Heating costs for each home open to retrofitting, annually, if no further retrofit measures are undertaken.
                                                                                                                                                                                Present In 2 Views: Used By
                                                                                                                                                                                • Total Cost of Ownership of Average Home Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v8 #42
                                                                                                                                                                                A
                                                                                                                                                                                Average Energy Costs if Retrofitted (Dollar/(Year*House))
                                                                                                                                                                                Average Energy Costs if Retrofitted[Cohort,Heating and Cooling System] =
                                                                                                                                                                                Optimal Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                Description: Energy costs per year for each retrofitting house if homes retrofit to the optimal U value.
                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                HeatPumpModel_v31 #57
                                                                                                                                                                                C
                                                                                                                                                                                Average Time To Consider Switching (Year )
                                                                                                                                                                                = 15
                                                                                                                                                                                Description: The average time it takes for a house to consider switching their heating and cooling system.
                                                                                                                                                                                Present In 2 Views:
                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v18 #65
                                                                                                                                                                                L
                                                                                                                                                                                Code U (kBTU / (sf * Year * F))
                                                                                                                                                                                = -
                                                                                                                                                                                Decrease in Code U dt + Initial Code U Value
                                                                                                                                                                                Description: U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                Present In 2 Views: Used By
                                                                                                                                                                                • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                • Decrease in Code U The change in code U from policy.
                                                                                                                                                                                • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                .housingagingchain v8 #66
                                                                                                                                                                                C
                                                                                                                                                                                Cohort Duration (Year )
                                                                                                                                                                                = 10
                                                                                                                                                                                Description: The width (duration) of each cohort.
                                                                                                                                                                                Present In 2 Views:
                                                                                                                                                                                Used By
                                                                                                                                                                                • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                HeatPumpModel_v31 #88
                                                                                                                                                                                C
                                                                                                                                                                                Demolition Hazard Rate (1 / Year )
                                                                                                                                                                                = 0.01
                                                                                                                                                                                Description: Proportion of homes demolished every year. Value is assumed to be equal across both retrofitting and non-retrofitting homes. Heuristically chosen so total housing stock grows at net 1%/year.
                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                HeatPumpModel_v31 #89
                                                                                                                                                                                F,A
                                                                                                                                                                                Demolitions (House / Year)
                                                                                                                                                                                Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                Demolition Hazard Rate* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]*(1- No Turnover Switch)
                                                                                                                                                                                Description: Homes that are destroyed every year.
                                                                                                                                                                                Present In 3 Views: Used By
                                                                                                                                                                                • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                .housingagingchain v15 #115
                                                                                                                                                                                SM,A
                                                                                                                                                                                Expected Heating Energy Price (Dollar / kBTU)
                                                                                                                                                                                Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                                                                                                                                                Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                Present In 6 Views: Used By
                                                                                                                                                                                • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v15 #119
                                                                                                                                                                                SM,A
                                                                                                                                                                                Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                = SMOOTH3(
                                                                                                                                                                                Implemented MassSave Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                Present In 4 Views: Used By
                                                                                                                                                                                • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v15 #123
                                                                                                                                                                                A
                                                                                                                                                                                Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                Energy Savings[ Cohort, Heating and Cooling System]>= HOMES Cut Off for Savings, HOMES Expected Higher Subsidy, HOMES Expected Lower Lump Sum Subsidy)+ MassSave Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]+ EEHIC Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                                                                                                                                                Present In 4 Views: Used By
                                                                                                                                                                                • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v5 testing #128
                                                                                                                                                                                C
                                                                                                                                                                                Fixed Cost (Dollar / House )
                                                                                                                                                                                = 0
                                                                                                                                                                                Description: Fixed cost of retrofitting, due to permitting, finding contractors, etc. This is not taken into account in the marginal cost of retrofitting, and this model assumes that households have not yet paid a fixed cost when deciding to retrofit. This cost only applies to existing housing.Set this equal to 0, because almost all costs for retrofits seem to be variable (except for permitting, which isn't usually used), and there's no data to suggest otherwise.
                                                                                                                                                                                Present In 2 Views:
                                                                                                                                                                                Used By
                                                                                                                                                                                • Expected Fixed Cost Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v5 testing #127
                                                                                                                                                                                A
                                                                                                                                                                                Fixed Cost per Unit Area (Dollar / sf)
                                                                                                                                                                                Fixed Cost per Unit Area[Cohort] = ZIDZ(
                                                                                                                                                                                Expected Fixed Cost, Average Area[ Cohort,Open to Retrofitting])
                                                                                                                                                                                Description: The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                Present In 2 Views: Used By
                                                                                                                                                                                • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v5 testing #130
                                                                                                                                                                                A
                                                                                                                                                                                Fraction of Houses Switching (dmnl)
                                                                                                                                                                                Fraction of Houses Switching[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                Fraction of Houses Switching[Cohort,Gas Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                Description: Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                Present In 2 Views: Used By
                                                                                                                                                                                • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v5 testing #143
                                                                                                                                                                                A
                                                                                                                                                                                Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                Heating Energy Price[Heating and Cooling System] =
                                                                                                                                                                                Initial Heating Energy Price[ Heating and Cooling System]* Input 0
                                                                                                                                                                                Description: The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                Present In 6 Views: Used By
                                                                                                                                                                                • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                .housingagingchain v15 #149
                                                                                                                                                                                SM,A
                                                                                                                                                                                HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                                                                                                                                                = SMOOTH3(
                                                                                                                                                                                HOMES Implemented Lower Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                HeatPumpModel_v31 #156
                                                                                                                                                                                A
                                                                                                                                                                                Houses Considering Switching System (Houses / Year)
                                                                                                                                                                                Houses Considering Switching System[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                Housing[ Cohort, Heating and Cooling System, Retrofitting Status]/ Average Time To Consider Switching
                                                                                                                                                                                Description: The number of houses per year considering switching their heating and cooling system.
                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                HeatPumpModel_v31 #158
                                                                                                                                                                                A
                                                                                                                                                                                Houses Retrofitting (Houses)
                                                                                                                                                                                Houses Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                Description: Total amount of houses retrofitting in each cohort and heating and cooling system.
                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                  HeatPumpModel_v31 #160
                                                                                                                                                                                  F,A
                                                                                                                                                                                  Houses Switching Sources (House / Year)
                                                                                                                                                                                  Houses Switching Sources[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                  Fraction of Houses Switching[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                                                  Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Fraction of Houses Switching[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Fossil Fuel Heating, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                                                  Description: The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                  Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                  HeatPumpModel_v31 #174
                                                                                                                                                                                  L
                                                                                                                                                                                  Housing (House)
                                                                                                                                                                                  Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                                                  Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                  Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                  Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                  Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                                                                                                                                                  HeatPumpModel_v31 #161
                                                                                                                                                                                  A
                                                                                                                                                                                  Housing by Cohort and Heating and Cooling System (Houses)
                                                                                                                                                                                  Housing by Cohort and Heating and Cooling System[Cohort,Heating and Cooling System] = SUM(
                                                                                                                                                                                  Housing[ Cohort, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                  Description: Housing by heating and cooling system and cohort, irrespective of retrofit status.
                                                                                                                                                                                  Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                  HeatPumpModel_v31 #166
                                                                                                                                                                                  C
                                                                                                                                                                                  Housing Fractional Growth Rate (1 / Year )
                                                                                                                                                                                  = 0.02
                                                                                                                                                                                  Description: The annual growth rate in housing. Heuristically chosen so that total housing stock grows at net 1%/year.
                                                                                                                                                                                  Present In 1 View:
                                                                                                                                                                                  Used By
                                                                                                                                                                                  • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                  HeatPumpModel_v31 #173
                                                                                                                                                                                  F,A
                                                                                                                                                                                  Housing Starts (Houses / Year)
                                                                                                                                                                                  Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                                                                                                  Housing Fractional Growth Rate*SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])* Active Cohort Indicator[ Cohort]*(1- No Turnover Switch)
                                                                                                                                                                                  Description: Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                  Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [2,2] (-) 0  [0,0]
                                                                                                                                                                                  HeatPumpModel_v31 #167
                                                                                                                                                                                  A
                                                                                                                                                                                  Housing Starts Across Cohorts ()
                                                                                                                                                                                  = SUM(
                                                                                                                                                                                  Housing Starts In Each Cohort[ Cohort!])
                                                                                                                                                                                  Description: Housing starts across all cohorts.
                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    HeatPumpModel_v31 #169
                                                                                                                                                                                    A
                                                                                                                                                                                    Housing Starts In Each Cohort (House / Year)
                                                                                                                                                                                    Housing Starts In Each Cohort[Cohort] = SUM(
                                                                                                                                                                                    Housing Starts[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                    Description: Housing starts across heating and cooling systems.
                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    .housingagingchain v18 #181
                                                                                                                                                                                    F,A
                                                                                                                                                                                    Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                    Increase in U Value from Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                                                                                                    Housing Starts[ Cohort, Heating and Cooling System]* U Value of Housing Starts[ Cohort, Heating and Cooling System]
                                                                                                                                                                                    Description: New U value from new homes being built.
                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                    • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    HeatPumpModel_v31 #182
                                                                                                                                                                                    A
                                                                                                                                                                                    Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                    Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                    Affinity of Retrofitting[ Cohort, Heating and Cooling System]/( Affinity of Retrofitting[ Cohort, Heating and Cooling System]+ Affinity of Not Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                    Description: Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    HeatPumpModel_v31 #183
                                                                                                                                                                                    A
                                                                                                                                                                                    Indicated Homes Retrofitting (House)
                                                                                                                                                                                    Indicated Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                    Indicated Fraction of Homes Retrofitting[ Cohort, Heating and Cooling System]* Housing by Cohort and Heating and Cooling System[ Cohort, Heating and Cooling System]
                                                                                                                                                                                    Description: Number of homes that, once delays are taken into account, will be open to retrofitting.
                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                    HeatPumpModel_v31 #187
                                                                                                                                                                                    C
                                                                                                                                                                                    Initial Average U Value (kBTU/(Year*sf*F))
                                                                                                                                                                                    Initial Average U Value[Cohort] = 0.19235
                                                                                                                                                                                    Description: The initial average U, equal to the average U value of MA SFH in 2022, from EIA RECS.
                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                    Used By
                                                                                                                                                                                    • Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    HeatPumpModel_v31 #190
                                                                                                                                                                                    C
                                                                                                                                                                                    Initial Fraction of Homes Retrofitting (dmnl )
                                                                                                                                                                                    = 0.1
                                                                                                                                                                                    Description: Initial fraction of homes open to retrofitting. Heuristically chosen to be 0.1 to match low level of retrofitting that current occurs.
                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    .housingagingchain v5 testing #192
                                                                                                                                                                                    LI,A
                                                                                                                                                                                    Initial Homes Not Retrofitting (House)
                                                                                                                                                                                    Initial Homes Not Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                                                                                                                                    Initial Homes Not Retrofitting[Preexisting Cohorts,Heating and Cooling System] = (1-
                                                                                                                                                                                    Initial Fraction of Homes Retrofitting)* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                                                                                                                                    Description: Initial homes not open to retrofitting.
                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                    • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    .housingagingchain v5 testing #193
                                                                                                                                                                                    LI,A
                                                                                                                                                                                    Initial Homes Retrofitting (Houses)
                                                                                                                                                                                    Initial Homes Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                                                                                                                                    Initial Homes Retrofitting[Preexisting Cohorts,Heating and Cooling System] =
                                                                                                                                                                                    Initial Fraction of Homes Retrofitting* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                                                                                                                                    Description: Homes that are open to retrofitting initially.
                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                    • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    HeatPumpModel_v31 #195
                                                                                                                                                                                    C
                                                                                                                                                                                    Initial Housing (House)
                                                                                                                                                                                    Initial Housing[Cohort,Heating and Cooling System] = 2.2e+06
                                                                                                                                                                                    Description: The total number of houses that begin in each cohort and heating and cooling source. Taken from CIN file.
                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    .housingagingchain v15 #197
                                                                                                                                                                                    LI,A
                                                                                                                                                                                    Initial U Value (House * kBTU / (Year * F * sf))
                                                                                                                                                                                    Initial U Value[Cohort,Heating and Cooling System,Retrofitting Status] = 0
                                                                                                                                                                                    Initial U Value[Preexisting Cohorts,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                    Initial Average U Value[ Preexisting Cohorts]* Housing[ Preexisting Cohorts, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                    Description: Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                    • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    .housingagingchain v15 #214
                                                                                                                                                                                    C
                                                                                                                                                                                    Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                    = 0.75
                                                                                                                                                                                    Description: Proportion of total retrofit cost that will be credited as part of a proportional subsidy. Theoretically, this can vary between current housing and housing under construction.Based off Mass Save data: https://www.masssave.com/en/residential/rebates-and-incentives/insulation-and-windows/insulation-and-air-sealing
                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    .housingagingchain v15 #218
                                                                                                                                                                                    A
                                                                                                                                                                                    MassSave Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                    MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = MIN(
                                                                                                                                                                                    Proportional Subsidy Switch for Retrofits* Expected MassSave Proportional Subsidy Rate for Retrofits* Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status], Expected MassSave Maximum Subsidy for Retrofits)
                                                                                                                                                                                    Description: The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                    HeatPumpModel_v31 #226
                                                                                                                                                                                    A
                                                                                                                                                                                    Monthly Total Heat Pump Sales (Houses/ Month)
                                                                                                                                                                                    =
                                                                                                                                                                                    Total Heat Pump Sales/ Months per Year
                                                                                                                                                                                    Description: The number of homes buying heat pumps, every year.
                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      HeatPumpModel_v31 #227
                                                                                                                                                                                      C
                                                                                                                                                                                      Months per Year (Month / Year )
                                                                                                                                                                                      = 12
                                                                                                                                                                                      Description: The number of months per year.
                                                                                                                                                                                      Present In 1 View:
                                                                                                                                                                                      Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      HeatPumpModel_v31 #233
                                                                                                                                                                                      F,A
                                                                                                                                                                                      Net Change in Homes Retrofitting (Houses / Year)
                                                                                                                                                                                      Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] = (
                                                                                                                                                                                      Indicated Homes Retrofitting[ Cohort, Heating and Cooling System]- Housing[ Cohort, Heating and Cooling System,Open to Retrofitting])/ Time to Decide to Retrofit
                                                                                                                                                                                      Description: Homes that are in the process of deciding to retrofit.
                                                                                                                                                                                      Present In 3 Views: Used By
                                                                                                                                                                                      • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                      • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                      • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                      • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                      Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [2,2]
                                                                                                                                                                                      HeatPumpModel_v31 #234
                                                                                                                                                                                      F,A
                                                                                                                                                                                      Net U Value Change from Retrofitting Home Shifts (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                      Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                      Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, U Value by Grouping[ Cohort, Heating and Cooling System,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                      Description: Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                      • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                      Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                      HeatPumpModel_v31 #235
                                                                                                                                                                                      C
                                                                                                                                                                                      No Turnover Switch (dmnl )
                                                                                                                                                                                      = 0
                                                                                                                                                                                      Description: Switch for having no turnover in housing stock-- i.e., no housing demolitions or constructions.
                                                                                                                                                                                      Present In 1 View:
                                                                                                                                                                                      Used By
                                                                                                                                                                                      • Demolitions Homes that are destroyed every year.
                                                                                                                                                                                      • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      .housingagingchain v18 #253
                                                                                                                                                                                      A
                                                                                                                                                                                      Optimal U for New Homes (kBTU / (sf * Year * F))
                                                                                                                                                                                      Optimal U for New Homes[Cohort,Heating and Cooling System] = ((
                                                                                                                                                                                      Expected Reference Marginal Cost/( Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]/ Discount Rate))^(1/ Sensitivity of Marginal Cost to U Value))* Reference U Value*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)
                                                                                                                                                                                      Description: The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                      Present In 2 Views: Used By
                                                                                                                                                                                      • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                      • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      .housingagingchain v4 testing #254
                                                                                                                                                                                      A
                                                                                                                                                                                      Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                                                      Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                                                      Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                      Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                      Present In 8 Views: Used By
                                                                                                                                                                                      • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                      • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                      • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                      • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                      • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                      • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                      • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                      • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                      • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      HeatPumpModel_v31 #263
                                                                                                                                                                                      A
                                                                                                                                                                                      Perceived Cost of Retrofitting (Dollar / (House * Year))
                                                                                                                                                                                      Perceived Cost of Retrofitting[Cohort,Heating and Cooling System] = (1-
                                                                                                                                                                                      Weight on Upfront Cost)* Total Cost of Ownership of Retrofitted Homes[ Cohort, Heating and Cooling System]+ Weight on Upfront Cost* Amoritized Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]
                                                                                                                                                                                      Description: Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      .housingagingchain v15 #271
                                                                                                                                                                                      C
                                                                                                                                                                                      Proportional MassSave Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                      = 2020
                                                                                                                                                                                      Description: Time at which the proportional subsidy will take effect.
                                                                                                                                                                                      Present In 2 Views:
                                                                                                                                                                                      Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      .housingagingchain v5 testing #283
                                                                                                                                                                                      C
                                                                                                                                                                                      Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )
                                                                                                                                                                                      = 12.88
                                                                                                                                                                                      Description: The marginal cost of retrofitting at the reference EUI. In particular, the marginal cost of retrofitting at some EUI is Reference U *( (Reference U / U) ^ Sensitivity )This was calculated by setting sensitivity of marginal cost equal to 1.25, and finding the MC where a 31% reduction in U value from the reference costs a total of 4.95 / (1 - 0.21) dollars per square foot. The sensitivity value is explained in the sensitivity variable. Less et al. (2021, pg. 17-18) note that in their project database, the median cost per square foot for retrofits after subsidies was $4.95, while subsidies accounted for 21% of the total project cost for the median project. The median cost reduced energy use by 28% - 33% (of which I took the average), and I use the lower bound value to account for the fact that energy savings may occur not only due to increase in U value.Obviously all of this is extraordinarily rough.Less et al. (2021): https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
                                                                                                                                                                                      Present In 2 Views:
                                                                                                                                                                                      Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      HeatPumpModel_v31 #284
                                                                                                                                                                                      C
                                                                                                                                                                                      Reference Retrofit Cost (Dollar / (House * Year) )
                                                                                                                                                                                      = 8740
                                                                                                                                                                                      Description: Perceived cost of home heating to which households compare the perceived cost of retrofitting to when deciding to retrofit.Taken from average retrofit cost in Less et al. (2021)'s dataset, shown on page 17: https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
                                                                                                                                                                                      Present In 2 Views:
                                                                                                                                                                                      Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      HeatPumpModel_v31 #286
                                                                                                                                                                                      C
                                                                                                                                                                                      Retrofit Delay (Year )
                                                                                                                                                                                      = 2
                                                                                                                                                                                      Description: Time to retrofit. Assumed to be on average six months.
                                                                                                                                                                                      Present In 2 Views:
                                                                                                                                                                                      Used By
                                                                                                                                                                                      • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                      • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                      HeatPumpModel_v31 #288
                                                                                                                                                                                      F,A
                                                                                                                                                                                      Retrofitting (House * kBTU / (sf * F* Year) / Year)
                                                                                                                                                                                      Retrofitting[Cohort,Heating and Cooling System] = MAX(0,
                                                                                                                                                                                      Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]*( U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]- Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])/ Retrofit Delay)
                                                                                                                                                                                      Description: Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                      HeatPumpModel_v31 #287
                                                                                                                                                                                      A
                                                                                                                                                                                      Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
                                                                                                                                                                                      = SUM(
                                                                                                                                                                                      Retrofitting[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                                      Description: The total amount of retrofits across all cohorts and heating/cooling systems.
                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                        .housingagingchain v5 testing #291
                                                                                                                                                                                        C
                                                                                                                                                                                        Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                                                                                                                        = 3.25
                                                                                                                                                                                        Description: Measures the sensitivity of marginal retrofit costs as a function of optimal U value. In particular, marginal Retrofit Cost is equal to Constant * (U Value retrofitted away ^ Convexity). This must be greater than 1.This is taken from pg. 69 of Caswell (2022), where she calculates the total retrofit cost curve as a function of percent savings as having an exponent of 2.25. Because this is the total retrofit cost curve, the exponent for the marginal cost is -2.25 - 1. Because percent savings is inversely proportional to U, the exponent in the total cost curve will be the negation of 2.25, which is ensured in the marginal cost curve formulation in other variables.
                                                                                                                                                                                        Present In 4 Views:
                                                                                                                                                                                        Used By
                                                                                                                                                                                        • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                        • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                        • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                        • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                        • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                        • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                        • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                        HeatPumpModel_v31 #292
                                                                                                                                                                                        C
                                                                                                                                                                                        Sensitivity of Retrofits to Cost (dmnl )
                                                                                                                                                                                        = 10
                                                                                                                                                                                        Description: Sensitivity of affinity (and fraction of houses retrofitting) to NPV of retrofitting.
                                                                                                                                                                                        Present In 2 Views:
                                                                                                                                                                                        Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                        HeatPumpModel_v31 #305
                                                                                                                                                                                        C
                                                                                                                                                                                        System Switching SWITCH (dmnl )
                                                                                                                                                                                        = 1
                                                                                                                                                                                        Description: Switch for allowing houses to switch heating and cooling systems. If 1, they can switch.
                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                        Used By
                                                                                                                                                                                        • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                        HeatPumpModel_v31 #307
                                                                                                                                                                                        C
                                                                                                                                                                                        Time to Decide to Retrofit (Year )
                                                                                                                                                                                        = 3
                                                                                                                                                                                        Description: Time to decide to retrofit.
                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                        Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                        HeatPumpModel_v31 #313
                                                                                                                                                                                        A
                                                                                                                                                                                        Total Cost of Ownership of Average Home (Dollar / (Year * House))
                                                                                                                                                                                        Total Cost of Ownership of Average Home[Cohort,Heating and Cooling System] =
                                                                                                                                                                                        Average Energy Costs for Retrofitting Home[ Cohort, Heating and Cooling System]
                                                                                                                                                                                        Description: Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                        Present In 2 Views: Used By
                                                                                                                                                                                        • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                        HeatPumpModel_v31 #316
                                                                                                                                                                                        A
                                                                                                                                                                                        Total Heat Pump Sales (House / Year)
                                                                                                                                                                                        = SUM(
                                                                                                                                                                                        Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump Only]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Gas]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Oil])
                                                                                                                                                                                        Description: Number of houses buying heat pumps every year.
                                                                                                                                                                                        Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                        HeatPumpModel_v31 #321
                                                                                                                                                                                        C
                                                                                                                                                                                        Total Initial Homes (Houses )
                                                                                                                                                                                        = 20
                                                                                                                                                                                        Description: Total number of houses, including those retrofitting or not. Number taken from Census's list of households in MA in 2022: https://www.census.gov/quickfacts/fact/table/MA/PST045222
                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                        Used By
                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                          HeatPumpModel_v31 #327
                                                                                                                                                                                          L
                                                                                                                                                                                          Total U Value (House * kBTU / (Year * F * sf) )
                                                                                                                                                                                          Total U Value[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                                                          Increase in U Value from Housing Starts[ Cohort, Heating and Cooling System]- Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System])- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Not Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Not Open to Retrofitting])) dt + Initial U Value[ Cohort, Heating and Cooling System,Not Open to Retrofitting]
                                                                                                                                                                                          Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] = ((( Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System]- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Open to Retrofitting])))- Retrofitting[ Cohort, Heating and Cooling Systemdt + Initial U Value[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                          Description: Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                          HeatPumpModel_v31 #329
                                                                                                                                                                                          A
                                                                                                                                                                                          U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                                          U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                          Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                                          Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                          Present In 8 Views: Used By
                                                                                                                                                                                          • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                          • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                          • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                          • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                          • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                          • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                          • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                          • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                          • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                          • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                          • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                          • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                          • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                          Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                          HeatPumpModel_v31 #331
                                                                                                                                                                                          F,A
                                                                                                                                                                                          U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                          U Value Loss from Demolition[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                          U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Demolitions[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                          Description: Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                          • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                          Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                          .housingagingchain v18 #332
                                                                                                                                                                                          A
                                                                                                                                                                                          U Value of Housing Starts (kBTU / (Year * F * sf))
                                                                                                                                                                                          U Value of Housing Starts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                          Additional Cost of Building to U Value[ Cohort, Heating and Cooling System]<0:AND: Optimal U for New Homes[ Cohort, Heating and Cooling System]< Code U, Optimal U for New Homes[ Cohort, Heating and Cooling System], Code U)
                                                                                                                                                                                          Description: Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                          HeatPumpModel_v31 #334
                                                                                                                                                                                          L
                                                                                                                                                                                          U Value Retrofitted Away (House * kBTU / (Year * F * sf))
                                                                                                                                                                                          = SUM(
                                                                                                                                                                                          Retrofitting[ Cohort!, Heating and Cooling System!]) dt + 0.0
                                                                                                                                                                                          Description: Total amount of U value that has been retrofitted away.
                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            HeatPumpModel_v31 #335
                                                                                                                                                                                            F,A
                                                                                                                                                                                            U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                            U Value Shift from Source Switching[Cohort,Heat Pump Heating and Cooling,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                            Houses Switching Sources[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]
                                                                                                                                                                                            U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] = Houses Switching Sources[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Fossil Fuel Heating, Retrofitting Status]
                                                                                                                                                                                            Description: The shift in total U value coming from switching sources.
                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                            • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                            • U Value Increase from Source Switching The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v8 #339
                                                                                                                                                                                            A
                                                                                                                                                                                            Unsubsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                            Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                            Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort,Open to Retrofitting]
                                                                                                                                                                                            Description: Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                            Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v5 testing #338
                                                                                                                                                                                            A
                                                                                                                                                                                            Unsubsidized Retrofit Cost Intensity (Dollar / sf)
                                                                                                                                                                                            Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] = MAX(IF THEN ELSE(
                                                                                                                                                                                            U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06,( Expected Reference Marginal Cost* Reference U Value/(- Sensitivity of Marginal Cost to U Value+1))*((( Reference U Value/ U Value of Retrofitting Homes[ Cohort, Heating and Cooling System])^ Sensitivity of Marginal Cost to U Value-1)-(( Reference U Value/ Optimal U Value for Existing Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value-1)))+ Fixed Cost per Unit Area[ Cohort],0),0)
                                                                                                                                                                                            Description: Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                            Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            HeatPumpModel_v31 #340
                                                                                                                                                                                            C
                                                                                                                                                                                            Weight on Upfront Cost (dmnl )
                                                                                                                                                                                            = 0.5
                                                                                                                                                                                            Description: How much homeowners weigh upfront (amoritized) costs of retrofits as opposed to the total cost of ownership due to being more perceptive of short-term costs.
                                                                                                                                                                                            Present In 2 Views:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                            • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .Control #196
                                                                                                                                                                                            C
                                                                                                                                                                                            INITIAL TIME (Year)
                                                                                                                                                                                            = 2020
                                                                                                                                                                                            Description: The initial time for the simulation.
                                                                                                                                                                                            Present In 3 Views:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                            • Average Area of Housing Starts The average area of housing starts.
                                                                                                                                                                                            • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            (View) Input Test (59 Variables)
                                                                                                                                                                                            Top (View) Input Test (59 Variables)
                                                                                                                                                                                            Group
                                                                                                                                                                                            Type
                                                                                                                                                                                            Variable Name And Description
                                                                                                                                                                                            .housingagingchain v8 #24
                                                                                                                                                                                            L
                                                                                                                                                                                            Autocorrelated Noise (Dimensionless)
                                                                                                                                                                                            =
                                                                                                                                                                                            Change in AC Noise dt + 0.0
                                                                                                                                                                                            Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                            • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                            • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                            .housingagingchain v8 #22
                                                                                                                                                                                            L
                                                                                                                                                                                            Autocorrelated Noise 0 (Dimensionless)
                                                                                                                                                                                            =
                                                                                                                                                                                            Change in AC Noise 0 dt + 0.0
                                                                                                                                                                                            Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                            • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                            HeatPumpModel_v31 #23
                                                                                                                                                                                            L
                                                                                                                                                                                            Autocorrelated Noise 1 (Dimensionless)
                                                                                                                                                                                            =
                                                                                                                                                                                            Change in AC Noise 1 dt + 0.0
                                                                                                                                                                                            Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                            • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                            .housingagingchain v8 #64
                                                                                                                                                                                            F,A
                                                                                                                                                                                            Change in AC Noise (1/Year)
                                                                                                                                                                                            = (
                                                                                                                                                                                            White Noise- Autocorrelated Noise)/ Noise Correlation Time
                                                                                                                                                                                            Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                            • Autocorrelated Noise First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                            .housingagingchain v8 #62
                                                                                                                                                                                            F,A
                                                                                                                                                                                            Change in AC Noise 0 (1/Year)
                                                                                                                                                                                            = (
                                                                                                                                                                                            White Noise 0- Autocorrelated Noise 0)/ Noise Correlation Time 0
                                                                                                                                                                                            Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                            • Autocorrelated Noise 0 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                            HeatPumpModel_v31 #63
                                                                                                                                                                                            F,A
                                                                                                                                                                                            Change in AC Noise 1 (1/Year)
                                                                                                                                                                                            = (
                                                                                                                                                                                            White Noise 1- Autocorrelated Noise 1)/ Noise Correlation Time 1
                                                                                                                                                                                            Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                            • Autocorrelated Noise 1 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                            HeatPumpModel_v31 #70
                                                                                                                                                                                            A
                                                                                                                                                                                            Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                            =
                                                                                                                                                                                            Initial Cooling Energy Price* Input 1
                                                                                                                                                                                            Description: Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                            Present In 3 Views: Used By
                                                                                                                                                                                            • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            HeatPumpModel_v31 #69
                                                                                                                                                                                            C
                                                                                                                                                                                            Cooling Energy Price Step Height 1 (Dimensionless )
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: Height of step input to customer orders, as fraction of initial value.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v8 #100
                                                                                                                                                                                            C
                                                                                                                                                                                            Energy Price Exponential Growth Rate (1/Year )
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: The exogenous growth fraction for the test input.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            HeatPumpModel_v31 #99
                                                                                                                                                                                            C
                                                                                                                                                                                            Energy Price Exponential Growth Rate 1 (1/Year )
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: The exogenous growth fraction for the test input.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v8 #102
                                                                                                                                                                                            C
                                                                                                                                                                                            Energy Price Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: The quantity to be injected to customer orders, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            HeatPumpModel_v31 #101
                                                                                                                                                                                            C
                                                                                                                                                                                            Energy Price Pulse Quantity 1 (Dimensionless*Year)
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: Pulse value, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v8 #104
                                                                                                                                                                                            C
                                                                                                                                                                                            Energy Price Ramp Slope (1/Year )
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            HeatPumpModel_v31 #103
                                                                                                                                                                                            C
                                                                                                                                                                                            Energy Price Ramp Slope 1 (1/Year )
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v8 #105
                                                                                                                                                                                            C
                                                                                                                                                                                            Energy Price Step Height (Dimensionless )
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: Height of step input to customer orders, as fraction of initial value.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v5 testing #143
                                                                                                                                                                                            A
                                                                                                                                                                                            Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                            Heating Energy Price[Heating and Cooling System] =
                                                                                                                                                                                            Initial Heating Energy Price[ Heating and Cooling System]* Input 0
                                                                                                                                                                                            Description: The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                            Present In 6 Views: Used By
                                                                                                                                                                                            • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v8 #168
                                                                                                                                                                                            C
                                                                                                                                                                                            Housing Starts Exponential Growth Rate (1/Year )
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: The exogenous growth fraction for the test input.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v8 #170
                                                                                                                                                                                            C
                                                                                                                                                                                            Housing Starts Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: The quantity to be injected to customer orders, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v8 #171
                                                                                                                                                                                            C
                                                                                                                                                                                            Housing Starts Ramp Slope (1/Year )
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v8 #172
                                                                                                                                                                                            C
                                                                                                                                                                                            Housing Starts Step Height (Dimensionless )
                                                                                                                                                                                            = 0
                                                                                                                                                                                            Description: Height of step input to customer orders, as fraction of initial value.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            HeatPumpModel_v31 #189
                                                                                                                                                                                            C
                                                                                                                                                                                            Initial Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                            = 0.062
                                                                                                                                                                                            Description: The price to cool a home per BTU. This is the price of electricity as all cooling systems, as air conditioning systems, use electricity.
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Cooling Energy Price Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            .housingagingchain v5 testing #191
                                                                                                                                                                                            C
                                                                                                                                                                                            Initial Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                            Initial Heating Energy Price[Heat Pump Heating and Cooling] = 0.062
                                                                                                                                                                                            Initial Heating Energy Price[Gas Heating] = 0.0142
                                                                                                                                                                                            Initial Heating Energy Price[Oil Heating] = 0.017
                                                                                                                                                                                            Description: Price of energy used in each technology: heat pump, central AC, window AC, no AC, gas, and oil. For heat pumps and air conditioners, this is electricity.Data from (using annual 2020 data for MA):electricity: https://www.eia.gov/electricity/data/browser/#/topic/7?agg=1,0&geo=vvvvvvvvvvvvo&endsec=8&freq=M&start=200101&ctype=linechart&ltype=pin&rtype=s&pin=&rse=0&maptype=0,natural gas:https://www.eia.gov/dnav/ng/ng_pri_sum_a_EPG0_PRS_DMcf_a.htmheating oil: https://www.eia.gov/petroleum/heatingoilpropane/
                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                            Used By
                                                                                                                                                                                            • Heating Energy Price The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                            . #194
                                                                                                                                                                                            A
                                                                                                                                                                                            Initial Housing Starts (House/Year)
                                                                                                                                                                                            Initial Housing Starts[Heating and Cooling System] =
                                                                                                                                                                                            Total Initial Housing Starts/ELMCOUNT( Heating and Cooling System)
                                                                                                                                                                                            Description: Initial value of housing starts, initialized at 10 total houses.
                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                              .housingagingchain v8 #200
                                                                                                                                                                                              A
                                                                                                                                                                                              Input (Dimensionless)
                                                                                                                                                                                              = 1+STEP(
                                                                                                                                                                                              Housing Starts Step Height, INITIAL TIME+ Step Time)+( Housing Starts Pulse Quantity/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time, TIME STEP)+RAMP( Housing Starts Ramp Slope, INITIAL TIME+ Ramp Start Time, INITIAL TIME+ Ramp End Time)+(STEP(1, INITIAL TIME)*(exp( Housing Starts Exponential Growth Rate*( Time- INITIAL TIME))-1))+ Sine Amplitude*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period)+STEP(1, INITIAL TIME+ Noise Start Time)* Autocorrelated Noise
                                                                                                                                                                                              Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #198
                                                                                                                                                                                                A
                                                                                                                                                                                                Input 0 (Dimensionless)
                                                                                                                                                                                                = 1+STEP(
                                                                                                                                                                                                Energy Price Step Height, INITIAL TIME+ Step Time 0)+( Energy Price Pulse Quantity/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time 0, TIME STEP)+RAMP( Energy Price Ramp Slope, INITIAL TIME+ Ramp Start Time 0, INITIAL TIME+ Ramp End Time 0)+(STEP(1, INITIAL TIME)*(exp( Energy Price Exponential Growth Rate*( Time- INITIAL TIME))-1))+ Sine Amplitude 0*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period 0)+STEP(1, INITIAL TIME+ Noise Start Time 0)* Autocorrelated Noise 0
                                                                                                                                                                                                Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                • Heating Energy Price The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #199
                                                                                                                                                                                                A
                                                                                                                                                                                                Input 1 (Dimensionless)
                                                                                                                                                                                                = 1+STEP(
                                                                                                                                                                                                Cooling Energy Price Step Height 1, INITIAL TIME+ Step Time 1)+( Energy Price Pulse Quantity 1/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time 1, TIME STEP)+RAMP( Energy Price Ramp Slope 1, INITIAL TIME+ Ramp Start Time 1, INITIAL TIME+ Ramp End Time 1)+(STEP(1, INITIAL TIME)*(exp( Energy Price Exponential Growth Rate 1*( Time- INITIAL TIME))-1))+ Sine Amplitude 1*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period 1)+STEP(1, INITIAL TIME+ Noise Start Time 1)* Autocorrelated Noise 1
                                                                                                                                                                                                Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                • Cooling Energy Price Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #238
                                                                                                                                                                                                C
                                                                                                                                                                                                Noise Correlation Time (Year)
                                                                                                                                                                                                = 4
                                                                                                                                                                                                Description: The correlation time constant for Pink Noise.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                • White Noise White noise input to the pink noise process.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #236
                                                                                                                                                                                                C
                                                                                                                                                                                                Noise Correlation Time 0 (Year)
                                                                                                                                                                                                = 4
                                                                                                                                                                                                Description: The correlation time constant for Pink Noise.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                • White Noise 0 White noise input to the pink noise process.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #237
                                                                                                                                                                                                C
                                                                                                                                                                                                Noise Correlation Time 1 (Year)
                                                                                                                                                                                                = 4
                                                                                                                                                                                                Description: The correlation time constant for Pink Noise.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                • White Noise 1 White noise input to the pink noise process.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #241
                                                                                                                                                                                                C
                                                                                                                                                                                                Noise Standard Deviation (Dimensionless)
                                                                                                                                                                                                = 0
                                                                                                                                                                                                Description: The standard deviation of the pink noise process.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • White Noise White noise input to the pink noise process.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #239
                                                                                                                                                                                                C
                                                                                                                                                                                                Noise Standard Deviation 0 (Dimensionless)
                                                                                                                                                                                                = 0
                                                                                                                                                                                                Description: The standard deviation of the pink noise process.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #240
                                                                                                                                                                                                C
                                                                                                                                                                                                Noise Standard Deviation 1 (Dimensionless)
                                                                                                                                                                                                = 0
                                                                                                                                                                                                Description: The standard deviation of the pink noise process.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #244
                                                                                                                                                                                                C
                                                                                                                                                                                                Noise Start Time (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Start time for the random input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #242
                                                                                                                                                                                                C
                                                                                                                                                                                                Noise Start Time 0 (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Start time for the random input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #243
                                                                                                                                                                                                C
                                                                                                                                                                                                Noise Start Time 1 (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Start time for the random input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #275
                                                                                                                                                                                                C
                                                                                                                                                                                                Pulse Time (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Time at which the pulse in Input occurs.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #273
                                                                                                                                                                                                C
                                                                                                                                                                                                Pulse Time 0 (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Time at which the pulse in Input occurs.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #274
                                                                                                                                                                                                C
                                                                                                                                                                                                Pulse Time 1 (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Time at which the pulse in Input occurs.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #278
                                                                                                                                                                                                C
                                                                                                                                                                                                Ramp End Time (Year)
                                                                                                                                                                                                = 1e+09
                                                                                                                                                                                                Description: End time for the ramp input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #276
                                                                                                                                                                                                C
                                                                                                                                                                                                Ramp End Time 0 (Year)
                                                                                                                                                                                                = 1e+09
                                                                                                                                                                                                Description: End time for the ramp input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #277
                                                                                                                                                                                                C
                                                                                                                                                                                                Ramp End Time 1 (Year)
                                                                                                                                                                                                = 1e+09
                                                                                                                                                                                                Description: End time for the ramp input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #281
                                                                                                                                                                                                C
                                                                                                                                                                                                Ramp Start Time (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Start time for the ramp input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #279
                                                                                                                                                                                                C
                                                                                                                                                                                                Ramp Start Time 0 (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Start time for the ramp input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #280
                                                                                                                                                                                                C
                                                                                                                                                                                                Ramp Start Time 1 (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Start time for the ramp input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #295
                                                                                                                                                                                                C
                                                                                                                                                                                                Sine Amplitude (Dimensionless)
                                                                                                                                                                                                = 0
                                                                                                                                                                                                Description: Amplitude of sine wave in customer orders (fraction of mean).
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #293
                                                                                                                                                                                                C
                                                                                                                                                                                                Sine Amplitude 0 (Dimensionless)
                                                                                                                                                                                                = 0
                                                                                                                                                                                                Description: Amplitude of sine wave in customer orders (fraction of mean).
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #294
                                                                                                                                                                                                C
                                                                                                                                                                                                Sine Amplitude 1 (Dimensionless)
                                                                                                                                                                                                = 0
                                                                                                                                                                                                Description: Amplitude of sine wave in customer orders (fraction of mean).
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #298
                                                                                                                                                                                                C
                                                                                                                                                                                                Sine Period (Year)
                                                                                                                                                                                                = 50
                                                                                                                                                                                                Description: Period of sine wave in customer demand. Set initially to 50 weeks (1 year).
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #296
                                                                                                                                                                                                C
                                                                                                                                                                                                Sine Period 0 (Year)
                                                                                                                                                                                                = 50
                                                                                                                                                                                                Description: Period of sine wave in customer demand. Set initially to 50 weeks (1 year).
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #297
                                                                                                                                                                                                C
                                                                                                                                                                                                Sine Period 1 (Year)
                                                                                                                                                                                                = 50
                                                                                                                                                                                                Description: Period of sine wave. Set initially to 50 weeks (1 year).
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #302
                                                                                                                                                                                                C
                                                                                                                                                                                                Step Time (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Time for the step input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #300
                                                                                                                                                                                                C
                                                                                                                                                                                                Step Time 0 (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Time for the step input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #301
                                                                                                                                                                                                C
                                                                                                                                                                                                Step Time 1 (Year)
                                                                                                                                                                                                = 5
                                                                                                                                                                                                Description: Time for the step input.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #322
                                                                                                                                                                                                C
                                                                                                                                                                                                Total Initial Housing Starts (Houses / Year )
                                                                                                                                                                                                = 0.5
                                                                                                                                                                                                Description: Total number of houses that are built per year, across all systems.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #343
                                                                                                                                                                                                A
                                                                                                                                                                                                White Noise (Dimensionless)
                                                                                                                                                                                                =
                                                                                                                                                                                                Noise Standard Deviation*((24* Noise Correlation Time/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                                                                                                                                Description: White noise input to the pink noise process.
                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v8 #341
                                                                                                                                                                                                A
                                                                                                                                                                                                White Noise 0 (Dimensionless)
                                                                                                                                                                                                =
                                                                                                                                                                                                Noise Standard Deviation 0*((24* Noise Correlation Time 0/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                                                                                                                                Description: White noise input to the pink noise process.
                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #342
                                                                                                                                                                                                A
                                                                                                                                                                                                White Noise 1 (Dimensionless)
                                                                                                                                                                                                =
                                                                                                                                                                                                Noise Standard Deviation 1*((24* Noise Correlation Time 1/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                                                                                                                                Description: White noise input to the pink noise process.
                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .Control #196
                                                                                                                                                                                                C
                                                                                                                                                                                                INITIAL TIME (Year)
                                                                                                                                                                                                = 2020
                                                                                                                                                                                                Description: The initial time for the simulation.
                                                                                                                                                                                                Present In 3 Views:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                                • Average Area of Housing Starts The average area of housing starts.
                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .Control #306
                                                                                                                                                                                                C
                                                                                                                                                                                                TIME STEP (Year )
                                                                                                                                                                                                = 0.03125
                                                                                                                                                                                                Description: The time step for the simulation.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                • SAVEPER The frequency with which output is stored.
                                                                                                                                                                                                • White Noise White noise input to the pink noise process.
                                                                                                                                                                                                • White Noise 0 White noise input to the pink noise process.
                                                                                                                                                                                                • White Noise 1 White noise input to the pink noise process.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                (View) Optimal U & Retrofit Costs (42 Variables)
                                                                                                                                                                                                Top (View) Optimal U & Retrofit Costs (42 Variables)
                                                                                                                                                                                                Group
                                                                                                                                                                                                Type
                                                                                                                                                                                                Variable Name And Description
                                                                                                                                                                                                HeatPumpModel_v31 #11
                                                                                                                                                                                                C
                                                                                                                                                                                                Amoritization Period (Year )
                                                                                                                                                                                                = 20
                                                                                                                                                                                                Description: Time period over which incurred retrofit cost is amoritized; should be related to lifetime of a home.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                .housingagingchain v15 #12
                                                                                                                                                                                                A
                                                                                                                                                                                                Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))
                                                                                                                                                                                                Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]/ Amoritization Period
                                                                                                                                                                                                Description: The incurred total retrofit cost amoritized over the specified amoritization period.
                                                                                                                                                                                                Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #29
                                                                                                                                                                                                A
                                                                                                                                                                                                Average Area (sf / House)
                                                                                                                                                                                                Average Area[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                                                                                                                Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                                                                                                                Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                Present In 7 Views: Used By
                                                                                                                                                                                                • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                                                                • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                HeatPumpModel_v31 #52
                                                                                                                                                                                                C
                                                                                                                                                                                                Average Income (Dollar / Hour / House )
                                                                                                                                                                                                = 55
                                                                                                                                                                                                Description: The average income of single family homeowners in Massachusetts. Calculated from 2020 EIA RECS data for MA SFH, where each individual was assigned the average income of their reported income bracket, other than those making more than $150K/year, who were assigned $175,000. Hourly wage calculated by assuming working 8 hours a day, 5 days a week, for 50 weeks in a year.
                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                Used By
                                                                                                                                                                                                • Soft Costs of Retrofitting The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                HeatPumpModel_v31 #53
                                                                                                                                                                                                A
                                                                                                                                                                                                Average Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                = SUM(
                                                                                                                                                                                                Indicated Homes Retrofitting[ Cohort!, Heating and Cooling System!])/ Total Housing Stock
                                                                                                                                                                                                Description: The average fraction of homes that will retrofit retrofitting after decision delayacross all housing.
                                                                                                                                                                                                Present In 2 Views: Used By
                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                  HeatPumpModel_v31 #56
                                                                                                                                                                                                  A
                                                                                                                                                                                                  Average Subsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                  = SUM(
                                                                                                                                                                                                  Housing[ Cohort!, Heating and Cooling System!,Open to Retrofitting]* Subsidized Retrofit Cost[ Cohort!, Heating and Cooling System!])/SUM( Housing[ Cohort!, Heating and Cooling System!,Open to Retrofitting])
                                                                                                                                                                                                  Description: The average subsidized retrofit cost across all houses.
                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #67
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Cooling Degree Days (F )
                                                                                                                                                                                                    = 1029
                                                                                                                                                                                                    Description: The difference between temperature setpoint (65 F) and outside temperature for heating. Typically called cooling degree days, but units are solely in terms of fahrenheit.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. Use set point of 65°F, in line with industry standard, as at that temperature little heating or cooling is necessary.
                                                                                                                                                                                                    Present In 3 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #72
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Cooling System Efficiency (dmnl)
                                                                                                                                                                                                    Cooling System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                    Heat Pump Cooling COP TABLE( Time)
                                                                                                                                                                                                    Cooling System Efficiency[Central AC Cooling] = 2.93
                                                                                                                                                                                                    Cooling System Efficiency[Window AC Cooling] = 2.49* Effect of Air Leakage from Window AC on Efficiency
                                                                                                                                                                                                    Cooling System Efficiency[No AC Cooling] = NAREPLACEMENT
                                                                                                                                                                                                    Description: The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #90
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Discount Rate (1 / Year )
                                                                                                                                                                                                    = 0.05
                                                                                                                                                                                                    Description: Discount rate for discounting energy savings cash flows.Average and bounds from demand-side discount rate from MassDEP's analysis of pathways for net zero (pg. 103): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadhttps://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                    Present In 4 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #94
                                                                                                                                                                                                    C
                                                                                                                                                                                                    EEHIC Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                    = 2033
                                                                                                                                                                                                    Description: The year in which the EEHIC is phased out. If final time, then has no ending data.Source: https://www.irs.gov/credits-deductions/energy-efficient-home-improvement-credit
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #111
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Cooling Energy Price, Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                    Description: Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                    • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #112
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Implemented EEHIC Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                    Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #113
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Implemented EEHIC Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                    Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #114
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Fixed Cost (Dollar / House)
                                                                                                                                                                                                    = SMOOTH(
                                                                                                                                                                                                    Fixed Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                    Description: Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #115
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Heating Energy Price (Dollar / kBTU)
                                                                                                                                                                                                    Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                                                                                                                                                                    Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                    Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                    Present In 6 Views: Used By
                                                                                                                                                                                                    • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                    • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #119
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Implemented MassSave Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                    Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #121
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                    = SMOOTH(
                                                                                                                                                                                                    Reference Marginal Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                    Description: Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #123
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                    Energy Savings[ Cohort, Heating and Cooling System]>= HOMES Cut Off for Savings, HOMES Expected Higher Subsidy, HOMES Expected Lower Lump Sum Subsidy)+ MassSave Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]+ EEHIC Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                    Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #127
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Fixed Cost per Unit Area (Dollar / sf)
                                                                                                                                                                                                    Fixed Cost per Unit Area[Cohort] = ZIDZ(
                                                                                                                                                                                                    Expected Fixed Cost, Average Area[ Cohort,Open to Retrofitting])
                                                                                                                                                                                                    Description: The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #141
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Heating Degree Days (F )
                                                                                                                                                                                                    = 5026
                                                                                                                                                                                                    Description: The difference between temperature setpoint (65 F) and outside temperature.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. In line with industry standard, use set point of 65°F, as thattemperature little heating or cooling is needed.
                                                                                                                                                                                                    Present In 3 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #143
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                                    Heating Energy Price[Heating and Cooling System] =
                                                                                                                                                                                                    Initial Heating Energy Price[ Heating and Cooling System]* Input 0
                                                                                                                                                                                                    Description: The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                    Present In 6 Views: Used By
                                                                                                                                                                                                    • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #145
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Heating System Efficiency (dmnl)
                                                                                                                                                                                                    Heating System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                    Heat Pump Heating COP TABLE( Time)
                                                                                                                                                                                                    Heating System Efficiency[Gas Heating] = Gas COP TABLE( Time)
                                                                                                                                                                                                    Heating System Efficiency[Oil Heating] = Oil COP TABLE( Time)
                                                                                                                                                                                                    Description: The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                    Present In 3 Views: Used By
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #146
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Homeowner Hours Spent Retrofitting (Hour )
                                                                                                                                                                                                    = 750
                                                                                                                                                                                                    Description: The amount of hours a homeowners spends retrofitting their home themselves, i.e., the hours spent deciding to retrofit, supervising audits, moving out of the home as necessary, etc. No hard data on this, calibrated so that the initial fraction of homes willing to retrofit is 10%.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Soft Costs of Retrofitting The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #174
                                                                                                                                                                                                    L
                                                                                                                                                                                                    Housing (House)
                                                                                                                                                                                                    Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                                                                    Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                    Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                    Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                    Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                                                                                                                                                                    HeatPumpModel_v31 #209
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)
                                                                                                                                                                                                    Lifetime Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]/ Discount Rate
                                                                                                                                                                                                    Description: The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #210
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))
                                                                                                                                                                                                    Marginal Cooling Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Expected Cooling Energy Price* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Description: The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #211
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))
                                                                                                                                                                                                    Marginal Cost at Binding U Value without EEHIC[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Expected Reference Marginal Cost*(ZIDZ( Reference U Value, U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]))^ Sensitivity of Marginal Cost to U Value
                                                                                                                                                                                                    Description: This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #212
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)
                                                                                                                                                                                                    Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Marginal Cooling Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]+ Marginal Heating Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                    Description: Total cost reductions from retrofitting away one unit of U value for existing homes, including reductions in both heating and cooling costs.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #213
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))
                                                                                                                                                                                                    Marginal Heating Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Expected Heating Energy Price[ Heating and Cooling System]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Description: The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #255
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Optimal U Value for Existing Homes (kBTU / (sf * F * Year))
                                                                                                                                                                                                    Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                    U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]< Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System],IF THEN ELSE( Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]> Marginal Cost at Binding U Value without EEHIC[ Cohort, Heating and Cooling System], Optimal U Value with No EEHIC Proportional Subsidy[ Cohort, Heating and Cooling System], U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]))
                                                                                                                                                                                                    Description: This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v4 testing #254
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                                    Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    Present In 8 Views: Used By
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #256
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))
                                                                                                                                                                                                    Optimal U Value with No EEHIC Proportional Subsidy[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                                    Description: Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #269
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                                                                                                                                                                                                    Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                    = 2023
                                                                                                                                                                                                    Description: Time at which the proportional subsidy will take effect from the Energy Efficiency Home Improvement Credit.Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                    Present In 2 Views:
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                                                                                                                                                                                                    .housingagingchain v9 #285
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Reference U Value (kBTU / (sf * Year * F) )
                                                                                                                                                                                                    = 0.006
                                                                                                                                                                                                    Description: Reference U Value to ensure base of exponent in marginally optimal U value is dimensionless. This must be equal to or greater than code U value.Value taken as the average of U values of single family homes in MA in 2020 for our sample.
                                                                                                                                                                                                    Present In 3 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #291
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                                                                                                                                    = 3.25
                                                                                                                                                                                                    Description: Measures the sensitivity of marginal retrofit costs as a function of optimal U value. In particular, marginal Retrofit Cost is equal to Constant * (U Value retrofitted away ^ Convexity). This must be greater than 1.This is taken from pg. 69 of Caswell (2022), where she calculates the total retrofit cost curve as a function of percent savings as having an exponent of 2.25. Because this is the total retrofit cost curve, the exponent for the marginal cost is -2.25 - 1. Because percent savings is inversely proportional to U, the exponent in the total cost curve will be the negation of 2.25, which is ensured in the marginal cost curve formulation in other variables.
                                                                                                                                                                                                    Present In 4 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
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                                                                                                                                                                                                    HeatPumpModel_v31 #299
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Soft Costs of Retrofitting (Dollar / Home)
                                                                                                                                                                                                    =
                                                                                                                                                                                                    Average Income* Homeowner Hours Spent Retrofitting
                                                                                                                                                                                                    Description: The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
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                                                                                                                                                                                                    .housingagingchain v15 #304
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Subsidized Retrofit Cost (Dollar /House)
                                                                                                                                                                                                    Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]- Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System,Open to Retrofitting]+ Soft Costs of Retrofitting
                                                                                                                                                                                                    Description: The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #328
                                                                                                                                                                                                    A
                                                                                                                                                                                                    U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))
                                                                                                                                                                                                    U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                    U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06:AND: Expected EEHIC Proportional Subsidy Rate for Retrofits>1e-06, Reference U Value*(( Sensitivity of Marginal Cost to U Value-1)*((( Expected EEHIC Maximum Subsidy for Retrofits- Expected EEHIC Proportional Subsidy Rate for Retrofits* Expected Fixed Cost)/( U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]* Expected EEHIC Proportional Subsidy Rate for Retrofits* Expected Reference Marginal Cost* Average Area[ Cohort,Open to Retrofitting]))-(1/(- Sensitivity of Marginal Cost to U Value+1))*(( U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]/ Reference U Value)^(- Sensitivity of Marginal Cost to U Value+1)))^(1/(- Sensitivity of Marginal Cost to U Value+1))),0)
                                                                                                                                                                                                    Description: This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #329
                                                                                                                                                                                                    A
                                                                                                                                                                                                    U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                                                    U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                    Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                                                    Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                    Present In 8 Views: Used By
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                    • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                    • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                    • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                    • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                    Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                                    HeatPumpModel_v31 #333
                                                                                                                                                                                                    A
                                                                                                                                                                                                    U Value of Retrofitting Homes (kBTU / (sf * Year * F))
                                                                                                                                                                                                    U Value of Retrofitting Homes[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                    Description: The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v8 #339
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Unsubsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                    Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort,Open to Retrofitting]
                                                                                                                                                                                                    Description: Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                    Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #338
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Unsubsidized Retrofit Cost Intensity (Dollar / sf)
                                                                                                                                                                                                    Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] = MAX(IF THEN ELSE(
                                                                                                                                                                                                    U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06,( Expected Reference Marginal Cost* Reference U Value/(- Sensitivity of Marginal Cost to U Value+1))*((( Reference U Value/ U Value of Retrofitting Homes[ Cohort, Heating and Cooling System])^ Sensitivity of Marginal Cost to U Value-1)-(( Reference U Value/ Optimal U Value for Existing Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value-1)))+ Fixed Cost per Unit Area[ Cohort],0),0)
                                                                                                                                                                                                    Description: Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    (View) Perceived Subsidies & Costs (64 Variables)
                                                                                                                                                                                                    Top (View) Perceived Subsidies & Costs (64 Variables)
                                                                                                                                                                                                    Group
                                                                                                                                                                                                    Type
                                                                                                                                                                                                    Variable Name And Description
                                                                                                                                                                                                    HeatPumpModel_v31 #29
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Average Area (sf / House)
                                                                                                                                                                                                    Average Area[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                                                                                                                    Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                                                                                                                    Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                    Present In 7 Views: Used By
                                                                                                                                                                                                    • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                    • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                    • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                    Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                    HeatPumpModel_v31 #70
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                    =
                                                                                                                                                                                                    Initial Cooling Energy Price* Input 1
                                                                                                                                                                                                    Description: Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                                    Present In 3 Views: Used By
                                                                                                                                                                                                    • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #85
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Delay in Changing Subsidy Expectations (Year )
                                                                                                                                                                                                    = 0.5
                                                                                                                                                                                                    Description: Delay in perceiving any changes to subsidies. Assumed to be the same for both subsidies.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #86
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Delay in Forming Expectations of Energy Price (Year )
                                                                                                                                                                                                    = 1
                                                                                                                                                                                                    Description: Delay in perceiving changes in energy price.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                    • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #87
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Delay in Forming Expectations of Retrofit Costs (Year )
                                                                                                                                                                                                    = 1.5
                                                                                                                                                                                                    Description: Delay in perceiving changes in fixed retrofit cost and reference marginal cost. Assumed to be the same for both types of costs.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Expected Fixed Cost Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                    • Expected Reference Marginal Cost Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #90
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Discount Rate (1 / Year )
                                                                                                                                                                                                    = 0.05
                                                                                                                                                                                                    Description: Discount rate for discounting energy savings cash flows.Average and bounds from demand-side discount rate from MassDEP's analysis of pathways for net zero (pg. 103): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadhttps://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                    Present In 4 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #91
                                                                                                                                                                                                    A
                                                                                                                                                                                                    EEHIC Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = MIN(
                                                                                                                                                                                                    Proportional Subsidy Switch for Retrofits* Expected EEHIC Proportional Subsidy Rate for Retrofits* Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status], Expected EEHIC Maximum Subsidy for Retrofits)
                                                                                                                                                                                                    Description: The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #92
                                                                                                                                                                                                    C
                                                                                                                                                                                                    EEHIC Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                    = 1200
                                                                                                                                                                                                    Description: The maximum proportional subsidy that will be offered from Energy Efficient Home Improvement Credit, regardless of that subsidy's discount. Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #93
                                                                                                                                                                                                    C
                                                                                                                                                                                                    EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                    = 0.3
                                                                                                                                                                                                    Description: Proportion of total retrofit cost that will be credited with the Energy Efficiency Home Improvement Credit.Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Implemented EEHIC Subsidy Proportional Rate for Retrofits The implemented proportional subsidy rate for retrofits from the IRA, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #94
                                                                                                                                                                                                    C
                                                                                                                                                                                                    EEHIC Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                    = 2033
                                                                                                                                                                                                    Description: The year in which the EEHIC is phased out. If final time, then has no ending data.Source: https://www.irs.gov/credits-deductions/energy-efficient-home-improvement-credit
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #106
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Energy Savings (dmnl)
                                                                                                                                                                                                    Energy Savings[Cohort,Heating and Cooling System] = MAX(0,ABS(ZIDZ((
                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]- U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]), U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting])))
                                                                                                                                                                                                    Description: The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #111
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Cooling Energy Price, Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                    Description: Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                    • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #112
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Implemented EEHIC Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                    Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #113
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Implemented EEHIC Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                    Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #114
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Fixed Cost (Dollar / House)
                                                                                                                                                                                                    = SMOOTH(
                                                                                                                                                                                                    Fixed Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                    Description: Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #115
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Heating Energy Price (Dollar / kBTU)
                                                                                                                                                                                                    Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                                                                                                                                                                    Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                    Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                    Present In 6 Views: Used By
                                                                                                                                                                                                    • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                    • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #116
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    IRA Implemented Subsidy Proportional Rate for Heat Pumps, Delay in Changing Subsidy Expectations)* Proportional IRA Subsidy Switch for Heat Pumps
                                                                                                                                                                                                    Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #118
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Implemented MassSave Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                    Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #119
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Implemented MassSave Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                    Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #120
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Implemented IRA Maximum Proportional Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                    Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #121
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                    = SMOOTH(
                                                                                                                                                                                                    Reference Marginal Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                    Description: Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #122
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Expected Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                    =
                                                                                                                                                                                                    MassSave Expected Lump Sum Subsidy for Heat Pumps+ IRA Expected Proportional Subsidy for Heat Pumps
                                                                                                                                                                                                    Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidies.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #123
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                    Energy Savings[ Cohort, Heating and Cooling System]>= HOMES Cut Off for Savings, HOMES Expected Higher Subsidy, HOMES Expected Lower Lump Sum Subsidy)+ MassSave Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]+ EEHIC Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                    Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #128
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Fixed Cost (Dollar / House )
                                                                                                                                                                                                    = 0
                                                                                                                                                                                                    Description: Fixed cost of retrofitting, due to permitting, finding contractors, etc. This is not taken into account in the marginal cost of retrofitting, and this model assumes that households have not yet paid a fixed cost when deciding to retrofit. This cost only applies to existing housing.Set this equal to 0, because almost all costs for retrofits seem to be variable (except for permitting, which isn't usually used), and there's no data to suggest otherwise.
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Expected Fixed Cost Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #143
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                                    Heating Energy Price[Heating and Cooling System] =
                                                                                                                                                                                                    Initial Heating Energy Price[ Heating and Cooling System]* Input 0
                                                                                                                                                                                                    Description: The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                    Present In 6 Views: Used By
                                                                                                                                                                                                    • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #147
                                                                                                                                                                                                    C
                                                                                                                                                                                                    HOMES Cut Off for Savings (dmnl )
                                                                                                                                                                                                    = 0.35
                                                                                                                                                                                                    Description: The percent energy savings needed to get the higher subsidy amount from the Home Owner Managing Energy Savings rebate. Taken from: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #148
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    HOMES Expected Higher Subsidy (Dollar / House)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    HOMES Implemented High Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                    Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #149
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    HOMES Implemented Lower Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                    Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #150
                                                                                                                                                                                                    C
                                                                                                                                                                                                    HOMES High Subsidy Amount (Dollar / House )
                                                                                                                                                                                                    = 4000
                                                                                                                                                                                                    Description: The subsidy from the home owner managing energy savings rebate for retrofits saving more than 35% of energy.Source: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #151
                                                                                                                                                                                                    A
                                                                                                                                                                                                    HOMES Implemented High Subsidy (Dollar / House)
                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                    Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES High Subsidy Amount,0)
                                                                                                                                                                                                    Description: Implemented higher subsidy from the HOMES rebate program.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Actual HOMES Subsidy for Retrofits The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                                                                                                                                                                    • HOMES Expected Higher Subsidy Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #152
                                                                                                                                                                                                    A
                                                                                                                                                                                                    HOMES Implemented Lower Subsidy (Dollar / House)
                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                    Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES Lower Subsidy Amount,0)
                                                                                                                                                                                                    Description: Lump sum subsidy that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #153
                                                                                                                                                                                                    C
                                                                                                                                                                                                    HOMES Lower Subsidy Amount (Dollar / House )
                                                                                                                                                                                                    = 2000
                                                                                                                                                                                                    Description: The lump sum subsidy given for retrofits that save less than 35% of their energy from the Home Owner Managing Energy Savings tax credit.Source: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • HOMES Implemented Lower Subsidy Lump sum subsidy that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #154
                                                                                                                                                                                                    C
                                                                                                                                                                                                    HOMES Subsidy Final Year (Year)
                                                                                                                                                                                                    = 2032
                                                                                                                                                                                                    Description: Final year of Home Owner Managing Energy Savings rebate, assumed to be the same as that of the EEHIC.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #155
                                                                                                                                                                                                    C
                                                                                                                                                                                                    HOMES Subsidy Implementation Year (Year )
                                                                                                                                                                                                    = 2025
                                                                                                                                                                                                    Description: The year in which the lump sum subsidy will activate.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #175
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                    Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: Time<= EEHIC Subsidy for Retrofits Final Year, EEHIC Maximum Subsidy for Retrofits,0)
                                                                                                                                                                                                    Description: Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #176
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                    Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: EEHIC Subsidy for Retrofits Final Year>= Time, EEHIC Proportional Subsidy Rate for Retrofits,0)
                                                                                                                                                                                                    Description: The implemented proportional subsidy rate for retrofits from the IRA, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #177
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                    Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: Time<= IRA Lump Sum Subsidy for Heat Pumps Final Year, IRA Maximum Proportional Subsidy for Heat Pumps,0)
                                                                                                                                                                                                    Description: Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #178
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                    Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: Time<= MassSave Subsidy for Retrofits Final Year, MassSave Maximum Subsidy for Retrofits,0)
                                                                                                                                                                                                    Description: Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #179
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                    Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: MassSave Subsidy for Retrofits Final Year>= Time, Mass Save Proportional Subsidy Rate for Retrofits,0)
                                                                                                                                                                                                    Description: The implemented proportional subsidy rate from the state, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #202
                                                                                                                                                                                                    A
                                                                                                                                                                                                    IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                    = MIN(
                                                                                                                                                                                                    Proportional IRA Subsidy Switch for Heat Pumps* Expected IRA Proportional Subsidy Rate for Heat Pumps* Unsubsidized Cost of Heat Pumps, Expected Maximum IRA Proportional Subsidy for Heat Pumps)
                                                                                                                                                                                                    Description: The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect.
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #203
                                                                                                                                                                                                    A
                                                                                                                                                                                                    IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                    Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: IRA Lump Sum Subsidy for Heat Pumps Final Year>= Time, IRA Proportional Subsidy Rate for Heat Pumps,0)
                                                                                                                                                                                                    Description: The implemented proportional subsidy rate, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy rate afterwards.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #204
                                                                                                                                                                                                    C
                                                                                                                                                                                                    IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )
                                                                                                                                                                                                    = 2032
                                                                                                                                                                                                    Description: The year in which the subsidy is phased out. If final time, then has no ending date.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #205
                                                                                                                                                                                                    C
                                                                                                                                                                                                    IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )
                                                                                                                                                                                                    = 2000
                                                                                                                                                                                                    Description: The maximum proportional subsidy for heat pumps that will be offered, regardless of the subsidy rate. For instance, if the proportional subsidy is 50% but the maximum is $1000, then for a retrofit project that costs $3000 only a $1000 subsidy will be given.Taken from: https://www.energystar.gov/about/federal-tax-credits
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #206
                                                                                                                                                                                                    C
                                                                                                                                                                                                    IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                    = 2023
                                                                                                                                                                                                    Description: Time at which the proportional subsidy will take effect from the Inflation Reduction Act, from https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #207
                                                                                                                                                                                                    C
                                                                                                                                                                                                    IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
                                                                                                                                                                                                    = 0.3
                                                                                                                                                                                                    Description: Proportion of total heat pump cost that will be credited as part of a proportional subsidy.Taken from: https://www.energystar.gov/about/federal-tax-credits
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #214
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                    = 0.75
                                                                                                                                                                                                    Description: Proportion of total retrofit cost that will be credited as part of a proportional subsidy. Theoretically, this can vary between current housing and housing under construction.Based off Mass Save data: https://www.masssave.com/en/residential/rebates-and-incentives/insulation-and-windows/insulation-and-air-sealing
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #217
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    MassSave Implemented Lump Sum Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                    Description: Expected lump sum subsidy that lowers subsidized retrofit costs from the state, taking into account information delays.
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #218
                                                                                                                                                                                                    A
                                                                                                                                                                                                    MassSave Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = MIN(
                                                                                                                                                                                                    Proportional Subsidy Switch for Retrofits* Expected MassSave Proportional Subsidy Rate for Retrofits* Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status], Expected MassSave Maximum Subsidy for Retrofits)
                                                                                                                                                                                                    Description: The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #219
                                                                                                                                                                                                    A
                                                                                                                                                                                                    MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                    = MIN(
                                                                                                                                                                                                    Unsubsidized Cost of Heat Pumps,IF THEN ELSE( Time>= MassSave Lump Sum Subsidy Implementation Year for Heat Pumps:AND: Time<= MassSave Lump Sum Subsidy for Heat Pumps Final Year, MassSave Lump Sum Subsidy Amount for Heat Pumps,0))
                                                                                                                                                                                                    Description: Lump sum subsidy from MassSave that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #220
                                                                                                                                                                                                    C
                                                                                                                                                                                                    MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )
                                                                                                                                                                                                    = 10000
                                                                                                                                                                                                    Description: The total amount of money offered by the lump sum subsidy.Taken from: https://www.masssave.com/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #221
                                                                                                                                                                                                    C
                                                                                                                                                                                                    MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)
                                                                                                                                                                                                    = 2200
                                                                                                                                                                                                    Description: The year in which the state's subsidy for heat pumps is phased out.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #222
                                                                                                                                                                                                    C
                                                                                                                                                                                                    MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                    = 2020
                                                                                                                                                                                                    Description: The year in which the state's lump sum subsidy for heat pumps will activate.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #223
                                                                                                                                                                                                    C
                                                                                                                                                                                                    MassSave Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                    = 1e+07
                                                                                                                                                                                                    Description: The maximum proportional subsidy that will be offered, regardless of that subsidy's discount. For instance, if the proportional subsidy is 50% but the maximum is $1000, then for a retrofit project that costs $3000 only a $1000 subsidy will be given.If very large, then no maximum subsidy given.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #224
                                                                                                                                                                                                    A
                                                                                                                                                                                                    MassSave Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                    =
                                                                                                                                                                                                    FINAL TIME
                                                                                                                                                                                                    Description: The year in which the subsidy is phased out. If final time, then has no ending data.
                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v4 testing #254
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                                    Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    Present In 8 Views: Used By
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #269
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                    = 2023
                                                                                                                                                                                                    Description: Time at which the proportional subsidy will take effect from the Energy Efficiency Home Improvement Credit.Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #270
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
                                                                                                                                                                                                    = 1
                                                                                                                                                                                                    Description: Turns proportional subsidy's effect on retrofit cost on/off.
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #271
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Proportional MassSave Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                    = 2020
                                                                                                                                                                                                    Description: Time at which the proportional subsidy will take effect.
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #272
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Proportional Subsidy Switch for Retrofits (dmnl )
                                                                                                                                                                                                    = 1
                                                                                                                                                                                                    Description: Turns proportional subsidy's effect on retrofit cost on/off.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #283
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )
                                                                                                                                                                                                    = 12.88
                                                                                                                                                                                                    Description: The marginal cost of retrofitting at the reference EUI. In particular, the marginal cost of retrofitting at some EUI is Reference U *( (Reference U / U) ^ Sensitivity )This was calculated by setting sensitivity of marginal cost equal to 1.25, and finding the MC where a 31% reduction in U value from the reference costs a total of 4.95 / (1 - 0.21) dollars per square foot. The sensitivity value is explained in the sensitivity variable. Less et al. (2021, pg. 17-18) note that in their project database, the median cost per square foot for retrofits after subsidies was $4.95, while subsidies accounted for 21% of the total project cost for the median project. The median cost reduced energy use by 28% - 33% (of which I took the average), and I use the lower bound value to account for the fact that energy savings may occur not only due to increase in U value.Obviously all of this is extraordinarily rough.Less et al. (2021): https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #329
                                                                                                                                                                                                    A
                                                                                                                                                                                                    U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                                                    U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                    Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                                                    Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                    Present In 8 Views: Used By
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                    • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                    • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                    • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                    • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                    Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                                    HeatPumpModel_v31 #337
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Unsubsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                    =
                                                                                                                                                                                                    Unsubsidized Cost of Heat Pump Over Time TABLE( Time)
                                                                                                                                                                                                    Description: The unsubsidized cost of heat pumps, instantiated at each time.
                                                                                                                                                                                                    Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #338
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Unsubsidized Retrofit Cost Intensity (Dollar / sf)
                                                                                                                                                                                                    Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] = MAX(IF THEN ELSE(
                                                                                                                                                                                                    U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06,( Expected Reference Marginal Cost* Reference U Value/(- Sensitivity of Marginal Cost to U Value+1))*((( Reference U Value/ U Value of Retrofitting Homes[ Cohort, Heating and Cooling System])^ Sensitivity of Marginal Cost to U Value-1)-(( Reference U Value/ Optimal U Value for Existing Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value-1)))+ Fixed Cost per Unit Area[ Cohort],0),0)
                                                                                                                                                                                                    Description: Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .Control #126
                                                                                                                                                                                                    C
                                                                                                                                                                                                    FINAL TIME (Year)
                                                                                                                                                                                                    = 2050
                                                                                                                                                                                                    Description: The final time for the simulation.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    (View) Retrofitting Decision Making (23 Variables)
                                                                                                                                                                                                    Top (View) Retrofitting Decision Making (23 Variables)
                                                                                                                                                                                                    Group
                                                                                                                                                                                                    Type
                                                                                                                                                                                                    Variable Name And Description
                                                                                                                                                                                                    HeatPumpModel_v31 #6
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Affinity of Not Retrofitting (dmnl)
                                                                                                                                                                                                    Affinity of Not Retrofitting[Cohort,Heating and Cooling System] = exp(-
                                                                                                                                                                                                    Sensitivity of Retrofits to Cost* Perceived Cost of Not Retrofitting[ Cohort, Heating and Cooling System]/ Reference Retrofit Cost)
                                                                                                                                                                                                    Description: The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v4 testing #7
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Affinity of Retrofitting (dmnl)
                                                                                                                                                                                                    Affinity of Retrofitting[Cohort,Heating and Cooling System] = exp(-
                                                                                                                                                                                                    Sensitivity of Retrofits to Cost* Perceived Cost of Retrofitting[ Cohort, Heating and Cooling System]/ Reference Retrofit Cost)
                                                                                                                                                                                                    Description: Affinity of retrofitting, where utility value is equal to its NPV.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #12
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))
                                                                                                                                                                                                    Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]/ Amoritization Period
                                                                                                                                                                                                    Description: The incurred total retrofit cost amoritized over the specified amoritization period.
                                                                                                                                                                                                    Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #40
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Average Energy Cost (Dollar / (Year * House))
                                                                                                                                                                                                    Average Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                    Average Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                    Description: The average cost of both heating and cooling a home, by grouping.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #41
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Average Energy Costs for Retrofitting Home (Dollar / Year / House)
                                                                                                                                                                                                    Average Energy Costs for Retrofitting Home[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Average Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                    Description: Heating costs for each home open to retrofitting, annually, if no further retrofit measures are undertaken.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Total Cost of Ownership of Average Home Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v8 #42
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Average Energy Costs if Retrofitted (Dollar/(Year*House))
                                                                                                                                                                                                    Average Energy Costs if Retrofitted[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Optimal Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                    Description: Energy costs per year for each retrofitting house if homes retrofit to the optimal U value.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #121
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                    = SMOOTH(
                                                                                                                                                                                                    Reference Marginal Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                    Description: Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #123
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                    Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                    Energy Savings[ Cohort, Heating and Cooling System]>= HOMES Cut Off for Savings, HOMES Expected Higher Subsidy, HOMES Expected Lower Lump Sum Subsidy)+ MassSave Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]+ EEHIC Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                    Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #182
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                    Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Affinity of Retrofitting[ Cohort, Heating and Cooling System]/( Affinity of Retrofitting[ Cohort, Heating and Cooling System]+ Affinity of Not Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                    Description: Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #248
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Optimal Energy Cost (Dollar / (Year * House))
                                                                                                                                                                                                    Optimal Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                    Optimal Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Optimal Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                    Description: Total energy cost if optimal U value is achieved.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v4 testing #254
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                                    Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    Present In 8 Views: Used By
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #262
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Perceived Cost of Not Retrofitting (Dollar / (House * Year))
                                                                                                                                                                                                    Perceived Cost of Not Retrofitting[Cohort,Heating and Cooling System] = (1-
                                                                                                                                                                                                    Weight on Upfront Cost)* Total Cost of Ownership of Average Home[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                    Description: Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Affinity of Not Retrofitting The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #263
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Perceived Cost of Retrofitting (Dollar / (House * Year))
                                                                                                                                                                                                    Perceived Cost of Retrofitting[Cohort,Heating and Cooling System] = (1-
                                                                                                                                                                                                    Weight on Upfront Cost)* Total Cost of Ownership of Retrofitted Homes[ Cohort, Heating and Cooling System]+ Weight on Upfront Cost* Amoritized Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                    Description: Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #284
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Reference Retrofit Cost (Dollar / (House * Year) )
                                                                                                                                                                                                    = 8740
                                                                                                                                                                                                    Description: Perceived cost of home heating to which households compare the perceived cost of retrofitting to when deciding to retrofit.Taken from average retrofit cost in Less et al. (2021)'s dataset, shown on page 17: https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v9 #285
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Reference U Value (kBTU / (sf * Year * F) )
                                                                                                                                                                                                    = 0.006
                                                                                                                                                                                                    Description: Reference U Value to ensure base of exponent in marginally optimal U value is dimensionless. This must be equal to or greater than code U value.Value taken as the average of U values of single family homes in MA in 2020 for our sample.
                                                                                                                                                                                                    Present In 3 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #291
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                                                                                                                                    = 3.25
                                                                                                                                                                                                    Description: Measures the sensitivity of marginal retrofit costs as a function of optimal U value. In particular, marginal Retrofit Cost is equal to Constant * (U Value retrofitted away ^ Convexity). This must be greater than 1.This is taken from pg. 69 of Caswell (2022), where she calculates the total retrofit cost curve as a function of percent savings as having an exponent of 2.25. Because this is the total retrofit cost curve, the exponent for the marginal cost is -2.25 - 1. Because percent savings is inversely proportional to U, the exponent in the total cost curve will be the negation of 2.25, which is ensured in the marginal cost curve formulation in other variables.
                                                                                                                                                                                                    Present In 4 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #292
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Sensitivity of Retrofits to Cost (dmnl )
                                                                                                                                                                                                    = 10
                                                                                                                                                                                                    Description: Sensitivity of affinity (and fraction of houses retrofitting) to NPV of retrofitting.
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #313
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Total Cost of Ownership of Average Home (Dollar / (Year * House))
                                                                                                                                                                                                    Total Cost of Ownership of Average Home[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Average Energy Costs for Retrofitting Home[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                    Description: Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #314
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))
                                                                                                                                                                                                    Total Cost of Ownership of Retrofitted Homes[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Amoritized Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]+ Average Energy Costs if Retrofitted[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                    Description: The total cost of ownership of owning a home that has been retrofitted to the optimal U.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #329
                                                                                                                                                                                                    A
                                                                                                                                                                                                    U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                                                    U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                    Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                                                    Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                    Present In 8 Views: Used By
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                    • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                    • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                    • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                    • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                    Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                                    .housingagingchain v8 #339
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Unsubsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                    Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort,Open to Retrofitting]
                                                                                                                                                                                                    Description: Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                    Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #338
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Unsubsidized Retrofit Cost Intensity (Dollar / sf)
                                                                                                                                                                                                    Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] = MAX(IF THEN ELSE(
                                                                                                                                                                                                    U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06,( Expected Reference Marginal Cost* Reference U Value/(- Sensitivity of Marginal Cost to U Value+1))*((( Reference U Value/ U Value of Retrofitting Homes[ Cohort, Heating and Cooling System])^ Sensitivity of Marginal Cost to U Value-1)-(( Reference U Value/ Optimal U Value for Existing Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value-1)))+ Fixed Cost per Unit Area[ Cohort],0),0)
                                                                                                                                                                                                    Description: Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #340
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Weight on Upfront Cost (dmnl )
                                                                                                                                                                                                    = 0.5
                                                                                                                                                                                                    Description: How much homeowners weigh upfront (amoritized) costs of retrofits as opposed to the total cost of ownership due to being more perceptive of short-term costs.
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                    • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    (View) Social Influence in Retrofitting Decisions (1 Variables)
                                                                                                                                                                                                    Top (View) Social Influence in Retrofitting Decisions (1 Variables)
                                                                                                                                                                                                    Group
                                                                                                                                                                                                    Type
                                                                                                                                                                                                    Variable Name And Description
                                                                                                                                                                                                    .housingagingchain v4 testing #320
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Total Housing Stock (House)
                                                                                                                                                                                                    = SUM(
                                                                                                                                                                                                    Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                    Description: Total number of houses across all cohorts, heating/cooling systems, and retrofitting status.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    (View) Switching Systems (34 Variables)
                                                                                                                                                                                                    Top (View) Switching Systems (34 Variables)
                                                                                                                                                                                                    Group
                                                                                                                                                                                                    Type
                                                                                                                                                                                                    Variable Name And Description
                                                                                                                                                                                                    HeatPumpModel_v31 #5
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Affinity of Heating and Cooling Systems (dmnl)
                                                                                                                                                                                                    Affinity of Heating and Cooling Systems[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]>0,exp(- Sensitivity of Affinity to Cost* Cost of Switching Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Reference Lifetime Cost of Heating and Cooling Systems),0)
                                                                                                                                                                                                    Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = IF THEN ELSE( Cost of Switching Heating and Cooling Systems[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]>0,exp(- Sensitivity of Affinity to Cost* Cost of Switching Heating and Cooling Systems[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]/ Reference Lifetime Cost of Heating and Cooling Systems),0)
                                                                                                                                                                                                    Description: The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #29
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Average Area (sf / House)
                                                                                                                                                                                                    Average Area[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                                                                                                                    Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                                                                                                                    Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                    Present In 7 Views: Used By
                                                                                                                                                                                                    • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                    • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                    • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                    Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                    HeatPumpModel_v31 #54
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Average Lifetime of Cooling Technology (Years)
                                                                                                                                                                                                    Average Lifetime of Cooling Technology[Heat Pump Heating and Cooling] = 12.5
                                                                                                                                                                                                    Average Lifetime of Cooling Technology[Central AC Cooling] = 12.5
                                                                                                                                                                                                    Average Lifetime of Cooling Technology[Window AC Cooling] = 9
                                                                                                                                                                                                    Average Lifetime of Cooling Technology[No AC Cooling] =
                                                                                                                                                                                                    NAREPLACEMENT
                                                                                                                                                                                                    Description: The average lifetime of each cooling system.Central AC data from: https://www.energy.gov/energysaver/central-air-conditioningWindow AC data from: https://www.consumerreports.org/air-conditioner/is-it-time-to-get-a-new-window-air-conditioner-a1532530762/
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #55
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Average Lifetime of Heating Technology (Year)
                                                                                                                                                                                                    Average Lifetime of Heating Technology[Heat Pump Heating and Cooling] = 12.5
                                                                                                                                                                                                    Average Lifetime of Heating Technology[Gas Heating] = 20
                                                                                                                                                                                                    Average Lifetime of Heating Technology[Oil Heating] = 20
                                                                                                                                                                                                    Description: The average lifetime of each heating system.Heat pump data from: https://glascohvac.com/heating/heat-pumps/long-heat-pump-last/Gas data from: https://www.carrier.com/residential/en/us/products/furnaces/how-long-does-a-furnaces-last/Oil data from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #57
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Average Time To Consider Switching (Year )
                                                                                                                                                                                                    = 15
                                                                                                                                                                                                    Description: The average time it takes for a house to consider switching their heating and cooling system.
                                                                                                                                                                                                    Present In 2 Views:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #67
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Cooling Degree Days (F )
                                                                                                                                                                                                    = 1029
                                                                                                                                                                                                    Description: The difference between temperature setpoint (65 F) and outside temperature for heating. Typically called cooling degree days, but units are solely in terms of fahrenheit.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. Use set point of 65°F, in line with industry standard, as at that temperature little heating or cooling is necessary.
                                                                                                                                                                                                    Present In 3 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #71
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Cooling Energy Use Under Alternatives (kBTU / (House * Year))
                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Not Open to Retrofitting,Heating and Cooling System] =
                                                                                                                                                                                                    U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Traditional Cooling,Not Open to Retrofitting,Heating and Cooling System] = U Value by Grouping[ Cohort, Traditional Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] = 0
                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Fossil Fuel Heating,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Description: The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #72
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Cooling System Efficiency (dmnl)
                                                                                                                                                                                                    Cooling System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                    Heat Pump Cooling COP TABLE( Time)
                                                                                                                                                                                                    Cooling System Efficiency[Central AC Cooling] = 2.93
                                                                                                                                                                                                    Cooling System Efficiency[Window AC Cooling] = 2.49* Effect of Air Leakage from Window AC on Efficiency
                                                                                                                                                                                                    Cooling System Efficiency[No AC Cooling] = NAREPLACEMENT
                                                                                                                                                                                                    Description: The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #73
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Cost of Bad Air Conditioning (Dollar / House )
                                                                                                                                                                                                    Cost of Bad Air Conditioning[Window AC Cooling] = 80000
                                                                                                                                                                                                    Cost of Bad Air Conditioning[No AC Cooling] = 100000
                                                                                                                                                                                                    Description: Willingness of Window AC users and those without AC to pay for central AC or heat pumps due to those technologies' inability to heat homes and their noisiness.Chosen to be sufficiently high that very few or no houses choose to keep window AC or no AC.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #74
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Cost of Cooling System Replacement (Dollar / House)
                                                                                                                                                                                                    Cost of Cooling System Replacement[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                    Subsidized Cost of Heat Pumps
                                                                                                                                                                                                    Cost of Cooling System Replacement[Central AC Cooling] = 5800
                                                                                                                                                                                                    Cost of Cooling System Replacement[Window AC Cooling] = 1600
                                                                                                                                                                                                    Cost of Cooling System Replacement[No AC Cooling] = 0
                                                                                                                                                                                                    Description: The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #75
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Cost of Heating System Replacement (Dollar / House )
                                                                                                                                                                                                    Cost of Heating System Replacement[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                    Subsidized Cost of Heat Pumps
                                                                                                                                                                                                    Cost of Heating System Replacement[Gas Heating] = 10000
                                                                                                                                                                                                    Cost of Heating System Replacement[Oil Heating] = 7450
                                                                                                                                                                                                    Description: The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #76
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems (Dollar / House)
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Heat Pump Only] =
                                                                                                                                                                                                    Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]+ Cost of Heating System Replacement[Gas and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heat Pump and Gas] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Heat Pump Only]+ Cost of Heating System Replacement[Heat Pump Only]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Heat Pump and Gas]+ Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Gas and Central AC] = Cost of Cooling System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Oil and Central AC] = Cost of Heating System Replacement[Oil and Central AC]+ Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Gas and Central AC] = Cost of Heating System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heat Pump and Oil] = Cost of Heating System Replacement[Heat Pump and Oil]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Heat Pump and Oil]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Oil and Central AC] = Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Gas and Central AC] = Cost of Heating System Replacement[Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heat Pump and Oil] = Cost of Heating System Replacement[Heat Pump and Oil]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Heat Pump and Oil]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Oil and Central AC] = Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Oil and Central AC] = Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Oil] = Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Heat Pump and Oil]
                                                                                                                                                                                                    Description: Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #90
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Discount Rate (1 / Year )
                                                                                                                                                                                                    = 0.05
                                                                                                                                                                                                    Description: Discount rate for discounting energy savings cash flows.Average and bounds from demand-side discount rate from MassDEP's analysis of pathways for net zero (pg. 103): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadhttps://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                    Present In 4 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #111
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Cooling Energy Price, Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                    Description: Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                    • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #115
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Heating Energy Price (Dollar / kBTU)
                                                                                                                                                                                                    Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                                                                                                                                                                    Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                    Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                    Present In 6 Views: Used By
                                                                                                                                                                                                    • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                    • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #122
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Expected Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                    =
                                                                                                                                                                                                    MassSave Expected Lump Sum Subsidy for Heat Pumps+ IRA Expected Proportional Subsidy for Heat Pumps
                                                                                                                                                                                                    Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidies.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #130
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Fraction of Houses Switching (dmnl)
                                                                                                                                                                                                    Fraction of Houses Switching[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                    Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                                    Fraction of Houses Switching[Cohort,Gas Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                                    Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                                    Description: Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #141
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Heating Degree Days (F )
                                                                                                                                                                                                    = 5026
                                                                                                                                                                                                    Description: The difference between temperature setpoint (65 F) and outside temperature.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. In line with industry standard, use set point of 65°F, as thattemperature little heating or cooling is needed.
                                                                                                                                                                                                    Present In 3 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #143
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                                    Heating Energy Price[Heating and Cooling System] =
                                                                                                                                                                                                    Initial Heating Energy Price[ Heating and Cooling System]* Input 0
                                                                                                                                                                                                    Description: The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                    Present In 6 Views: Used By
                                                                                                                                                                                                    • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #144
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Heating Energy Use Under Alternatives (kBTU / (House * Year))
                                                                                                                                                                                                    Heating Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Not Open to Retrofitting,Heating and Cooling System] =
                                                                                                                                                                                                    U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Not Open to Retrofitting,Heating and Cooling System] = U Value by Grouping[ Cohort, Fossil Fuel Heating,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Heating Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Fossil Fuel Heating,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Description: The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #145
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Heating System Efficiency (dmnl)
                                                                                                                                                                                                    Heating System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                    Heat Pump Heating COP TABLE( Time)
                                                                                                                                                                                                    Heating System Efficiency[Gas Heating] = Gas COP TABLE( Time)
                                                                                                                                                                                                    Heating System Efficiency[Oil Heating] = Oil COP TABLE( Time)
                                                                                                                                                                                                    Description: The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                    Present In 3 Views: Used By
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v4 testing #254
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                                    Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    Present In 8 Views: Used By
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                    • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #265
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Present Value of Cooling Operating Costs (Dollars / (House))
                                                                                                                                                                                                    Present Value of Cooling Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = (
                                                                                                                                                                                                    Expected Cooling Energy Price* Cooling Energy Use Under Alternatives[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Cooling Technology[ Heating and Cooling System]))
                                                                                                                                                                                                    Present Value of Cooling Operating Costs[Cohort,Traditional Cooling,Retrofitting Status,Heating and Cooling System] = ( Expected Cooling Energy Price* Cooling Energy Use Under Alternatives[ Cohort, Traditional Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Cooling Technology[ Heating and Cooling System]))
                                                                                                                                                                                                    Present Value of Cooling Operating Costs[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] = 0
                                                                                                                                                                                                    Description: The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #266
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Present Value of Heating Operating Costs (Dollar / (House))
                                                                                                                                                                                                    Present Value of Heating Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = (
                                                                                                                                                                                                    Expected Heating Energy Price[ Heating and Cooling System]* Heating Energy Use Under Alternatives[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Heating Technology[ Heating and Cooling System]))
                                                                                                                                                                                                    Present Value of Heating Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = ( Expected Heating Energy Price[ Heating and Cooling System]* Heating Energy Use Under Alternatives[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Heating Technology[ Heating and Cooling System]))
                                                                                                                                                                                                    Description: The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #267
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Present Value of Operating Costs (Dollar / (House) )
                                                                                                                                                                                                    Present Value of Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                    Present Value of Cooling Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]+ Present Value of Heating Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]
                                                                                                                                                                                                    Present Value of Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Present Value of Cooling Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]+ Present Value of Heating Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]
                                                                                                                                                                                                    Description: Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #268
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Present Value Replacement Cost (Dollar / House)
                                                                                                                                                                                                    Present Value Replacement Cost[Heating and Cooling System] =
                                                                                                                                                                                                    Cost of Cooling System Replacement[ Heating and Cooling System]/( Average Lifetime of Cooling Technology[ Heating and Cooling System]* Discount Rate)+ Cost of Heating System Replacement[ Heating and Cooling System]/( Average Lifetime of Heating Technology[ Heating and Cooling System]* Discount Rate)
                                                                                                                                                                                                    Present Value Replacement Cost[Heat Pump Heating and Cooling] = Cost of Cooling System Replacement[ Heat Pump Heating and Cooling]/( Average Lifetime of Cooling Technology[ Heat Pump Heating and Cooling]* Discount Rate)
                                                                                                                                                                                                    Present Value Replacement Cost[No AC Cooling] = 0
                                                                                                                                                                                                    Description: Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #282
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )
                                                                                                                                                                                                    = 30000
                                                                                                                                                                                                    Description: The reference value of lifetime heating and cooling combinations when people calculate affinity of each combo. Hand calibrated to roughly match heat pump sales in https://www.masssave.com/en/about/news-and-events/news/mass-save-sponsors-announce-record-number-of-heat-pump-installations-across-massachusetts
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #290
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Sensitivity of Affinity to Cost (dmnl )
                                                                                                                                                                                                    = 10
                                                                                                                                                                                                    Description: Sensitivity of affinity to each heating and cooling combination having higher cost. The higher this, the fewer houses will convert to more expensive combinations.Calculated by hand calibration-- value ensures that amount of heat pumps sold 2020 - 2024 begins at about 10K and goes to about 20K in 2024, in accordance with MassSave data from https://www.masssave.com/en/about/news-and-events/news/mass-save-sponsors-announce-record-number-of-heat-pump-installations-across-massachusetts
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #303
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Subsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                    = MAX(0,
                                                                                                                                                                                                    Unsubsidized Cost of Heat Pumps- Expected Subsidy for Heat Pumps)
                                                                                                                                                                                                    Description: The upfront cost of heat pump once subsidies are taken into account.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Cost of Cooling System Replacement The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                    • Cost of Heating System Replacement The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #316
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Total Heat Pump Sales (House / Year)
                                                                                                                                                                                                    = SUM(
                                                                                                                                                                                                    Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump Only]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Gas]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Oil])
                                                                                                                                                                                                    Description: Number of houses buying heat pumps every year.
                                                                                                                                                                                                    Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #323
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Total Present Value of Cost (Dollar / House)
                                                                                                                                                                                                    Total Present Value of Cost[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                    Present Value of Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]+ Present Value Replacement Cost[ Heating and Cooling System]+ Cost of Bad Air Conditioning[ Heating and Cooling System]
                                                                                                                                                                                                    Total Present Value of Cost[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Present Value of Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]+ Present Value Replacement Cost[ Heating and Cooling System]+ Cost of Bad Air Conditioning[ Heating and Cooling System]
                                                                                                                                                                                                    Description: Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #329
                                                                                                                                                                                                    A
                                                                                                                                                                                                    U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                                                    U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                    Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                                                    Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                    Present In 8 Views: Used By
                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                    • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                    • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                    • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                    • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                    Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                                    HeatPumpModel_v31 #336
                                                                                                                                                                                                    A,T
                                                                                                                                                                                                    Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)
                                                                                                                                                                                                    Unsubsidized Cost of Heat Pump Over Time TABLE([(2020,5000)-(2050,10000)],(2020,22000),(2030,20483.7 ),(2040,18967.3),(2050,17448.6))

                                                                                                                                                                                                    Description: The cost of installing and buying a heat pump over time. Initial value taken from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then assume that ratio of future prices to initial is the same as average of reference and ductless heat pumps in MassDEP's Energy Pathways Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download. (That is, I took the ratio of the initial price to the initial price in that report, then I multiplied that ratio times all projections of future heat pump prices). I was unable to use the MassDEP report's prices directly, because they are based on national estimates from NREL, and MA is typically a more expensive state. In particular, the MassDEP projections say that heat pumps cost only $9K, but MassSave subsidy is $10K!Assumes rates of change are linear between projected points.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #337
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Unsubsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                    =
                                                                                                                                                                                                    Unsubsidized Cost of Heat Pump Over Time TABLE( Time)
                                                                                                                                                                                                    Description: The unsubsidized cost of heat pumps, instantiated at each time.
                                                                                                                                                                                                    Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    (View) U Value of Housing Starts (18 Variables)
                                                                                                                                                                                                    Top (View) U Value of Housing Starts (18 Variables)
                                                                                                                                                                                                    Group
                                                                                                                                                                                                    Type
                                                                                                                                                                                                    Variable Name And Description
                                                                                                                                                                                                    .housingagingchain v15 #4
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Additional Cost of Building to U Value (Dollar / sf)
                                                                                                                                                                                                    Additional Cost of Building to U Value[Cohort,Heating and Cooling System] = ((1-
                                                                                                                                                                                                    Expected MassSave Proportional Subsidy Rate for Retrofits)* Expected Reference Marginal Cost/(1- Sensitivity of Marginal Cost to U Value))*((( Reference U Value/ Code U)^ Sensitivity of Marginal Cost to U Value)* Code U-(( Reference U Value/ Optimal U for New Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value))* Optimal U for New Homes[ Cohort, Heating and Cooling System])- Expected Lump Sum Subsidy Intensity[New Housing]
                                                                                                                                                                                                    Description: Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #28
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Average Area of Housing Starts (sf / House)
                                                                                                                                                                                                    =
                                                                                                                                                                                                    Increase in Area per Year*( Time- INITIAL TIME)+ Initial Average Area of Housing Starts
                                                                                                                                                                                                    Description: The average area of housing starts.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v18 #65
                                                                                                                                                                                                    L
                                                                                                                                                                                                    Code U (kBTU / (sf * Year * F))
                                                                                                                                                                                                    = -
                                                                                                                                                                                                    Decrease in Code U dt + Initial Code U Value
                                                                                                                                                                                                    Description: U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Decrease in Code U The change in code U from policy.
                                                                                                                                                                                                    • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                    .housingagingchain v18 #84
                                                                                                                                                                                                    F,A
                                                                                                                                                                                                    Decrease in Code U (kBTU / (sf * Year * F) / Year)
                                                                                                                                                                                                    =
                                                                                                                                                                                                    Code U* Fractional Decrease in Code U
                                                                                                                                                                                                    Description: The change in code U from policy.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                    HeatPumpModel_v31 #90
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Discount Rate (1 / Year )
                                                                                                                                                                                                    = 0.05
                                                                                                                                                                                                    Description: Discount rate for discounting energy savings cash flows.Average and bounds from demand-side discount rate from MassDEP's analysis of pathways for net zero (pg. 103): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadhttps://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                    Present In 4 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #115
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Heating Energy Price (Dollar / kBTU)
                                                                                                                                                                                                    Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                                                                                                                                                                    Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                    Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                    Present In 6 Views: Used By
                                                                                                                                                                                                    • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                    • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #117
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Expected Lump Sum Subsidy Intensity (Dollar / sf)
                                                                                                                                                                                                    Expected Lump Sum Subsidy Intensity[Retrofit Cost] =
                                                                                                                                                                                                    HOMES Expected Lower Lump Sum Subsidy/ Average Area of Housing Starts
                                                                                                                                                                                                    Description: Lump sum subsidy for retrofits per square foot.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #119
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    Implemented MassSave Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                    Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #121
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                    = SMOOTH(
                                                                                                                                                                                                    Reference Marginal Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                    Description: Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #135
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Fractional Decrease in Code U (1 / Year )
                                                                                                                                                                                                    = 0
                                                                                                                                                                                                    Description: Fractional decrease in code per year. Exogenous and set by policymakers in the real world. For initial paper, assume that code U is constant.
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #149
                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                    HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                    HOMES Implemented Lower Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                    Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                    Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #188
                                                                                                                                                                                                    LI,C
                                                                                                                                                                                                    Initial Code U Value (kBTU / (sf * F * Year))
                                                                                                                                                                                                    = 0.003
                                                                                                                                                                                                    Description: The initial value of code U. For initial paper, assume that this is between initial optimal U (nearly 0) and average U (0.006).
                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    HeatPumpModel_v31 #210
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))
                                                                                                                                                                                                    Marginal Cooling Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Expected Cooling Energy Price* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                    Description: The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v15 #212
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)
                                                                                                                                                                                                    Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                    Marginal Cooling Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]+ Marginal Heating Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                    Description: Total cost reductions from retrofitting away one unit of U value for existing homes, including reductions in both heating and cooling costs.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v18 #253
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Optimal U for New Homes (kBTU / (sf * Year * F))
                                                                                                                                                                                                    Optimal U for New Homes[Cohort,Heating and Cooling System] = ((
                                                                                                                                                                                                    Expected Reference Marginal Cost/( Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]/ Discount Rate))^(1/ Sensitivity of Marginal Cost to U Value))* Reference U Value*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)
                                                                                                                                                                                                    Description: The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v9 #285
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Reference U Value (kBTU / (sf * Year * F) )
                                                                                                                                                                                                    = 0.006
                                                                                                                                                                                                    Description: Reference U Value to ensure base of exponent in marginally optimal U value is dimensionless. This must be equal to or greater than code U value.Value taken as the average of U values of single family homes in MA in 2020 for our sample.
                                                                                                                                                                                                    Present In 3 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v5 testing #291
                                                                                                                                                                                                    C
                                                                                                                                                                                                    Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                                                                                                                                    = 3.25
                                                                                                                                                                                                    Description: Measures the sensitivity of marginal retrofit costs as a function of optimal U value. In particular, marginal Retrofit Cost is equal to Constant * (U Value retrofitted away ^ Convexity). This must be greater than 1.This is taken from pg. 69 of Caswell (2022), where she calculates the total retrofit cost curve as a function of percent savings as having an exponent of 2.25. Because this is the total retrofit cost curve, the exponent for the marginal cost is -2.25 - 1. Because percent savings is inversely proportional to U, the exponent in the total cost curve will be the negation of 2.25, which is ensured in the marginal cost curve formulation in other variables.
                                                                                                                                                                                                    Present In 4 Views:
                                                                                                                                                                                                    Used By
                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    .housingagingchain v18 #332
                                                                                                                                                                                                    A
                                                                                                                                                                                                    U Value of Housing Starts (kBTU / (Year * F * sf))
                                                                                                                                                                                                    U Value of Housing Starts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                    Additional Cost of Building to U Value[ Cohort, Heating and Cooling System]<0:AND: Optimal U for New Homes[ Cohort, Heating and Cooling System]< Code U, Optimal U for New Homes[ Cohort, Heating and Cooling System], Code U)
                                                                                                                                                                                                    Description: Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                    Top (Group) . (1 Variables)
                                                                                                                                                                                                    Group
                                                                                                                                                                                                    Type
                                                                                                                                                                                                    Variable Name And Description
                                                                                                                                                                                                    . #194
                                                                                                                                                                                                    A
                                                                                                                                                                                                    Initial Housing Starts (House/Year)
                                                                                                                                                                                                    Initial Housing Starts[Heating and Cooling System] =
                                                                                                                                                                                                    Total Initial Housing Starts/ELMCOUNT( Heating and Cooling System)
                                                                                                                                                                                                    Description: Initial value of housing starts, initialized at 10 total houses.
                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                      Top (Group) .Control (4 Variables)
                                                                                                                                                                                                      Group
                                                                                                                                                                                                      Type
                                                                                                                                                                                                      Variable Name And Description
                                                                                                                                                                                                      .Control #126
                                                                                                                                                                                                      C
                                                                                                                                                                                                      FINAL TIME (Year)
                                                                                                                                                                                                      = 2050
                                                                                                                                                                                                      Description: The final time for the simulation.
                                                                                                                                                                                                      Present In 1 View:
                                                                                                                                                                                                      Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                      .Control #196
                                                                                                                                                                                                      C
                                                                                                                                                                                                      INITIAL TIME (Year)
                                                                                                                                                                                                      = 2020
                                                                                                                                                                                                      Description: The initial time for the simulation.
                                                                                                                                                                                                      Present In 3 Views:
                                                                                                                                                                                                      Used By
                                                                                                                                                                                                      • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                                      • Average Area of Housing Starts The average area of housing starts.
                                                                                                                                                                                                      • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                      • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                      • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                      .Control #289
                                                                                                                                                                                                      A
                                                                                                                                                                                                      SAVEPER (Year )
                                                                                                                                                                                                      =
                                                                                                                                                                                                      TIME STEP
                                                                                                                                                                                                      Description: The frequency with which output is stored.
                                                                                                                                                                                                      Present In 0 Views:
                                                                                                                                                                                                        Used By
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .Control #306
                                                                                                                                                                                                          C
                                                                                                                                                                                                          TIME STEP (Year )
                                                                                                                                                                                                          = 0.03125
                                                                                                                                                                                                          Description: The time step for the simulation.
                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                          Used By
                                                                                                                                                                                                          • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                          • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                          • SAVEPER The frequency with which output is stored.
                                                                                                                                                                                                          • White Noise White noise input to the pink noise process.
                                                                                                                                                                                                          • White Noise 0 White noise input to the pink noise process.
                                                                                                                                                                                                          • White Noise 1 White noise input to the pink noise process.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          Top (Group) .housingagingchain v15 (28 Variables)
                                                                                                                                                                                                          Group
                                                                                                                                                                                                          Type
                                                                                                                                                                                                          Variable Name And Description
                                                                                                                                                                                                          .housingagingchain v15 #4
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Additional Cost of Building to U Value (Dollar / sf)
                                                                                                                                                                                                          Additional Cost of Building to U Value[Cohort,Heating and Cooling System] = ((1-
                                                                                                                                                                                                          Expected MassSave Proportional Subsidy Rate for Retrofits)* Expected Reference Marginal Cost/(1- Sensitivity of Marginal Cost to U Value))*((( Reference U Value/ Code U)^ Sensitivity of Marginal Cost to U Value)* Code U-(( Reference U Value/ Optimal U for New Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value))* Optimal U for New Homes[ Cohort, Heating and Cooling System])- Expected Lump Sum Subsidy Intensity[New Housing]
                                                                                                                                                                                                          Description: Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                          • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #12
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))
                                                                                                                                                                                                          Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                          Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]/ Amoritization Period
                                                                                                                                                                                                          Description: The incurred total retrofit cost amoritized over the specified amoritization period.
                                                                                                                                                                                                          Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #41
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Average Energy Costs for Retrofitting Home (Dollar / Year / House)
                                                                                                                                                                                                          Average Energy Costs for Retrofitting Home[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                          Average Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                          Description: Heating costs for each home open to retrofitting, annually, if no further retrofit measures are undertaken.
                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                          • Total Cost of Ownership of Average Home Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #76
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems (Dollar / House)
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Heat Pump Only] =
                                                                                                                                                                                                          Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]+ Cost of Heating System Replacement[Gas and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heat Pump and Gas] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Heat Pump Only]+ Cost of Heating System Replacement[Heat Pump Only]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Heat Pump and Gas]+ Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Gas and Central AC] = Cost of Cooling System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Oil and Central AC] = Cost of Heating System Replacement[Oil and Central AC]+ Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Gas and Central AC] = Cost of Heating System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heat Pump and Oil] = Cost of Heating System Replacement[Heat Pump and Oil]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Heat Pump and Oil]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Oil and Central AC] = Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Gas and Central AC] = Cost of Heating System Replacement[Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heat Pump and Oil] = Cost of Heating System Replacement[Heat Pump and Oil]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Heat Pump and Oil]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Oil and Central AC] = Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Oil and Central AC] = Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Oil] = Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Heat Pump and Oil]
                                                                                                                                                                                                          Description: Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                          • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #85
                                                                                                                                                                                                          C
                                                                                                                                                                                                          Delay in Changing Subsidy Expectations (Year )
                                                                                                                                                                                                          = 0.5
                                                                                                                                                                                                          Description: Delay in perceiving any changes to subsidies. Assumed to be the same for both subsidies.
                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #86
                                                                                                                                                                                                          C
                                                                                                                                                                                                          Delay in Forming Expectations of Energy Price (Year )
                                                                                                                                                                                                          = 1
                                                                                                                                                                                                          Description: Delay in perceiving changes in energy price.
                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                          Used By
                                                                                                                                                                                                          • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                          • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #87
                                                                                                                                                                                                          C
                                                                                                                                                                                                          Delay in Forming Expectations of Retrofit Costs (Year )
                                                                                                                                                                                                          = 1.5
                                                                                                                                                                                                          Description: Delay in perceiving changes in fixed retrofit cost and reference marginal cost. Assumed to be the same for both types of costs.
                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                          Used By
                                                                                                                                                                                                          • Expected Fixed Cost Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                          • Expected Reference Marginal Cost Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #114
                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                          Expected Fixed Cost (Dollar / House)
                                                                                                                                                                                                          = SMOOTH(
                                                                                                                                                                                                          Fixed Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                          Description: Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                          • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                          • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #115
                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                          Expected Heating Energy Price (Dollar / kBTU)
                                                                                                                                                                                                          Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                                                                                                                                                                          Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                          Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                          Present In 6 Views: Used By
                                                                                                                                                                                                          • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                          • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                          • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                          • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #117
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Expected Lump Sum Subsidy Intensity (Dollar / sf)
                                                                                                                                                                                                          Expected Lump Sum Subsidy Intensity[Retrofit Cost] =
                                                                                                                                                                                                          HOMES Expected Lower Lump Sum Subsidy/ Average Area of Housing Starts
                                                                                                                                                                                                          Description: Lump sum subsidy for retrofits per square foot.
                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                          • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #118
                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                          Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                          Implemented MassSave Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                          Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #119
                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                          Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                          Implemented MassSave Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                          Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                          Present In 4 Views: Used By
                                                                                                                                                                                                          • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                          • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                          • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                          • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                          • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #121
                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                          Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                          = SMOOTH(
                                                                                                                                                                                                          Reference Marginal Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                          Description: Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                          Present In 4 Views: Used By
                                                                                                                                                                                                          • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                          • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                          • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                          • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                          • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                          • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                          • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #123
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                          Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                          Energy Savings[ Cohort, Heating and Cooling System]>= HOMES Cut Off for Savings, HOMES Expected Higher Subsidy, HOMES Expected Lower Lump Sum Subsidy)+ MassSave Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]+ EEHIC Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                          Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                                                                                                                                                                          Present In 4 Views: Used By
                                                                                                                                                                                                          • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #149
                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                          HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                          HOMES Implemented Lower Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                          Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                          Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #152
                                                                                                                                                                                                          A
                                                                                                                                                                                                          HOMES Implemented Lower Subsidy (Dollar / House)
                                                                                                                                                                                                          = IF THEN ELSE(
                                                                                                                                                                                                          Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES Lower Subsidy Amount,0)
                                                                                                                                                                                                          Description: Lump sum subsidy that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #153
                                                                                                                                                                                                          C
                                                                                                                                                                                                          HOMES Lower Subsidy Amount (Dollar / House )
                                                                                                                                                                                                          = 2000
                                                                                                                                                                                                          Description: The lump sum subsidy given for retrofits that save less than 35% of their energy from the Home Owner Managing Energy Savings tax credit.Source: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                          Used By
                                                                                                                                                                                                          • HOMES Implemented Lower Subsidy Lump sum subsidy that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #155
                                                                                                                                                                                                          C
                                                                                                                                                                                                          HOMES Subsidy Implementation Year (Year )
                                                                                                                                                                                                          = 2025
                                                                                                                                                                                                          Description: The year in which the lump sum subsidy will activate.
                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #178
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                          = IF THEN ELSE(
                                                                                                                                                                                                          Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: Time<= MassSave Subsidy for Retrofits Final Year, MassSave Maximum Subsidy for Retrofits,0)
                                                                                                                                                                                                          Description: Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #179
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                          = IF THEN ELSE(
                                                                                                                                                                                                          Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: MassSave Subsidy for Retrofits Final Year>= Time, Mass Save Proportional Subsidy Rate for Retrofits,0)
                                                                                                                                                                                                          Description: The implemented proportional subsidy rate from the state, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #197
                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                          Initial U Value (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                          Initial U Value[Cohort,Heating and Cooling System,Retrofitting Status] = 0
                                                                                                                                                                                                          Initial U Value[Preexisting Cohorts,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                          Initial Average U Value[ Preexisting Cohorts]* Housing[ Preexisting Cohorts, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                          Description: Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                          • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #212
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)
                                                                                                                                                                                                          Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                          Marginal Cooling Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]+ Marginal Heating Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                          Description: Total cost reductions from retrofitting away one unit of U value for existing homes, including reductions in both heating and cooling costs.
                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                          • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                          • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #214
                                                                                                                                                                                                          C
                                                                                                                                                                                                          Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                          = 0.75
                                                                                                                                                                                                          Description: Proportion of total retrofit cost that will be credited as part of a proportional subsidy. Theoretically, this can vary between current housing and housing under construction.Based off Mass Save data: https://www.masssave.com/en/residential/rebates-and-incentives/insulation-and-windows/insulation-and-air-sealing
                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #218
                                                                                                                                                                                                          A
                                                                                                                                                                                                          MassSave Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                          MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = MIN(
                                                                                                                                                                                                          Proportional Subsidy Switch for Retrofits* Expected MassSave Proportional Subsidy Rate for Retrofits* Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status], Expected MassSave Maximum Subsidy for Retrofits)
                                                                                                                                                                                                          Description: The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #223
                                                                                                                                                                                                          C
                                                                                                                                                                                                          MassSave Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                          = 1e+07
                                                                                                                                                                                                          Description: The maximum proportional subsidy that will be offered, regardless of that subsidy's discount. For instance, if the proportional subsidy is 50% but the maximum is $1000, then for a retrofit project that costs $3000 only a $1000 subsidy will be given.If very large, then no maximum subsidy given.
                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #271
                                                                                                                                                                                                          C
                                                                                                                                                                                                          Proportional MassSave Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                          = 2020
                                                                                                                                                                                                          Description: Time at which the proportional subsidy will take effect.
                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #272
                                                                                                                                                                                                          C
                                                                                                                                                                                                          Proportional Subsidy Switch for Retrofits (dmnl )
                                                                                                                                                                                                          = 1
                                                                                                                                                                                                          Description: Turns proportional subsidy's effect on retrofit cost on/off.
                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v15 #304
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Subsidized Retrofit Cost (Dollar /House)
                                                                                                                                                                                                          Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                          Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]- Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System,Open to Retrofitting]+ Soft Costs of Retrofitting
                                                                                                                                                                                                          Description: The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          Top (Group) .housingagingchain v18 (5 Variables)
                                                                                                                                                                                                          Group
                                                                                                                                                                                                          Type
                                                                                                                                                                                                          Variable Name And Description
                                                                                                                                                                                                          .housingagingchain v18 #65
                                                                                                                                                                                                          L
                                                                                                                                                                                                          Code U (kBTU / (sf * Year * F))
                                                                                                                                                                                                          = -
                                                                                                                                                                                                          Decrease in Code U dt + Initial Code U Value
                                                                                                                                                                                                          Description: U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                          • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                          • Decrease in Code U The change in code U from policy.
                                                                                                                                                                                                          • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                          Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                          .housingagingchain v18 #84
                                                                                                                                                                                                          F,A
                                                                                                                                                                                                          Decrease in Code U (kBTU / (sf * Year * F) / Year)
                                                                                                                                                                                                          =
                                                                                                                                                                                                          Code U* Fractional Decrease in Code U
                                                                                                                                                                                                          Description: The change in code U from policy.
                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                          • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                          Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                          .housingagingchain v18 #181
                                                                                                                                                                                                          F,A
                                                                                                                                                                                                          Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                          Increase in U Value from Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                          Housing Starts[ Cohort, Heating and Cooling System]* U Value of Housing Starts[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                          Description: New U value from new homes being built.
                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                          • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v18 #253
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Optimal U for New Homes (kBTU / (sf * Year * F))
                                                                                                                                                                                                          Optimal U for New Homes[Cohort,Heating and Cooling System] = ((
                                                                                                                                                                                                          Expected Reference Marginal Cost/( Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]/ Discount Rate))^(1/ Sensitivity of Marginal Cost to U Value))* Reference U Value*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)
                                                                                                                                                                                                          Description: The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                          • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                          • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v18 #332
                                                                                                                                                                                                          A
                                                                                                                                                                                                          U Value of Housing Starts (kBTU / (Year * F * sf))
                                                                                                                                                                                                          U Value of Housing Starts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                          Additional Cost of Building to U Value[ Cohort, Heating and Cooling System]<0:AND: Optimal U for New Homes[ Cohort, Heating and Cooling System]< Code U, Optimal U for New Homes[ Cohort, Heating and Cooling System], Code U)
                                                                                                                                                                                                          Description: Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          Top (Group) .housingagingchain v4 testing (4 Variables)
                                                                                                                                                                                                          Group
                                                                                                                                                                                                          Type
                                                                                                                                                                                                          Variable Name And Description
                                                                                                                                                                                                          .housingagingchain v4 testing #7
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Affinity of Retrofitting (dmnl)
                                                                                                                                                                                                          Affinity of Retrofitting[Cohort,Heating and Cooling System] = exp(-
                                                                                                                                                                                                          Sensitivity of Retrofits to Cost* Perceived Cost of Retrofitting[ Cohort, Heating and Cooling System]/ Reference Retrofit Cost)
                                                                                                                                                                                                          Description: Affinity of retrofitting, where utility value is equal to its NPV.
                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                          • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                          .housingagingchain v4 testing #59
                                                                                                                                                                                                          A
                                                                                                                                                                                                          Average U Value in All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                          = ZIDZ(
                                                                                                                                                                                                          Total U Value Across All Groupings, Total Housing Stock)
                                                                                                                                                                                                          Description: The average U Value over the entire housing stock, not disaggregated by any groupings.
                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v4 testing #254
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                                                                            Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                            Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                                            Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                            Present In 8 Views: Used By
                                                                                                                                                                                                            • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                            • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                            • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                            • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                            • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                            • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                            • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                                            • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                            • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v4 testing #320
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Total Housing Stock (House)
                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                            Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                            Description: Total number of houses across all cohorts, heating/cooling systems, and retrofitting status.
                                                                                                                                                                                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            Top (Group) .housingagingchain v5 testing (14 Variables)
                                                                                                                                                                                                            Group
                                                                                                                                                                                                            Type
                                                                                                                                                                                                            Variable Name And Description
                                                                                                                                                                                                            .housingagingchain v5 testing #49
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Average Heating Cost (Dollar / (Year * House))
                                                                                                                                                                                                            Average Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                            Expected Heating Energy Price[ Heating and Cooling System]* Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                            Description: The costs per year to heat one house.
                                                                                                                                                                                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #128
                                                                                                                                                                                                            C
                                                                                                                                                                                                            Fixed Cost (Dollar / House )
                                                                                                                                                                                                            = 0
                                                                                                                                                                                                            Description: Fixed cost of retrofitting, due to permitting, finding contractors, etc. This is not taken into account in the marginal cost of retrofitting, and this model assumes that households have not yet paid a fixed cost when deciding to retrofit. This cost only applies to existing housing.Set this equal to 0, because almost all costs for retrofits seem to be variable (except for permitting, which isn't usually used), and there's no data to suggest otherwise.
                                                                                                                                                                                                            Present In 2 Views:
                                                                                                                                                                                                            Used By
                                                                                                                                                                                                            • Expected Fixed Cost Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #127
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Fixed Cost per Unit Area (Dollar / sf)
                                                                                                                                                                                                            Fixed Cost per Unit Area[Cohort] = ZIDZ(
                                                                                                                                                                                                            Expected Fixed Cost, Average Area[ Cohort,Open to Retrofitting])
                                                                                                                                                                                                            Description: The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                            • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #130
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Fraction of Houses Switching (dmnl)
                                                                                                                                                                                                            Fraction of Houses Switching[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                            Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                                            Fraction of Houses Switching[Cohort,Gas Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                                            Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                                            Description: Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                            • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #143
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                                            Heating Energy Price[Heating and Cooling System] =
                                                                                                                                                                                                            Initial Heating Energy Price[ Heating and Cooling System]* Input 0
                                                                                                                                                                                                            Description: The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                            Present In 6 Views: Used By
                                                                                                                                                                                                            • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #191
                                                                                                                                                                                                            C
                                                                                                                                                                                                            Initial Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                                            Initial Heating Energy Price[Heat Pump Heating and Cooling] = 0.062
                                                                                                                                                                                                            Initial Heating Energy Price[Gas Heating] = 0.0142
                                                                                                                                                                                                            Initial Heating Energy Price[Oil Heating] = 0.017
                                                                                                                                                                                                            Description: Price of energy used in each technology: heat pump, central AC, window AC, no AC, gas, and oil. For heat pumps and air conditioners, this is electricity.Data from (using annual 2020 data for MA):electricity: https://www.eia.gov/electricity/data/browser/#/topic/7?agg=1,0&geo=vvvvvvvvvvvvo&endsec=8&freq=M&start=200101&ctype=linechart&ltype=pin&rtype=s&pin=&rse=0&maptype=0,natural gas:https://www.eia.gov/dnav/ng/ng_pri_sum_a_EPG0_PRS_DMcf_a.htmheating oil: https://www.eia.gov/petroleum/heatingoilpropane/
                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                            Used By
                                                                                                                                                                                                            • Heating Energy Price The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #192
                                                                                                                                                                                                            LI,A
                                                                                                                                                                                                            Initial Homes Not Retrofitting (House)
                                                                                                                                                                                                            Initial Homes Not Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                                                                                                                                                            Initial Homes Not Retrofitting[Preexisting Cohorts,Heating and Cooling System] = (1-
                                                                                                                                                                                                            Initial Fraction of Homes Retrofitting)* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                                                                                                                                                            Description: Initial homes not open to retrofitting.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #193
                                                                                                                                                                                                            LI,A
                                                                                                                                                                                                            Initial Homes Retrofitting (Houses)
                                                                                                                                                                                                            Initial Homes Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                                                                                                                                                            Initial Homes Retrofitting[Preexisting Cohorts,Heating and Cooling System] =
                                                                                                                                                                                                            Initial Fraction of Homes Retrofitting* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                                                                                                                                                            Description: Homes that are open to retrofitting initially.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #213
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))
                                                                                                                                                                                                            Marginal Heating Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                            Expected Heating Energy Price[ Heating and Cooling System]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                            Description: The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #265
                                                                                                                                                                                                            C
                                                                                                                                                                                                            Present Value of Cooling Operating Costs (Dollars / (House))
                                                                                                                                                                                                            Present Value of Cooling Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = (
                                                                                                                                                                                                            Expected Cooling Energy Price* Cooling Energy Use Under Alternatives[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Cooling Technology[ Heating and Cooling System]))
                                                                                                                                                                                                            Present Value of Cooling Operating Costs[Cohort,Traditional Cooling,Retrofitting Status,Heating and Cooling System] = ( Expected Cooling Energy Price* Cooling Energy Use Under Alternatives[ Cohort, Traditional Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Cooling Technology[ Heating and Cooling System]))
                                                                                                                                                                                                            Present Value of Cooling Operating Costs[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] = 0
                                                                                                                                                                                                            Description: The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #266
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Present Value of Heating Operating Costs (Dollar / (House))
                                                                                                                                                                                                            Present Value of Heating Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = (
                                                                                                                                                                                                            Expected Heating Energy Price[ Heating and Cooling System]* Heating Energy Use Under Alternatives[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Heating Technology[ Heating and Cooling System]))
                                                                                                                                                                                                            Present Value of Heating Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = ( Expected Heating Energy Price[ Heating and Cooling System]* Heating Energy Use Under Alternatives[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Heating Technology[ Heating and Cooling System]))
                                                                                                                                                                                                            Description: The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #283
                                                                                                                                                                                                            C
                                                                                                                                                                                                            Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )
                                                                                                                                                                                                            = 12.88
                                                                                                                                                                                                            Description: The marginal cost of retrofitting at the reference EUI. In particular, the marginal cost of retrofitting at some EUI is Reference U *( (Reference U / U) ^ Sensitivity )This was calculated by setting sensitivity of marginal cost equal to 1.25, and finding the MC where a 31% reduction in U value from the reference costs a total of 4.95 / (1 - 0.21) dollars per square foot. The sensitivity value is explained in the sensitivity variable. Less et al. (2021, pg. 17-18) note that in their project database, the median cost per square foot for retrofits after subsidies was $4.95, while subsidies accounted for 21% of the total project cost for the median project. The median cost reduced energy use by 28% - 33% (of which I took the average), and I use the lower bound value to account for the fact that energy savings may occur not only due to increase in U value.Obviously all of this is extraordinarily rough.Less et al. (2021): https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
                                                                                                                                                                                                            Present In 2 Views:
                                                                                                                                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #291
                                                                                                                                                                                                            C
                                                                                                                                                                                                            Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                                                                                                                                            = 3.25
                                                                                                                                                                                                            Description: Measures the sensitivity of marginal retrofit costs as a function of optimal U value. In particular, marginal Retrofit Cost is equal to Constant * (U Value retrofitted away ^ Convexity). This must be greater than 1.This is taken from pg. 69 of Caswell (2022), where she calculates the total retrofit cost curve as a function of percent savings as having an exponent of 2.25. Because this is the total retrofit cost curve, the exponent for the marginal cost is -2.25 - 1. Because percent savings is inversely proportional to U, the exponent in the total cost curve will be the negation of 2.25, which is ensured in the marginal cost curve formulation in other variables.
                                                                                                                                                                                                            Present In 4 Views:
                                                                                                                                                                                                            Used By
                                                                                                                                                                                                            • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                            • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                            • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                            • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                            • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                            • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                            • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v5 testing #338
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Unsubsidized Retrofit Cost Intensity (Dollar / sf)
                                                                                                                                                                                                            Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] = MAX(IF THEN ELSE(
                                                                                                                                                                                                            U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06,( Expected Reference Marginal Cost* Reference U Value/(- Sensitivity of Marginal Cost to U Value+1))*((( Reference U Value/ U Value of Retrofitting Homes[ Cohort, Heating and Cooling System])^ Sensitivity of Marginal Cost to U Value-1)-(( Reference U Value/ Optimal U Value for Existing Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value-1)))+ Fixed Cost per Unit Area[ Cohort],0),0)
                                                                                                                                                                                                            Description: Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                            Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            Top (Group) .housingagingchain v8 (51 Variables)
                                                                                                                                                                                                            Group
                                                                                                                                                                                                            Type
                                                                                                                                                                                                            Variable Name And Description
                                                                                                                                                                                                            .housingagingchain v8 #0
                                                                                                                                                                                                            C
                                                                                                                                                                                                            Active Cohort Indicator (dmnl)
                                                                                                                                                                                                            Active Cohort Indicator[Cohort] = IF THEN ELSE(INTEGER((
                                                                                                                                                                                                            Time- INITIAL TIME)/ Cohort Duration)+1= Cohort-ELMCOUNT( Preexisting Cohorts),1,0)
                                                                                                                                                                                                            Active Cohort Indicator[Preexisting Cohorts] = 0
                                                                                                                                                                                                            Description: The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v8 #8
                                                                                                                                                                                                            F,A
                                                                                                                                                                                                            Age Removal (House * Year /Year)
                                                                                                                                                                                                            Age Removal[Cohort,Retrofitting Status] = SUM(
                                                                                                                                                                                                            Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])* Average Age[ Cohort, Retrofitting Status]
                                                                                                                                                                                                            Description: Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                            .housingagingchain v8 #10
                                                                                                                                                                                                            F,A
                                                                                                                                                                                                            Aging (House * Year / Year)
                                                                                                                                                                                                            Aging[Cohort,Retrofitting Status] =
                                                                                                                                                                                                            Aging per Year*SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                                                                                                                            Description: Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v8 #9
                                                                                                                                                                                                            C
                                                                                                                                                                                                            Aging per Year (Year / Year)
                                                                                                                                                                                                            = 1
                                                                                                                                                                                                            Description: Number of years a house ages per year (which must be one), used to ensure dimensional consistency and make the model clearer
                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                            Used By
                                                                                                                                                                                                            • Aging Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v8 #21
                                                                                                                                                                                                            L
                                                                                                                                                                                                            Area (sf)
                                                                                                                                                                                                            Area[Cohort,Not Open to Retrofitting] = (
                                                                                                                                                                                                            Area of New Homes[ Cohort]- Net Area Shift due to Retrofit Status Switching[ Cohort])- Area Removal[ Cohort,Not Open to Retrofitting] dt + Initial Area[ Cohort]*(1.0- Fraction Retrofitting by Cohort[ Cohort])
                                                                                                                                                                                                            Area[Preexisting Cohorts,Not Open to Retrofitting] = (- Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts])- Area Removal[ Preexisting Cohorts,Not Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]*(1.0- Fraction Retrofitting by Cohort[ Preexisting Cohorts])
                                                                                                                                                                                                            Area[Cohort,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Cohort]- Area Removal[ Cohort,Open to Retrofitting] dt + Initial Area[ Cohort]* Fraction Retrofitting by Cohort[ Cohort]
                                                                                                                                                                                                            Area[Preexisting Cohorts,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts]- Area Removal[ Preexisting Cohorts,Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]* Fraction Retrofitting by Cohort[ Preexisting Cohorts]
                                                                                                                                                                                                            Description: "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                            • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                            • Total Area The total area across all housing.
                                                                                                                                                                                                            Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                            .housingagingchain v8 #19
                                                                                                                                                                                                            F,A
                                                                                                                                                                                                            Area of New Homes (sf / Year)
                                                                                                                                                                                                            Area of New Homes[Cohort] =
                                                                                                                                                                                                            Average Area of Housing Starts*SUM( Housing Starts[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                            Description: The total Area added by the construction of new homes, by cohort.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                            .housingagingchain v8 #20
                                                                                                                                                                                                            F,A
                                                                                                                                                                                                            Area Removal (sf /Year)
                                                                                                                                                                                                            Area Removal[Cohort,Retrofitting Status] =
                                                                                                                                                                                                            Average Area[ Cohort, Retrofitting Status]*SUM( Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                                                                                                                            Description: Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                            .housingagingchain v8 #24
                                                                                                                                                                                                            L
                                                                                                                                                                                                            Autocorrelated Noise (Dimensionless)
                                                                                                                                                                                                            =
                                                                                                                                                                                                            Change in AC Noise dt + 0.0
                                                                                                                                                                                                            Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                            • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                            .housingagingchain v8 #22
                                                                                                                                                                                                            L
                                                                                                                                                                                                            Autocorrelated Noise 0 (Dimensionless)
                                                                                                                                                                                                            =
                                                                                                                                                                                                            Change in AC Noise 0 dt + 0.0
                                                                                                                                                                                                            Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                            • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                            .housingagingchain v8 #26
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Average Age (Year)
                                                                                                                                                                                                            Average Age[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                                                                                                                            Total Age[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                                                                                                                            Description: The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                            • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                            • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                                            Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                            .housingagingchain v8 #25
                                                                                                                                                                                                            A
                                                                                                                                                                                                            Average Age in All Housing (Year)
                                                                                                                                                                                                            = ZIDZ(SUM(
                                                                                                                                                                                                            Total Age[ Cohort!, Retrofitting Status!]), Total Housing Stock)
                                                                                                                                                                                                            Description: Average age of houses, regardless of cohort
                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #27
                                                                                                                                                                                                              A
                                                                                                                                                                                                              Average Area in All Housing (sf/ House)
                                                                                                                                                                                                              = ZIDZ(
                                                                                                                                                                                                              Total Area, Total Housing Stock)
                                                                                                                                                                                                              Description: The average are of all houses, regardless of what group they're in.
                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #42
                                                                                                                                                                                                              A
                                                                                                                                                                                                              Average Energy Costs if Retrofitted (Dollar/(Year*House))
                                                                                                                                                                                                              Average Energy Costs if Retrofitted[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                              Optimal Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                              Description: Energy costs per year for each retrofitting house if homes retrofit to the optimal U value.
                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #64
                                                                                                                                                                                                              F,A
                                                                                                                                                                                                              Change in AC Noise (1/Year)
                                                                                                                                                                                                              = (
                                                                                                                                                                                                              White Noise- Autocorrelated Noise)/ Noise Correlation Time
                                                                                                                                                                                                              Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                              • Autocorrelated Noise First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                              Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                              .housingagingchain v8 #62
                                                                                                                                                                                                              F,A
                                                                                                                                                                                                              Change in AC Noise 0 (1/Year)
                                                                                                                                                                                                              = (
                                                                                                                                                                                                              White Noise 0- Autocorrelated Noise 0)/ Noise Correlation Time 0
                                                                                                                                                                                                              Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                              • Autocorrelated Noise 0 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                              Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                              .housingagingchain v8 #66
                                                                                                                                                                                                              C
                                                                                                                                                                                                              Cohort Duration (Year )
                                                                                                                                                                                                              = 10
                                                                                                                                                                                                              Description: The width (duration) of each cohort.
                                                                                                                                                                                                              Present In 2 Views:
                                                                                                                                                                                                              Used By
                                                                                                                                                                                                              • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                                              • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #100
                                                                                                                                                                                                              C
                                                                                                                                                                                                              Energy Price Exponential Growth Rate (1/Year )
                                                                                                                                                                                                              = 0
                                                                                                                                                                                                              Description: The exogenous growth fraction for the test input.
                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                              Used By
                                                                                                                                                                                                              • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #102
                                                                                                                                                                                                              C
                                                                                                                                                                                                              Energy Price Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                                              = 0
                                                                                                                                                                                                              Description: The quantity to be injected to customer orders, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                              Used By
                                                                                                                                                                                                              • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #104
                                                                                                                                                                                                              C
                                                                                                                                                                                                              Energy Price Ramp Slope (1/Year )
                                                                                                                                                                                                              = 0
                                                                                                                                                                                                              Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                              Used By
                                                                                                                                                                                                              • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #105
                                                                                                                                                                                                              C
                                                                                                                                                                                                              Energy Price Step Height (Dimensionless )
                                                                                                                                                                                                              = 0
                                                                                                                                                                                                              Description: Height of step input to customer orders, as fraction of initial value.
                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                              Used By
                                                                                                                                                                                                              • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #168
                                                                                                                                                                                                              C
                                                                                                                                                                                                              Housing Starts Exponential Growth Rate (1/Year )
                                                                                                                                                                                                              = 0
                                                                                                                                                                                                              Description: The exogenous growth fraction for the test input.
                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                              Used By
                                                                                                                                                                                                              • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #170
                                                                                                                                                                                                              C
                                                                                                                                                                                                              Housing Starts Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                                              = 0
                                                                                                                                                                                                              Description: The quantity to be injected to customer orders, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                              Used By
                                                                                                                                                                                                              • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #171
                                                                                                                                                                                                              C
                                                                                                                                                                                                              Housing Starts Ramp Slope (1/Year )
                                                                                                                                                                                                              = 0
                                                                                                                                                                                                              Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                              Used By
                                                                                                                                                                                                              • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #172
                                                                                                                                                                                                              C
                                                                                                                                                                                                              Housing Starts Step Height (Dimensionless )
                                                                                                                                                                                                              = 0
                                                                                                                                                                                                              Description: Height of step input to customer orders, as fraction of initial value.
                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                              Used By
                                                                                                                                                                                                              • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #184
                                                                                                                                                                                                              LI,A
                                                                                                                                                                                                              Initial Age (House * Year)
                                                                                                                                                                                                              Initial Age[Cohort,Retrofitting Status] = INITIAL(0)
                                                                                                                                                                                                              Initial Age[Preexisting Cohorts,Retrofitting Status] = (
                                                                                                                                                                                                              Cohort Duration*(ELMCOUNT( Preexisting Cohorts)- Preexisting Cohorts+1))* Housing by Cohort and Retrofitting Status[ Preexisting Cohorts, Retrofitting Status]
                                                                                                                                                                                                              Description: The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                              • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                              .housingagingchain v8 #200
                                                                                                                                                                                                              A
                                                                                                                                                                                                              Input (Dimensionless)
                                                                                                                                                                                                              = 1+STEP(
                                                                                                                                                                                                              Housing Starts Step Height, INITIAL TIME+ Step Time)+( Housing Starts Pulse Quantity/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time, TIME STEP)+RAMP( Housing Starts Ramp Slope, INITIAL TIME+ Ramp Start Time, INITIAL TIME+ Ramp End Time)+(STEP(1, INITIAL TIME)*(exp( Housing Starts Exponential Growth Rate*( Time- INITIAL TIME))-1))+ Sine Amplitude*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period)+STEP(1, INITIAL TIME+ Noise Start Time)* Autocorrelated Noise
                                                                                                                                                                                                              Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                .housingagingchain v8 #198
                                                                                                                                                                                                                A
                                                                                                                                                                                                                Input 0 (Dimensionless)
                                                                                                                                                                                                                = 1+STEP(
                                                                                                                                                                                                                Energy Price Step Height, INITIAL TIME+ Step Time 0)+( Energy Price Pulse Quantity/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time 0, TIME STEP)+RAMP( Energy Price Ramp Slope, INITIAL TIME+ Ramp Start Time 0, INITIAL TIME+ Ramp End Time 0)+(STEP(1, INITIAL TIME)*(exp( Energy Price Exponential Growth Rate*( Time- INITIAL TIME))-1))+ Sine Amplitude 0*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period 0)+STEP(1, INITIAL TIME+ Noise Start Time 0)* Autocorrelated Noise 0
                                                                                                                                                                                                                Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                • Heating Energy Price The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                .housingagingchain v8 #225
                                                                                                                                                                                                                C
                                                                                                                                                                                                                Maximum Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                = 10
                                                                                                                                                                                                                Description: Shifts x-axis for graph of optimal retrofit amount as a function of energy price.
                                                                                                                                                                                                                Present In 0 Views:
                                                                                                                                                                                                                  Used By
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #231
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    Net Area Shift by System (sf / Year)
                                                                                                                                                                                                                    Net Area Shift by System[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                    Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, Average Area[ Cohort,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], Average Area[ Cohort,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                                    Description: The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #238
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Noise Correlation Time (Year)
                                                                                                                                                                                                                    = 4
                                                                                                                                                                                                                    Description: The correlation time constant for Pink Noise.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                    • White Noise White noise input to the pink noise process.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #236
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Noise Correlation Time 0 (Year)
                                                                                                                                                                                                                    = 4
                                                                                                                                                                                                                    Description: The correlation time constant for Pink Noise.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                    • White Noise 0 White noise input to the pink noise process.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #241
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Noise Standard Deviation (Dimensionless)
                                                                                                                                                                                                                    = 0
                                                                                                                                                                                                                    Description: The standard deviation of the pink noise process.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • White Noise White noise input to the pink noise process.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #239
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Noise Standard Deviation 0 (Dimensionless)
                                                                                                                                                                                                                    = 0
                                                                                                                                                                                                                    Description: The standard deviation of the pink noise process.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #244
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Noise Start Time (Year)
                                                                                                                                                                                                                    = 5
                                                                                                                                                                                                                    Description: Start time for the random input.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #242
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Noise Start Time 0 (Year)
                                                                                                                                                                                                                    = 5
                                                                                                                                                                                                                    Description: Start time for the random input.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #275
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Pulse Time (Year)
                                                                                                                                                                                                                    = 5
                                                                                                                                                                                                                    Description: Time at which the pulse in Input occurs.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #273
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Pulse Time 0 (Year)
                                                                                                                                                                                                                    = 5
                                                                                                                                                                                                                    Description: Time at which the pulse in Input occurs.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #278
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Ramp End Time (Year)
                                                                                                                                                                                                                    = 1e+09
                                                                                                                                                                                                                    Description: End time for the ramp input.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #276
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Ramp End Time 0 (Year)
                                                                                                                                                                                                                    = 1e+09
                                                                                                                                                                                                                    Description: End time for the ramp input.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #281
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Ramp Start Time (Year)
                                                                                                                                                                                                                    = 5
                                                                                                                                                                                                                    Description: Start time for the ramp input.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #279
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Ramp Start Time 0 (Year)
                                                                                                                                                                                                                    = 5
                                                                                                                                                                                                                    Description: Start time for the ramp input.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #295
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Sine Amplitude (Dimensionless)
                                                                                                                                                                                                                    = 0
                                                                                                                                                                                                                    Description: Amplitude of sine wave in customer orders (fraction of mean).
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #293
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Sine Amplitude 0 (Dimensionless)
                                                                                                                                                                                                                    = 0
                                                                                                                                                                                                                    Description: Amplitude of sine wave in customer orders (fraction of mean).
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #298
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Sine Period (Year)
                                                                                                                                                                                                                    = 50
                                                                                                                                                                                                                    Description: Period of sine wave in customer demand. Set initially to 50 weeks (1 year).
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #296
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Sine Period 0 (Year)
                                                                                                                                                                                                                    = 50
                                                                                                                                                                                                                    Description: Period of sine wave in customer demand. Set initially to 50 weeks (1 year).
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #302
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Step Time (Year)
                                                                                                                                                                                                                    = 5
                                                                                                                                                                                                                    Description: Time for the step input.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #300
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Step Time 0 (Year)
                                                                                                                                                                                                                    = 5
                                                                                                                                                                                                                    Description: Time for the step input.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #309
                                                                                                                                                                                                                    L
                                                                                                                                                                                                                    Total Age (House * Year)
                                                                                                                                                                                                                    Total Age[Cohort,Not Open to Retrofitting] = (
                                                                                                                                                                                                                    Aging[ Cohort,Not Open to Retrofitting]- Net Age Shift from Retrofitting Status Shifting[ Cohort])- Age Removal[ Cohort,Not Open to Retrofitting] dt + Initial Age[ Cohort,Not Open to Retrofitting]
                                                                                                                                                                                                                    Total Age[Cohort,Open to Retrofitting] = ( Net Age Shift from Retrofitting Status Shifting[ Cohort]+ Aging[ Cohort,Open to Retrofitting])- Age Removal[ Cohort,Open to Retrofitting] dt + Initial Age[ Cohort,Open to Retrofitting]
                                                                                                                                                                                                                    Description: "Total" age for each cohort of housing.
                                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                                    • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                                                                                    • Average Age in All Housing Average age of houses, regardless of cohort
                                                                                                                                                                                                                    Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                                    .housingagingchain v8 #339
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    Unsubsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                                    Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                    Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort,Open to Retrofitting]
                                                                                                                                                                                                                    Description: Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                                    Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #343
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    White Noise (Dimensionless)
                                                                                                                                                                                                                    =
                                                                                                                                                                                                                    Noise Standard Deviation*((24* Noise Correlation Time/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                                                                                                                                                    Description: White noise input to the pink noise process.
                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                    • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    .housingagingchain v8 #341
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    White Noise 0 (Dimensionless)
                                                                                                                                                                                                                    =
                                                                                                                                                                                                                    Noise Standard Deviation 0*((24* Noise Correlation Time 0/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                                                                                                                                                    Description: White noise input to the pink noise process.
                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                    • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    Top (Group) .housingagingchain v9 (1 Variables)
                                                                                                                                                                                                                    Group
                                                                                                                                                                                                                    Type
                                                                                                                                                                                                                    Variable Name And Description
                                                                                                                                                                                                                    .housingagingchain v9 #285
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Reference U Value (kBTU / (sf * Year * F) )
                                                                                                                                                                                                                    = 0.006
                                                                                                                                                                                                                    Description: Reference U Value to ensure base of exponent in marginally optimal U value is dimensionless. This must be equal to or greater than code U value.Value taken as the average of U values of single family homes in MA in 2020 for our sample.
                                                                                                                                                                                                                    Present In 3 Views:
                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    Top (Group) HeatPumpModel_v31 (234 Variables)
                                                                                                                                                                                                                    Group
                                                                                                                                                                                                                    Type
                                                                                                                                                                                                                    Variable Name And Description
                                                                                                                                                                                                                    HeatPumpModel_v31 #1
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    Actual EEHIC Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                    Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] = MIN(
                                                                                                                                                                                                                    Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]* Implemented EEHIC Subsidy Proportional Rate for Retrofits, Implemented EEHIC Maximum Subsidy for Retrofits)
                                                                                                                                                                                                                    Description: The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value.
                                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #2
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    Actual HOMES Subsidy for Retrofits (Dollar/ Home)
                                                                                                                                                                                                                    Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                    Energy Savings[ Cohort, Heating and Cooling System]< HOMES Cut Off for Savings, HOMES Implemented Lower Subsidy, HOMES Implemented High Subsidy)
                                                                                                                                                                                                                    Description: The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #3
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    Actual MassSave Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                    Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] = MIN(
                                                                                                                                                                                                                    Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]* Implemented MassSave Subsidy Proportional Rate for Retrofits, Implemented MassSave Maximum Subsidy for Retrofits)
                                                                                                                                                                                                                    Description: The actual subsidy offered for retrofits by MassSave, not the expected value.
                                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #5
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    Affinity of Heating and Cooling Systems (dmnl)
                                                                                                                                                                                                                    Affinity of Heating and Cooling Systems[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                    Cost of Switching Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]>0,exp(- Sensitivity of Affinity to Cost* Cost of Switching Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Reference Lifetime Cost of Heating and Cooling Systems),0)
                                                                                                                                                                                                                    Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = IF THEN ELSE( Cost of Switching Heating and Cooling Systems[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]>0,exp(- Sensitivity of Affinity to Cost* Cost of Switching Heating and Cooling Systems[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]/ Reference Lifetime Cost of Heating and Cooling Systems),0)
                                                                                                                                                                                                                    Description: The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                    • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #6
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    Affinity of Not Retrofitting (dmnl)
                                                                                                                                                                                                                    Affinity of Not Retrofitting[Cohort,Heating and Cooling System] = exp(-
                                                                                                                                                                                                                    Sensitivity of Retrofits to Cost* Perceived Cost of Not Retrofitting[ Cohort, Heating and Cooling System]/ Reference Retrofit Cost)
                                                                                                                                                                                                                    Description: The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                    • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #11
                                                                                                                                                                                                                    C
                                                                                                                                                                                                                    Amoritization Period (Year )
                                                                                                                                                                                                                    = 20
                                                                                                                                                                                                                    Description: Time period over which incurred retrofit cost is amoritized; should be related to lifetime of a home.
                                                                                                                                                                                                                    Present In 1 View:
                                                                                                                                                                                                                    Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #13
                                                                                                                                                                                                                    F,A
                                                                                                                                                                                                                    Annual Federal Subsidies (Dollar / Year)
                                                                                                                                                                                                                    =
                                                                                                                                                                                                                    Federal Annual Heat Pump Subsidy+ Federal Annual Retrofit Subsidy
                                                                                                                                                                                                                    Description: The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year.
                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                    • Cumulative Federal Subsidy The amount of money the federal government spends on subsidies for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #14
                                                                                                                                                                                                                    F,A
                                                                                                                                                                                                                    Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                                                                    =
                                                                                                                                                                                                                    Federal Annual Heat Pump Subsidy+ Massachusetts Annual Heat Pumps Subsidy
                                                                                                                                                                                                                    Description: The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #15
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    Annual Load from Heat Pumps (kBTU / Year)
                                                                                                                                                                                                                    = SUM(
                                                                                                                                                                                                                    Energy Use by Grouping[ Cohort!, Heat Pump Heating and Cooling!, Retrofitting Status!])
                                                                                                                                                                                                                    Description: The load on the electric grid from servicing heating and cooling demand from heat pumps, across the whole year.
                                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #16
                                                                                                                                                                                                                    F,A
                                                                                                                                                                                                                    Annual MA Subsidies (Dollar / Year)
                                                                                                                                                                                                                    =
                                                                                                                                                                                                                    Massachusetts Annual Retrofit Subsidy+ Massachusetts Annual Heat Pumps Subsidy
                                                                                                                                                                                                                    Description: The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps.
                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                    • Cumulative MA Subsidy The amount of subsidies that the Massachusetts state government has given out for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #17
                                                                                                                                                                                                                    F,A
                                                                                                                                                                                                                    Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                    =
                                                                                                                                                                                                                    Federal Annual Retrofit Subsidy+ Massachusetts Annual Retrofit Subsidy
                                                                                                                                                                                                                    Description: The subsidies for retrofits paid out every year.
                                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                    HeatPumpModel_v31 #18
                                                                                                                                                                                                                    A
                                                                                                                                                                                                                    Annual Subsidies (Dollar / Year)
                                                                                                                                                                                                                    =
                                                                                                                                                                                                                    Annual Heat Pump Subsidy+ Annual Retrofit Subsidy
                                                                                                                                                                                                                    Description: The amount of subsidies spent on heat pumps and retrofits every year.
                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                      HeatPumpModel_v31 #23
                                                                                                                                                                                                                      L
                                                                                                                                                                                                                      Autocorrelated Noise 1 (Dimensionless)
                                                                                                                                                                                                                      =
                                                                                                                                                                                                                      Change in AC Noise 1 dt + 0.0
                                                                                                                                                                                                                      Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                      • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                      • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                      Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                      HeatPumpModel_v31 #29
                                                                                                                                                                                                                      A
                                                                                                                                                                                                                      Average Area (sf / House)
                                                                                                                                                                                                                      Average Area[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                                                                                                                                      Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                                                                                                                                      Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                                      Present In 7 Views: Used By
                                                                                                                                                                                                                      • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                      • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                      • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                                                                                      • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                      • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                      • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                      • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                                      • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                      • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                                      • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                                      • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                      • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                      • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                      • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                      • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                      • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                                      Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                                      HeatPumpModel_v31 #28
                                                                                                                                                                                                                      A
                                                                                                                                                                                                                      Average Area of Housing Starts (sf / House)
                                                                                                                                                                                                                      =
                                                                                                                                                                                                                      Increase in Area per Year*( Time- INITIAL TIME)+ Initial Average Area of Housing Starts
                                                                                                                                                                                                                      Description: The average area of housing starts.
                                                                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                      HeatPumpModel_v31 #31
                                                                                                                                                                                                                      A
                                                                                                                                                                                                                      Average Cooling Cost (Dollar / (Year * House))
                                                                                                                                                                                                                      Average Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                      Expected Cooling Energy Price* Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                      Description: The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                      HeatPumpModel_v31 #30
                                                                                                                                                                                                                      A
                                                                                                                                                                                                                      Average Cooling Cost Across All Homes (Dollar / House/ Year)
                                                                                                                                                                                                                      =
                                                                                                                                                                                                                      Total Cooling Cost/SUM( Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                      Description: The average cost to cool a home, for all cohorts and systems.
                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                        HeatPumpModel_v31 #33
                                                                                                                                                                                                                        C
                                                                                                                                                                                                                        Average Cooling Energy Use (kBTU / (Year * House))
                                                                                                                                                                                                                        Average Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                        U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                        Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                                                                        Description: The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                        Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                        HeatPumpModel_v31 #32
                                                                                                                                                                                                                        A
                                                                                                                                                                                                                        Average Cooling Energy Use Across All Homes (kBTU / Year / House)
                                                                                                                                                                                                                        = ZIDZ(
                                                                                                                                                                                                                        Total Cooling Energy Use, Total Housing Stock)
                                                                                                                                                                                                                        Description: The amount of energy an average home spends on cooling, regardless of cohort, retrofit status, etc.
                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                          HeatPumpModel_v31 #34
                                                                                                                                                                                                                          A
                                                                                                                                                                                                                          Average Daily Load from Heat Pumps (kBTU / Day)
                                                                                                                                                                                                                          =
                                                                                                                                                                                                                          Annual Load from Heat Pumps/ Days per Year
                                                                                                                                                                                                                          Description: The average load on the electric grid from heat pumps, per day.
                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                            HeatPumpModel_v31 #39
                                                                                                                                                                                                                            A
                                                                                                                                                                                                                            Average Emissions (tCO2 / House / Year)
                                                                                                                                                                                                                            = ZIDZ(
                                                                                                                                                                                                                            Emissions, Total Housing Stock)
                                                                                                                                                                                                                            Description: The average CO2 emissions for a household, not disaggregated into any grouping.
                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                              HeatPumpModel_v31 #35
                                                                                                                                                                                                                              A
                                                                                                                                                                                                                              Average Emissions by Grouping (tCO2 / (Year * House))
                                                                                                                                                                                                                              Average Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                              Average Emissions from Cooling by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Emissions from Heating by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                              Description: The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                              HeatPumpModel_v31 #36
                                                                                                                                                                                                                              A
                                                                                                                                                                                                                              Average Emissions by Heating and Cooling System (tCO2 / Year / House)
                                                                                                                                                                                                                              Average Emissions by Heating and Cooling System[Heating and Cooling System] = ZIDZ(
                                                                                                                                                                                                                              Emissions by Heating and Cooling System[ Heating and Cooling System], Housing by Heating and Cooling System[ Heating and Cooling System])
                                                                                                                                                                                                                              Description: The average CO2 emissions for each house, by heating and cooling system.
                                                                                                                                                                                                                              Present In 2 Views: Used By
                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                HeatPumpModel_v31 #37
                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                Average Emissions from Cooling by Grouping (tCO2 / (House * Year))
                                                                                                                                                                                                                                Average Emissions from Cooling by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Cooling Emissions Factor/ Pounds per Ton
                                                                                                                                                                                                                                Description: The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status.
                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                HeatPumpModel_v31 #38
                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                Average Emissions from Heating by Grouping (tCO2 / (House * Year))
                                                                                                                                                                                                                                Average Emissions from Heating by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Heating Emissions Factors[ Heating and Cooling System]/ Pounds per Ton
                                                                                                                                                                                                                                Description: Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc.
                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                HeatPumpModel_v31 #40
                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                Average Energy Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                Average Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                Average Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                Description: The average cost of both heating and cooling a home, by grouping.
                                                                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                HeatPumpModel_v31 #45
                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                Average Energy Use (kBTU / (Year * House))
                                                                                                                                                                                                                                Average Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                Description: Average energy use to both heat and cool a home.
                                                                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                HeatPumpModel_v31 #43
                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                Average Energy Use by Heating and Cooling System (kBTU / (House * Year))
                                                                                                                                                                                                                                Average Energy Use by Heating and Cooling System[Heating and Cooling System] = ZIDZ(SUM(
                                                                                                                                                                                                                                Energy Use by Grouping[ Cohort!, Heating and Cooling System, Retrofitting Status!]),SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!]))
                                                                                                                                                                                                                                Description: The average energy use for each home by heating and cooling system.
                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                  HeatPumpModel_v31 #44
                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                  Average Energy Use in All Housing (kBTU / Year / House)
                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                  Total Energy Use/ Total Housing Stock
                                                                                                                                                                                                                                  Description: The average energy use across all stocks.
                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                  HeatPumpModel_v31 #46
                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                  Average EUI by Grouping (kBTU / (sf * Year))
                                                                                                                                                                                                                                  Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = XIDZ(
                                                                                                                                                                                                                                  Average Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status], Average Area[ Cohort, Retrofitting Status], NAREPLACEMENT)
                                                                                                                                                                                                                                  Description: The average energy use intensity by grouping
                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                    HeatPumpModel_v31 #47
                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                    Average EUI in All Housing (kBTU / (sf * Year))
                                                                                                                                                                                                                                    =
                                                                                                                                                                                                                                    Average Energy Use in All Housing/ Average Area in All Housing
                                                                                                                                                                                                                                    Description: The average energy use intensity across all housing.
                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                      HeatPumpModel_v31 #48
                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                      Average Heating Cost Across All Homes (Dollar / Year / House)
                                                                                                                                                                                                                                      = ZIDZ(
                                                                                                                                                                                                                                      Total Heating Cost,SUM( Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!]))
                                                                                                                                                                                                                                      Description: The average amount a home spends on heating, regardless of cohort or heating and cooling system.
                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                        HeatPumpModel_v31 #51
                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                        Average Heating Energy Use (kBTU / (Year * House))
                                                                                                                                                                                                                                        Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                        U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                        Description: The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                        Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                        HeatPumpModel_v31 #50
                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                        Average Heating Energy Use Across All Homes (kBTU / (Year * House))
                                                                                                                                                                                                                                        = ZIDZ(
                                                                                                                                                                                                                                        Total Heating Energy Use, Total Housing Stock)
                                                                                                                                                                                                                                        Description: The average heating energy use per home, regardless of cohort, system,etc.
                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                          HeatPumpModel_v31 #52
                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                          Average Income (Dollar / Hour / House )
                                                                                                                                                                                                                                          = 55
                                                                                                                                                                                                                                          Description: The average income of single family homeowners in Massachusetts. Calculated from 2020 EIA RECS data for MA SFH, where each individual was assigned the average income of their reported income bracket, other than those making more than $150K/year, who were assigned $175,000. Hourly wage calculated by assuming working 8 hours a day, 5 days a week, for 50 weeks in a year.
                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                          • Soft Costs of Retrofitting The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                          HeatPumpModel_v31 #53
                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                          Average Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                          Indicated Homes Retrofitting[ Cohort!, Heating and Cooling System!])/ Total Housing Stock
                                                                                                                                                                                                                                          Description: The average fraction of homes that will retrofit retrofitting after decision delayacross all housing.
                                                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                            HeatPumpModel_v31 #54
                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                            Average Lifetime of Cooling Technology (Years)
                                                                                                                                                                                                                                            Average Lifetime of Cooling Technology[Heat Pump Heating and Cooling] = 12.5
                                                                                                                                                                                                                                            Average Lifetime of Cooling Technology[Central AC Cooling] = 12.5
                                                                                                                                                                                                                                            Average Lifetime of Cooling Technology[Window AC Cooling] = 9
                                                                                                                                                                                                                                            Average Lifetime of Cooling Technology[No AC Cooling] =
                                                                                                                                                                                                                                            NAREPLACEMENT
                                                                                                                                                                                                                                            Description: The average lifetime of each cooling system.Central AC data from: https://www.energy.gov/energysaver/central-air-conditioningWindow AC data from: https://www.consumerreports.org/air-conditioner/is-it-time-to-get-a-new-window-air-conditioner-a1532530762/
                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                            • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                            • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                            HeatPumpModel_v31 #55
                                                                                                                                                                                                                                            C
                                                                                                                                                                                                                                            Average Lifetime of Heating Technology (Year)
                                                                                                                                                                                                                                            Average Lifetime of Heating Technology[Heat Pump Heating and Cooling] = 12.5
                                                                                                                                                                                                                                            Average Lifetime of Heating Technology[Gas Heating] = 20
                                                                                                                                                                                                                                            Average Lifetime of Heating Technology[Oil Heating] = 20
                                                                                                                                                                                                                                            Description: The average lifetime of each heating system.Heat pump data from: https://glascohvac.com/heating/heat-pumps/long-heat-pump-last/Gas data from: https://www.carrier.com/residential/en/us/products/furnaces/how-long-does-a-furnaces-last/Oil data from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                                                            Used By
                                                                                                                                                                                                                                            • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                            • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                            HeatPumpModel_v31 #56
                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                            Average Subsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                            Housing[ Cohort!, Heating and Cooling System!,Open to Retrofitting]* Subsidized Retrofit Cost[ Cohort!, Heating and Cooling System!])/SUM( Housing[ Cohort!, Heating and Cooling System!,Open to Retrofitting])
                                                                                                                                                                                                                                            Description: The average subsidized retrofit cost across all houses.
                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                              HeatPumpModel_v31 #57
                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                              Average Time To Consider Switching (Year )
                                                                                                                                                                                                                                              = 15
                                                                                                                                                                                                                                              Description: The average time it takes for a house to consider switching their heating and cooling system.
                                                                                                                                                                                                                                              Present In 2 Views:
                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                              HeatPumpModel_v31 #58
                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                              Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                              Average U Value by Heating and Cooling System[Heating and Cooling System] = ZIDZ(
                                                                                                                                                                                                                                              Total U Value by Heating and Cooling System[ Heating and Cooling System], Housing by Heating and Cooling System[ Heating and Cooling System])
                                                                                                                                                                                                                                              Description: The U value of the average house using each heating and cooling system.
                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                HeatPumpModel_v31 #60
                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                Average U Value of Houses Switching Into Sources[Heating and Cooling System] = XIDZ(
                                                                                                                                                                                                                                                U Value Increase from Source Switching[ Heating and Cooling System], Houses Switching Into Sources[ Heating and Cooling System], NAREPLACEMENT)
                                                                                                                                                                                                                                                Description: The average U value of houses switching into each source, for each source.
                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #61
                                                                                                                                                                                                                                                  C
                                                                                                                                                                                                                                                  CDD on Coldest Day (F )
                                                                                                                                                                                                                                                  = 17.1
                                                                                                                                                                                                                                                  Description: The total CDD from hottest day.Data from https://www.degreedays.net/ for KOWD, weather station nearest to centre of population for MA, Natick. Calculated by finding CDDs from the past three years (February 2021 - January 2024), finding the highest CDD in each year, and averaging them. Following industry standard, used 65°F as set point.
                                                                                                                                                                                                                                                  Present In 1 View:
                                                                                                                                                                                                                                                  Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #63
                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                  Change in AC Noise 1 (1/Year)
                                                                                                                                                                                                                                                  = (
                                                                                                                                                                                                                                                  White Noise 1- Autocorrelated Noise 1)/ Noise Correlation Time 1
                                                                                                                                                                                                                                                  Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                  • Autocorrelated Noise 1 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #67
                                                                                                                                                                                                                                                  C
                                                                                                                                                                                                                                                  Cooling Degree Days (F )
                                                                                                                                                                                                                                                  = 1029
                                                                                                                                                                                                                                                  Description: The difference between temperature setpoint (65 F) and outside temperature for heating. Typically called cooling degree days, but units are solely in terms of fahrenheit.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. Use set point of 65°F, in line with industry standard, as at that temperature little heating or cooling is necessary.
                                                                                                                                                                                                                                                  Present In 3 Views:
                                                                                                                                                                                                                                                  Used By
                                                                                                                                                                                                                                                  • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                  • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                  • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                  • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #68
                                                                                                                                                                                                                                                  C
                                                                                                                                                                                                                                                  Cooling Emissions Factor (lb CO2 / kBTU)
                                                                                                                                                                                                                                                  = 614/3414.43
                                                                                                                                                                                                                                                  Description: Amount of CO2 emitted from using one kBTU to cool a home. Emissions factor is common, and is for electricity.Taken from: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/download
                                                                                                                                                                                                                                                  Present In 1 View:
                                                                                                                                                                                                                                                  Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #70
                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                  Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                  Initial Cooling Energy Price* Input 1
                                                                                                                                                                                                                                                  Description: Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                                                                                  Present In 3 Views: Used By
                                                                                                                                                                                                                                                  • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #69
                                                                                                                                                                                                                                                  C
                                                                                                                                                                                                                                                  Cooling Energy Price Step Height 1 (Dimensionless )
                                                                                                                                                                                                                                                  = 0
                                                                                                                                                                                                                                                  Description: Height of step input to customer orders, as fraction of initial value.
                                                                                                                                                                                                                                                  Present In 1 View:
                                                                                                                                                                                                                                                  Used By
                                                                                                                                                                                                                                                  • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #71
                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                  Cooling Energy Use Under Alternatives (kBTU / (House * Year))
                                                                                                                                                                                                                                                  Cooling Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Not Open to Retrofitting,Heating and Cooling System] =
                                                                                                                                                                                                                                                  U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                  Cooling Energy Use Under Alternatives[Cohort,Traditional Cooling,Not Open to Retrofitting,Heating and Cooling System] = U Value by Grouping[ Cohort, Traditional Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                  Cooling Energy Use Under Alternatives[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] = 0
                                                                                                                                                                                                                                                  Cooling Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                  Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Fossil Fuel Heating,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                  Description: The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                  • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #72
                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                  Cooling System Efficiency (dmnl)
                                                                                                                                                                                                                                                  Cooling System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                                                                  Heat Pump Cooling COP TABLE( Time)
                                                                                                                                                                                                                                                  Cooling System Efficiency[Central AC Cooling] = 2.93
                                                                                                                                                                                                                                                  Cooling System Efficiency[Window AC Cooling] = 2.49* Effect of Air Leakage from Window AC on Efficiency
                                                                                                                                                                                                                                                  Cooling System Efficiency[No AC Cooling] = NAREPLACEMENT
                                                                                                                                                                                                                                                  Description: The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                  Present In 4 Views: Used By
                                                                                                                                                                                                                                                  • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                  • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                  • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                  • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                  • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #73
                                                                                                                                                                                                                                                  C
                                                                                                                                                                                                                                                  Cost of Bad Air Conditioning (Dollar / House )
                                                                                                                                                                                                                                                  Cost of Bad Air Conditioning[Window AC Cooling] = 80000
                                                                                                                                                                                                                                                  Cost of Bad Air Conditioning[No AC Cooling] = 100000
                                                                                                                                                                                                                                                  Description: Willingness of Window AC users and those without AC to pay for central AC or heat pumps due to those technologies' inability to heat homes and their noisiness.Chosen to be sufficiently high that very few or no houses choose to keep window AC or no AC.
                                                                                                                                                                                                                                                  Present In 1 View:
                                                                                                                                                                                                                                                  Used By
                                                                                                                                                                                                                                                  • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #74
                                                                                                                                                                                                                                                  C
                                                                                                                                                                                                                                                  Cost of Cooling System Replacement (Dollar / House)
                                                                                                                                                                                                                                                  Cost of Cooling System Replacement[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                                                                  Subsidized Cost of Heat Pumps
                                                                                                                                                                                                                                                  Cost of Cooling System Replacement[Central AC Cooling] = 5800
                                                                                                                                                                                                                                                  Cost of Cooling System Replacement[Window AC Cooling] = 1600
                                                                                                                                                                                                                                                  Cost of Cooling System Replacement[No AC Cooling] = 0
                                                                                                                                                                                                                                                  Description: The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                  • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                  • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #75
                                                                                                                                                                                                                                                  C
                                                                                                                                                                                                                                                  Cost of Heating System Replacement (Dollar / House )
                                                                                                                                                                                                                                                  Cost of Heating System Replacement[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                                                                  Subsidized Cost of Heat Pumps
                                                                                                                                                                                                                                                  Cost of Heating System Replacement[Gas Heating] = 10000
                                                                                                                                                                                                                                                  Cost of Heating System Replacement[Oil Heating] = 7450
                                                                                                                                                                                                                                                  Description: The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                  • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                  • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                  HeatPumpModel_v31 #77
                                                                                                                                                                                                                                                  L
                                                                                                                                                                                                                                                  Cumulative Emissions (tCO2)
                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                  Emissions dt + 0.0
                                                                                                                                                                                                                                                  Description: The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                    HeatPumpModel_v31 #78
                                                                                                                                                                                                                                                    L
                                                                                                                                                                                                                                                    Cumulative Federal Subsidy (Dollar)
                                                                                                                                                                                                                                                    =
                                                                                                                                                                                                                                                    Annual Federal Subsidies dt + 0.0
                                                                                                                                                                                                                                                    Description: The amount of money the federal government spends on subsidies for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                      HeatPumpModel_v31 #79
                                                                                                                                                                                                                                                      L
                                                                                                                                                                                                                                                      Cumulative MA Subsidy (Dollar)
                                                                                                                                                                                                                                                      =
                                                                                                                                                                                                                                                      Annual MA Subsidies dt + 0.0
                                                                                                                                                                                                                                                      Description: The amount of subsidies that the Massachusetts state government has given out for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                        HeatPumpModel_v31 #81
                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                        Cumulative Subsidies (Dollar)
                                                                                                                                                                                                                                                        =
                                                                                                                                                                                                                                                        Cumulative Subsidy for Retrofits+ Cumulative Subsidies for Heat Pumps
                                                                                                                                                                                                                                                        Description: The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #80
                                                                                                                                                                                                                                                          L
                                                                                                                                                                                                                                                          Cumulative Subsidies for Heat Pumps (Dollar)
                                                                                                                                                                                                                                                          =
                                                                                                                                                                                                                                                          Annual Heat Pump Subsidy dt + 0.0
                                                                                                                                                                                                                                                          Description: The total amount of dollars spent on subsidizing heat pumps throughout the model's run.
                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                          • Cumulative Subsidies The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #82
                                                                                                                                                                                                                                                          L
                                                                                                                                                                                                                                                          Cumulative Subsidy for Retrofits (Dollar)
                                                                                                                                                                                                                                                          =
                                                                                                                                                                                                                                                          Annual Retrofit Subsidy dt + 0.0
                                                                                                                                                                                                                                                          Description: The total amount spent on retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                          • Cumulative Subsidies The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #83
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          Days per Year (Day / Year )
                                                                                                                                                                                                                                                          = 365
                                                                                                                                                                                                                                                          Description: The number of days each year. Used to convert yearly measures to daily ones.
                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #88
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          Demolition Hazard Rate (1 / Year )
                                                                                                                                                                                                                                                          = 0.01
                                                                                                                                                                                                                                                          Description: Proportion of homes demolished every year. Value is assumed to be equal across both retrofitting and non-retrofitting homes. Heuristically chosen so total housing stock grows at net 1%/year.
                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #89
                                                                                                                                                                                                                                                          F,A
                                                                                                                                                                                                                                                          Demolitions (House / Year)
                                                                                                                                                                                                                                                          Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                          Demolition Hazard Rate* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]*(1- No Turnover Switch)
                                                                                                                                                                                                                                                          Description: Homes that are destroyed every year.
                                                                                                                                                                                                                                                          Present In 3 Views: Used By
                                                                                                                                                                                                                                                          • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                          • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                          • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                          • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                          Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #90
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          Discount Rate (1 / Year )
                                                                                                                                                                                                                                                          = 0.05
                                                                                                                                                                                                                                                          Description: Discount rate for discounting energy savings cash flows.Average and bounds from demand-side discount rate from MassDEP's analysis of pathways for net zero (pg. 103): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadhttps://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                                                                          Present In 4 Views:
                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                          • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                                                                          • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                          • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                          • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                          • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #91
                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                          EEHIC Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                          EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = MIN(
                                                                                                                                                                                                                                                          Proportional Subsidy Switch for Retrofits* Expected EEHIC Proportional Subsidy Rate for Retrofits* Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status], Expected EEHIC Maximum Subsidy for Retrofits)
                                                                                                                                                                                                                                                          Description: The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #92
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          EEHIC Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                                                                          = 1200
                                                                                                                                                                                                                                                          Description: The maximum proportional subsidy that will be offered from Energy Efficient Home Improvement Credit, regardless of that subsidy's discount. Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #93
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                                                                          = 0.3
                                                                                                                                                                                                                                                          Description: Proportion of total retrofit cost that will be credited with the Energy Efficiency Home Improvement Credit.Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                          • Implemented EEHIC Subsidy Proportional Rate for Retrofits The implemented proportional subsidy rate for retrofits from the IRA, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #94
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          EEHIC Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                                                                          = 2033
                                                                                                                                                                                                                                                          Description: The year in which the EEHIC is phased out. If final time, then has no ending data.Source: https://www.irs.gov/credits-deductions/energy-efficient-home-improvement-credit
                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #95
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          Effect of Air Leakage from Window AC on Efficiency (dmnl)
                                                                                                                                                                                                                                                          = 0.9*10/11
                                                                                                                                                                                                                                                          Description: A window air conditioner typically does not perfectly cover its intended cavity, leading to more air leakage and therefore reducing efficiency.Taken from: https://www.energy.gov/sites/prod/files/2014/08/f18/ba_innovations_1-2-5_window_ac.pdf
                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                          • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #98
                                                                                                                                                                                                                                                          F,A
                                                                                                                                                                                                                                                          Emissions (tCO2 / Year)
                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                          Emissions by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                          Description: The total amount of emissions across all housing groups.
                                                                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                                                                          • Average Emissions The average CO2 emissions for a household, not disaggregated into any grouping.
                                                                                                                                                                                                                                                          • Cumulative Emissions The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #96
                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                          Emissions by Grouping (tCO2 / Year)
                                                                                                                                                                                                                                                          Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                          Housing[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Emissions by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                          Description: The total emissions for the most disaggregated grouping in the model.
                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #97
                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                          Emissions by Heating and Cooling System (tCO2 / Year)
                                                                                                                                                                                                                                                          Emissions by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                          Emissions by Grouping[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                          Description: The total amount of emissions for houses by Heating and Cooling System.
                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #99
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          Energy Price Exponential Growth Rate 1 (1/Year )
                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                          Description: The exogenous growth fraction for the test input.
                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #101
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          Energy Price Pulse Quantity 1 (Dimensionless*Year)
                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                          Description: Pulse value, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #103
                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                          Energy Price Ramp Slope 1 (1/Year )
                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                          Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #106
                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                          Energy Savings (dmnl)
                                                                                                                                                                                                                                                          Energy Savings[Cohort,Heating and Cooling System] = MAX(0,ABS(ZIDZ((
                                                                                                                                                                                                                                                          Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]- U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]), U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting])))
                                                                                                                                                                                                                                                          Description: The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                          HeatPumpModel_v31 #107
                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                          Energy Use by Gas Houses (kBTU/ Year)
                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                          Energy Use by Grouping[ Cohort!,Gas and Central AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Gas and Window AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Gas and No AC, Retrofitting Status!])
                                                                                                                                                                                                                                                          Description: The total amount of energy for heating and cooling used by homes which primarily use gas to heat their homes.
                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                            HeatPumpModel_v31 #108
                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                            Energy Use by Grouping (kBTU / Year)
                                                                                                                                                                                                                                                            Energy Use by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                            Average Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                            Description: The total amount of energy used for heating and cooling in each group.
                                                                                                                                                                                                                                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                            HeatPumpModel_v31 #109
                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                            Energy Use by Heat Pump Houses (kBTU / Year)
                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                            Energy Use by Grouping[ Cohort!,Heat Pump Only, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Heat Pump and Gas, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Heat Pump and Oil, Retrofitting Status!])
                                                                                                                                                                                                                                                            Description: The amount of energy used for heating and cooling by homes which primarily use heat pumps to heat their home.
                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                              HeatPumpModel_v31 #110
                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                              Energy Use by Oil Houses (kBTU / Year)
                                                                                                                                                                                                                                                              = SUM(
                                                                                                                                                                                                                                                              Energy Use by Grouping[ Cohort!,Oil and Central AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Oil and Window AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Oil and No AC, Retrofitting Status!])
                                                                                                                                                                                                                                                              Description: The total amount of energy for heating and cooling used by homes primarily using oil to heat their home.
                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                HeatPumpModel_v31 #111
                                                                                                                                                                                                                                                                SM,A
                                                                                                                                                                                                                                                                Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                = SMOOTH3(
                                                                                                                                                                                                                                                                Cooling Energy Price, Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                                                                                Description: Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                                                                                Present In 4 Views: Used By
                                                                                                                                                                                                                                                                • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                                                                                • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                                • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                                                                                • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                HeatPumpModel_v31 #112
                                                                                                                                                                                                                                                                SM,A
                                                                                                                                                                                                                                                                Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                = SMOOTH3(
                                                                                                                                                                                                                                                                Implemented EEHIC Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays.
                                                                                                                                                                                                                                                                Present In 2 Views: Used By
                                                                                                                                                                                                                                                                • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                HeatPumpModel_v31 #113
                                                                                                                                                                                                                                                                SM,A
                                                                                                                                                                                                                                                                Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                = SMOOTH3(
                                                                                                                                                                                                                                                                Implemented EEHIC Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                                                                                Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                Present In 2 Views: Used By
                                                                                                                                                                                                                                                                • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                HeatPumpModel_v31 #116
                                                                                                                                                                                                                                                                SM,A
                                                                                                                                                                                                                                                                Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                = SMOOTH3(
                                                                                                                                                                                                                                                                IRA Implemented Subsidy Proportional Rate for Heat Pumps, Delay in Changing Subsidy Expectations)* Proportional IRA Subsidy Switch for Heat Pumps
                                                                                                                                                                                                                                                                Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                HeatPumpModel_v31 #120
                                                                                                                                                                                                                                                                SM,A
                                                                                                                                                                                                                                                                Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                = SMOOTH3(
                                                                                                                                                                                                                                                                Implemented IRA Maximum Proportional Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                HeatPumpModel_v31 #122
                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                Expected Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                =
                                                                                                                                                                                                                                                                MassSave Expected Lump Sum Subsidy for Heat Pumps+ IRA Expected Proportional Subsidy for Heat Pumps
                                                                                                                                                                                                                                                                Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidies.
                                                                                                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                HeatPumpModel_v31 #124
                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                Federal Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                =
                                                                                                                                                                                                                                                                Total Heat Pump Sales* IRA Actual Subsidy for Heat Pumps
                                                                                                                                                                                                                                                                Description: The amount of subsidies the federal government spends on heat pumps through the Inflation Reduction Act every year.
                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                • Annual Federal Subsidies The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year.
                                                                                                                                                                                                                                                                • Annual Heat Pump Subsidy The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                HeatPumpModel_v31 #125
                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                Federal Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                = SUM((
                                                                                                                                                                                                                                                                Actual EEHIC Subsidy for Retrofits[ Cohort!, Heating and Cooling System!]+ Actual HOMES Subsidy for Retrofits[ Cohort!, Heating and Cooling System!])* Houses Retrofitting per Year[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                                                                                                                Description: The amount of federal subsidies spent by the federal government, through the IRA.
                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                HeatPumpModel_v31 #129
                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                Fraction of Houses in Each Heating and Cooling System (dmnl)
                                                                                                                                                                                                                                                                Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] = XIDZ(
                                                                                                                                                                                                                                                                Housing by Heating and Cooling System[ Heating and Cooling System], Total Housing Stock, NAREPLACEMENT)
                                                                                                                                                                                                                                                                Description: The fraction of houses using each heating and cooling system
                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #131
                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                  Fraction of Housing by Heating and Cooling System (dmnl)
                                                                                                                                                                                                                                                                  Fraction of Housing by Heating and Cooling System[Heating and Cooling System] =
                                                                                                                                                                                                                                                                  Housing by Heating and Cooling System[ Heating and Cooling System]/ Total Housing Stock
                                                                                                                                                                                                                                                                  Description: The fraction of the total housing stock using each heating and cooling system.
                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #134
                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                    Fraction Retrofitting (dmnl)
                                                                                                                                                                                                                                                                    =
                                                                                                                                                                                                                                                                    Housing by Retrofitting Status[Open to Retrofitting]/( Housing by Retrofitting Status[Not Open to Retrofitting]+ Housing by Retrofitting Status[Open to Retrofitting])
                                                                                                                                                                                                                                                                    Description: Proportion of housing that is open to retrofitting, across all cohorts and systems.
                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #132
                                                                                                                                                                                                                                                                      LI,A
                                                                                                                                                                                                                                                                      Fraction Retrofitting by Cohort (dmnl)
                                                                                                                                                                                                                                                                      Fraction Retrofitting by Cohort[Cohort] = ZIDZ(SUM(
                                                                                                                                                                                                                                                                      Housing[ Cohort, Heating and Cooling System!,Open to Retrofitting]),SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!]))
                                                                                                                                                                                                                                                                      Description: Fraction that are retrofitting, only by cohort.
                                                                                                                                                                                                                                                                      Present In 2 Views: Used By
                                                                                                                                                                                                                                                                      • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #133
                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                      Fraction Retrofitting by System and Cohort (dmnl)
                                                                                                                                                                                                                                                                      Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] = ZIDZ(
                                                                                                                                                                                                                                                                      Housing[ Cohort, Heating and Cooling System,Open to Retrofitting],SUM( Housing[ Cohort, Heating and Cooling System, Retrofitting Status!]))
                                                                                                                                                                                                                                                                      Description: The fraction of houses that are retrofitting, by heating/cooling system and cohort.
                                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #135
                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                        Fractional Decrease in Code U (1 / Year )
                                                                                                                                                                                                                                                                        = 0
                                                                                                                                                                                                                                                                        Description: Fractional decrease in code per year. Exogenous and set by policymakers in the real world. For initial paper, assume that code U is constant.
                                                                                                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                                                                                                        Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #136
                                                                                                                                                                                                                                                                        A,T
                                                                                                                                                                                                                                                                        Gas COP TABLE (dmnl)
                                                                                                                                                                                                                                                                        Gas COP TABLE([(2020,0)-(2050,1)],(2020,0.9),(2030,0.925),(2040,0.95),(2050,0.95))

                                                                                                                                                                                                                                                                        Description: Efficiency of gas systems over time. Taken as the average of projected efficiency for reference gas boilers and gas furnaces, from MassDEP's Energy Pathways for Deep Decarbonization Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                                                                                                        Used By
                                                                                                                                                                                                                                                                        • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #137
                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                        HDD on Coldest Day (F )
                                                                                                                                                                                                                                                                        = 55.2333
                                                                                                                                                                                                                                                                        Description: The total HDD from coldest day.Data from https://www.degreedays.net/ for KOWD, weather station nearest to centre of population for MA, Natick. Calculated by finding HDDs from the past three years (February 2021 - January 2024), finding the highest HDD in each year, and averaging them. Following industry standard, used set point of 65°F.
                                                                                                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                                                                                                        Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #138
                                                                                                                                                                                                                                                                        A,T
                                                                                                                                                                                                                                                                        Heat Pump Cooling COP TABLE (dmnl)
                                                                                                                                                                                                                                                                        Heat Pump Cooling COP TABLE([(2020,0)-(2050,10)],(2020,4.3),(2030,4.8),(2040,5.17),(2050,5.28))

                                                                                                                                                                                                                                                                        Description: The COP of heat pumps when used for cooling. Calculated by assuming the ratio of heating and cooling COP is constant over time -- as heating COP improves the ability to cool improves proportionally-- finding cooling COP in 2020, finding the COP for cooling of heating in 2018, and then using the ratio between the two in 2020 to project future values. Data on this was difficult to find.Projected heating COP from pg. 97 of MassDEP's Energy Pathways for Deep Decarbonization: https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadCooling COP in 2020 here: https://www.raleighheatingandair.com/blog/is-a-heat-pump-more-effective-at-cooling-or-heating/
                                                                                                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                                                                                                        Used By
                                                                                                                                                                                                                                                                        • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #139
                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                        Heat Pump COP on Coldest Days (dmnl )
                                                                                                                                                                                                                                                                        = 2.16438
                                                                                                                                                                                                                                                                        Description: The heat pump COP on coolest day of the year.Taken from NYSERDA/MassCEC study on heat pump performance on 41 heat pumps: https://e4thefuture.org/wp-content/uploads/2022/06/Residential-ccASHP-Building-Electrification_060322.pdf (pg. 24). Regressed COP on temperature and its square. Using daily data on HDD (set point 65°F) for 2021-2023 from degreedays.net, calculated temperature of coldest day on average. Plugged that into regression model to find COP on coldest day.
                                                                                                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                                                                                                        Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #140
                                                                                                                                                                                                                                                                        A,T
                                                                                                                                                                                                                                                                        Heat Pump Heating COP TABLE (dmnl)
                                                                                                                                                                                                                                                                        Heat Pump Heating COP TABLE([(2020,0)-(2050,10)],(2020,2.485),(2030,2.785),(2040,2.99),(2050,3.05))

                                                                                                                                                                                                                                                                        Description: The efficiency of heat pumps for heating, over time. Taken as the average of projected COP for reference ASHP and ductless mini-splits from MassDEP's Energy Pathways Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                                                                                                        Used By
                                                                                                                                                                                                                                                                        • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #141
                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                        Heating Degree Days (F )
                                                                                                                                                                                                                                                                        = 5026
                                                                                                                                                                                                                                                                        Description: The difference between temperature setpoint (65 F) and outside temperature.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. In line with industry standard, use set point of 65°F, as thattemperature little heating or cooling is needed.
                                                                                                                                                                                                                                                                        Present In 3 Views:
                                                                                                                                                                                                                                                                        Used By
                                                                                                                                                                                                                                                                        • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                        • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                        • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                                                                                        • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #142
                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                        Heating Emissions Factors (lb CO2 / kBTU)
                                                                                                                                                                                                                                                                        Heating Emissions Factors[Heat Pump Heating and Cooling] = 684/3414.43
                                                                                                                                                                                                                                                                        Heating Emissions Factors[Gas Heating] = 116.65/1000
                                                                                                                                                                                                                                                                        Heating Emissions Factors[Oil Heating] = 163.45/1000
                                                                                                                                                                                                                                                                        Description: The pounds of CO2 emitted per kBTU of heating energy provided, for each heating fuel.Data for heat pumps (electricity) is: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/downloadRest is from: https://www.eia.gov/environment/emissions/co2_vol_mass.phpIn line with that source, I assume that each heat pump will add to the grid and is not part of base demand, and so the marginal emissions from producing electricity from heat pumps will be constant at the value as it will come from natural gas generators (explanation of which is from here: https://willbrownsberger.com/how-green-will-the-power-be/
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                                                                                                                                                                                                                                                                        Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #144
                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                        Heating Energy Use Under Alternatives (kBTU / (House * Year))
                                                                                                                                                                                                                                                                        Heating Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Not Open to Retrofitting,Heating and Cooling System] =
                                                                                                                                                                                                                                                                        U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                        Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Not Open to Retrofitting,Heating and Cooling System] = U Value by Grouping[ Cohort, Fossil Fuel Heating,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                        Heating Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                        Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Fossil Fuel Heating,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                        Description: The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                        • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #145
                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                        Heating System Efficiency (dmnl)
                                                                                                                                                                                                                                                                        Heating System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                                                                                        Heat Pump Heating COP TABLE( Time)
                                                                                                                                                                                                                                                                        Heating System Efficiency[Gas Heating] = Gas COP TABLE( Time)
                                                                                                                                                                                                                                                                        Heating System Efficiency[Oil Heating] = Oil COP TABLE( Time)
                                                                                                                                                                                                                                                                        Description: The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                        Present In 3 Views: Used By
                                                                                                                                                                                                                                                                        • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                        • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                        • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                                                                                        • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #146
                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                        Homeowner Hours Spent Retrofitting (Hour )
                                                                                                                                                                                                                                                                        = 750
                                                                                                                                                                                                                                                                        Description: The amount of hours a homeowners spends retrofitting their home themselves, i.e., the hours spent deciding to retrofit, supervising audits, moving out of the home as necessary, etc. No hard data on this, calibrated so that the initial fraction of homes willing to retrofit is 10%.
                                                                                                                                                                                                                                                                        Present In 1 View:
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                                                                                                                                                                                                                                                                        • Soft Costs of Retrofitting The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #147
                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                        HOMES Cut Off for Savings (dmnl )
                                                                                                                                                                                                                                                                        = 0.35
                                                                                                                                                                                                                                                                        Description: The percent energy savings needed to get the higher subsidy amount from the Home Owner Managing Energy Savings rebate. Taken from: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                                                                                                                        Present In 2 Views:
                                                                                                                                                                                                                                                                        Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #148
                                                                                                                                                                                                                                                                        SM,A
                                                                                                                                                                                                                                                                        HOMES Expected Higher Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                        = SMOOTH3(
                                                                                                                                                                                                                                                                        HOMES Implemented High Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                        Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                                                                                                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #150
                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                        HOMES High Subsidy Amount (Dollar / House )
                                                                                                                                                                                                                                                                        = 4000
                                                                                                                                                                                                                                                                        Description: The subsidy from the home owner managing energy savings rebate for retrofits saving more than 35% of energy.Source: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                                                                                                        Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #151
                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                        HOMES Implemented High Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                        = IF THEN ELSE(
                                                                                                                                                                                                                                                                        Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES High Subsidy Amount,0)
                                                                                                                                                                                                                                                                        Description: Implemented higher subsidy from the HOMES rebate program.
                                                                                                                                                                                                                                                                        Present In 2 Views: Used By
                                                                                                                                                                                                                                                                        • Actual HOMES Subsidy for Retrofits The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                                                                                                                                                                                                                                        • HOMES Expected Higher Subsidy Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #154
                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                        HOMES Subsidy Final Year (Year)
                                                                                                                                                                                                                                                                        = 2032
                                                                                                                                                                                                                                                                        Description: Final year of Home Owner Managing Energy Savings rebate, assumed to be the same as that of the EEHIC.
                                                                                                                                                                                                                                                                        Present In 1 View:
                                                                                                                                                                                                                                                                        Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #156
                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                        Houses Considering Switching System (Houses / Year)
                                                                                                                                                                                                                                                                        Houses Considering Switching System[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                        Housing[ Cohort, Heating and Cooling System, Retrofitting Status]/ Average Time To Consider Switching
                                                                                                                                                                                                                                                                        Description: The number of houses per year considering switching their heating and cooling system.
                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                        • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                        Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #158
                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                        Houses Retrofitting (Houses)
                                                                                                                                                                                                                                                                        Houses Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                        Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                                                                                        Description: Total amount of houses retrofitting in each cohort and heating and cooling system.
                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #157
                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                          Houses Retrofitting per Year (House / Year)
                                                                                                                                                                                                                                                                          Houses Retrofitting per Year[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                          Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]< U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting], Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]/ Retrofit Delay,0)
                                                                                                                                                                                                                                                                          Description: The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #159
                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                          Houses Switching Into Sources (Houses / Year)
                                                                                                                                                                                                                                                                          Houses Switching Into Sources[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                          Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!, Heating and Cooling System])
                                                                                                                                                                                                                                                                          Description: The number of houses switching into each Heating and Cooling System, cohort, and retrofitting group due to system switching.
                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #160
                                                                                                                                                                                                                                                                          F,A
                                                                                                                                                                                                                                                                          Houses Switching Sources (House / Year)
                                                                                                                                                                                                                                                                          Houses Switching Sources[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                                                                                          Fraction of Houses Switching[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                                                                                                                                          Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Fraction of Houses Switching[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Fossil Fuel Heating, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                                                                                                                                          Description: The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                          Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #174
                                                                                                                                                                                                                                                                          L
                                                                                                                                                                                                                                                                          Housing (House)
                                                                                                                                                                                                                                                                          Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                                                                                                                                          Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                          Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                          Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                          Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #163
                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                          Housing by Cohort (House)
                                                                                                                                                                                                                                                                          Housing by Cohort[Cohort] = SUM(
                                                                                                                                                                                                                                                                          Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                          Description: Number of houses per cohort
                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #161
                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                            Housing by Cohort and Heating and Cooling System (Houses)
                                                                                                                                                                                                                                                                            Housing by Cohort and Heating and Cooling System[Cohort,Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                            Housing[ Cohort, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                                            Description: Housing by heating and cooling system and cohort, irrespective of retrofit status.
                                                                                                                                                                                                                                                                            Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #162
                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                            Housing by Cohort and Retrofitting Status (House)
                                                                                                                                                                                                                                                                            Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] = SUM(
                                                                                                                                                                                                                                                                            Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                                                                                                                                                                                            Description: Amount of housing by retrofit status and cohort.
                                                                                                                                                                                                                                                                            Present In 3 Views: Used By
                                                                                                                                                                                                                                                                            • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                                                                                                                                            • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                                                                                            • Housing by Retrofitting Status Amount of housing by retrofitting status, across all cohorts and systems.
                                                                                                                                                                                                                                                                            • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #164
                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                            Housing by Heating and Cooling System (House)
                                                                                                                                                                                                                                                                            Housing by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                            Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                                            Description: Number of houses by energy source across all cohorts.
                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #165
                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                            Housing by Retrofitting Status (House)
                                                                                                                                                                                                                                                                            Housing by Retrofitting Status[Retrofitting Status] = SUM(
                                                                                                                                                                                                                                                                            Housing by Cohort and Retrofitting Status[ Cohort!, Retrofitting Status])
                                                                                                                                                                                                                                                                            Description: Amount of housing by retrofitting status, across all cohorts and systems.
                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                            • Fraction Retrofitting Proportion of housing that is open to retrofitting, across all cohorts and systems.
                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #166
                                                                                                                                                                                                                                                                            C
                                                                                                                                                                                                                                                                            Housing Fractional Growth Rate (1 / Year )
                                                                                                                                                                                                                                                                            = 0.02
                                                                                                                                                                                                                                                                            Description: The annual growth rate in housing. Heuristically chosen so that total housing stock grows at net 1%/year.
                                                                                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                                                                                            Used By
                                                                                                                                                                                                                                                                            • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #173
                                                                                                                                                                                                                                                                            F,A
                                                                                                                                                                                                                                                                            Housing Starts (Houses / Year)
                                                                                                                                                                                                                                                                            Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                            Housing Fractional Growth Rate*SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])* Active Cohort Indicator[ Cohort]*(1- No Turnover Switch)
                                                                                                                                                                                                                                                                            Description: Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                            Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [2,2] (-) 0  [0,0]
                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #167
                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                            Housing Starts Across Cohorts ()
                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                            Housing Starts In Each Cohort[ Cohort!])
                                                                                                                                                                                                                                                                            Description: Housing starts across all cohorts.
                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #169
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Housing Starts In Each Cohort (House / Year)
                                                                                                                                                                                                                                                                              Housing Starts In Each Cohort[Cohort] = SUM(
                                                                                                                                                                                                                                                                              Housing Starts[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                              Description: Housing starts across heating and cooling systems.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #175
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                                                                                                                              Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: Time<= EEHIC Subsidy for Retrofits Final Year, EEHIC Maximum Subsidy for Retrofits,0)
                                                                                                                                                                                                                                                                              Description: Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #176
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                                                                                                                              Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: EEHIC Subsidy for Retrofits Final Year>= Time, EEHIC Proportional Subsidy Rate for Retrofits,0)
                                                                                                                                                                                                                                                                              Description: The implemented proportional subsidy rate for retrofits from the IRA, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #177
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                                                                                                                              Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: Time<= IRA Lump Sum Subsidy for Heat Pumps Final Year, IRA Maximum Proportional Subsidy for Heat Pumps,0)
                                                                                                                                                                                                                                                                              Description: Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #180
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              Increase in Area per Year (sf / Year / House )
                                                                                                                                                                                                                                                                              = 10.76
                                                                                                                                                                                                                                                                              Description: The exogenous increase in area per year, found by regressing area on year house was built in RECS 2020 data for MA SFG.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #182
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                                                                                              Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                              Affinity of Retrofitting[ Cohort, Heating and Cooling System]/( Affinity of Retrofitting[ Cohort, Heating and Cooling System]+ Affinity of Not Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                                                                                              Description: Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #183
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Indicated Homes Retrofitting (House)
                                                                                                                                                                                                                                                                              Indicated Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                              Indicated Fraction of Homes Retrofitting[ Cohort, Heating and Cooling System]* Housing by Cohort and Heating and Cooling System[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                              Description: Number of homes that, once delays are taken into account, will be open to retrofitting.
                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #185
                                                                                                                                                                                                                                                                              LI,C
                                                                                                                                                                                                                                                                              Initial Area (sf)
                                                                                                                                                                                                                                                                              Initial Area[Cohort] = 10
                                                                                                                                                                                                                                                                              Description: Total initial area across all houses, by cohort (assuming that average area is the same across systems).
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                              • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #186
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              Initial Average Area of Housing Starts (sf / House )
                                                                                                                                                                                                                                                                              = 2347
                                                                                                                                                                                                                                                                              Description: Initial average area of housing starts. Taken from average area of MA SFH homes built from 2015 to 2020, from EIA RECS data.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #187
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              Initial Average U Value (kBTU/(Year*sf*F))
                                                                                                                                                                                                                                                                              Initial Average U Value[Cohort] = 0.19235
                                                                                                                                                                                                                                                                              Description: The initial average U, equal to the average U value of MA SFH in 2022, from EIA RECS.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                              • Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #188
                                                                                                                                                                                                                                                                              LI,C
                                                                                                                                                                                                                                                                              Initial Code U Value (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                              = 0.003
                                                                                                                                                                                                                                                                              Description: The initial value of code U. For initial paper, assume that this is between initial optimal U (nearly 0) and average U (0.006).
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                              • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #189
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              Initial Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                              = 0.062
                                                                                                                                                                                                                                                                              Description: The price to cool a home per BTU. This is the price of electricity as all cooling systems, as air conditioning systems, use electricity.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                              • Cooling Energy Price Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #190
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              Initial Fraction of Homes Retrofitting (dmnl )
                                                                                                                                                                                                                                                                              = 0.1
                                                                                                                                                                                                                                                                              Description: Initial fraction of homes open to retrofitting. Heuristically chosen to be 0.1 to match low level of retrofitting that current occurs.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #195
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              Initial Housing (House)
                                                                                                                                                                                                                                                                              Initial Housing[Cohort,Heating and Cooling System] = 2.2e+06
                                                                                                                                                                                                                                                                              Description: The total number of houses that begin in each cohort and heating and cooling source. Taken from CIN file.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #199
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Input 1 (Dimensionless)
                                                                                                                                                                                                                                                                              = 1+STEP(
                                                                                                                                                                                                                                                                              Cooling Energy Price Step Height 1, INITIAL TIME+ Step Time 1)+( Energy Price Pulse Quantity 1/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time 1, TIME STEP)+RAMP( Energy Price Ramp Slope 1, INITIAL TIME+ Ramp Start Time 1, INITIAL TIME+ Ramp End Time 1)+(STEP(1, INITIAL TIME)*(exp( Energy Price Exponential Growth Rate 1*( Time- INITIAL TIME))-1))+ Sine Amplitude 1*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period 1)+STEP(1, INITIAL TIME+ Noise Start Time 1)* Autocorrelated Noise 1
                                                                                                                                                                                                                                                                              Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                              • Cooling Energy Price Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #201
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              IRA Actual Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                              = MIN(
                                                                                                                                                                                                                                                                              IRA Implemented Subsidy Proportional Rate for Heat Pumps* Unsubsidized Cost of Heat Pumps, Implemented IRA Maximum Proportional Subsidy for Heat Pumps)
                                                                                                                                                                                                                                                                              Description: The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #202
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                              = MIN(
                                                                                                                                                                                                                                                                              Proportional IRA Subsidy Switch for Heat Pumps* Expected IRA Proportional Subsidy Rate for Heat Pumps* Unsubsidized Cost of Heat Pumps, Expected Maximum IRA Proportional Subsidy for Heat Pumps)
                                                                                                                                                                                                                                                                              Description: The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #203
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                                                                                                                              Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: IRA Lump Sum Subsidy for Heat Pumps Final Year>= Time, IRA Proportional Subsidy Rate for Heat Pumps,0)
                                                                                                                                                                                                                                                                              Description: The implemented proportional subsidy rate, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy rate afterwards.
                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #204
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )
                                                                                                                                                                                                                                                                              = 2032
                                                                                                                                                                                                                                                                              Description: The year in which the subsidy is phased out. If final time, then has no ending date.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #205
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )
                                                                                                                                                                                                                                                                              = 2000
                                                                                                                                                                                                                                                                              Description: The maximum proportional subsidy for heat pumps that will be offered, regardless of the subsidy rate. For instance, if the proportional subsidy is 50% but the maximum is $1000, then for a retrofit project that costs $3000 only a $1000 subsidy will be given.Taken from: https://www.energystar.gov/about/federal-tax-credits
                                                                                                                                                                                                                                                                              Present In 2 Views:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #206
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                                                                                              = 2023
                                                                                                                                                                                                                                                                              Description: Time at which the proportional subsidy will take effect from the Inflation Reduction Act, from https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #207
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                              = 0.3
                                                                                                                                                                                                                                                                              Description: Proportion of total heat pump cost that will be credited as part of a proportional subsidy.Taken from: https://www.energystar.gov/about/federal-tax-credits
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #208
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              kBTU per kWH (kBTU / kWH )
                                                                                                                                                                                                                                                                              = 3.41214
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #209
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)
                                                                                                                                                                                                                                                                              Lifetime Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                              Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]/ Discount Rate
                                                                                                                                                                                                                                                                              Description: The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                              • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                              • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                              • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #210
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))
                                                                                                                                                                                                                                                                              Marginal Cooling Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                              Expected Cooling Energy Price* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                              Description: The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #211
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))
                                                                                                                                                                                                                                                                              Marginal Cost at Binding U Value without EEHIC[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                              Expected Reference Marginal Cost*(ZIDZ( Reference U Value, U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]))^ Sensitivity of Marginal Cost to U Value
                                                                                                                                                                                                                                                                              Description: This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                              • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #215
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                              =
                                                                                                                                                                                                                                                                              Total Heat Pump Sales* MassSave Implemented Lump Sum Subsidy for Heat Pumps
                                                                                                                                                                                                                                                                              Description: The actual subsidy provided for purchase of heat pumps by Massachusetts, as opposed to what the subsidy expected by homeowners is.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                              • Annual Heat Pump Subsidy The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                                                                                                                              • Annual MA Subsidies The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps.
                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #216
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Massachusetts Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                              = SUM(
                                                                                                                                                                                                                                                                              Houses Retrofitting per Year[ Cohort!, Heating and Cooling System!]* Actual MassSave Subsidy for Retrofits[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                                                                                                                              Description: Amount of money Massachusetts spends on MassSave subsidies for retrofits, yearly.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #217
                                                                                                                                                                                                                                                                              SM,A
                                                                                                                                                                                                                                                                              MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                              = SMOOTH3(
                                                                                                                                                                                                                                                                              MassSave Implemented Lump Sum Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                              Description: Expected lump sum subsidy that lowers subsidized retrofit costs from the state, taking into account information delays.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #219
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                              = MIN(
                                                                                                                                                                                                                                                                              Unsubsidized Cost of Heat Pumps,IF THEN ELSE( Time>= MassSave Lump Sum Subsidy Implementation Year for Heat Pumps:AND: Time<= MassSave Lump Sum Subsidy for Heat Pumps Final Year, MassSave Lump Sum Subsidy Amount for Heat Pumps,0))
                                                                                                                                                                                                                                                                              Description: Lump sum subsidy from MassSave that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #220
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )
                                                                                                                                                                                                                                                                              = 10000
                                                                                                                                                                                                                                                                              Description: The total amount of money offered by the lump sum subsidy.Taken from: https://www.masssave.com/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #221
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)
                                                                                                                                                                                                                                                                              = 2200
                                                                                                                                                                                                                                                                              Description: The year in which the state's subsidy for heat pumps is phased out.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #222
                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                              MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                                                                                              = 2020
                                                                                                                                                                                                                                                                              Description: The year in which the state's lump sum subsidy for heat pumps will activate.
                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #224
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              MassSave Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                                                                                              =
                                                                                                                                                                                                                                                                              FINAL TIME
                                                                                                                                                                                                                                                                              Description: The year in which the subsidy is phased out. If final time, then has no ending data.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #226
                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                              Monthly Total Heat Pump Sales (Houses/ Month)
                                                                                                                                                                                                                                                                              =
                                                                                                                                                                                                                                                                              Total Heat Pump Sales/ Months per Year
                                                                                                                                                                                                                                                                              Description: The number of homes buying heat pumps, every year.
                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #227
                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                Months per Year (Month / Year )
                                                                                                                                                                                                                                                                                = 12
                                                                                                                                                                                                                                                                                Description: The number of months per year.
                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #229
                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                Net Age Shift by System (Year * House / Year)
                                                                                                                                                                                                                                                                                Net Age Shift by System[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, Average Age[ Cohort,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], Average Age[ Cohort,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                                                                                                Description: The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #230
                                                                                                                                                                                                                                                                                F,A
                                                                                                                                                                                                                                                                                Net Age Shift from Retrofitting Status Shifting (House * Year / Year)
                                                                                                                                                                                                                                                                                Net Age Shift from Retrofitting Status Shifting[Cohort] = SUM(
                                                                                                                                                                                                                                                                                Net Age Shift by System[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                Description: Shift in age within each cohort due to houses becoming open or closed to retrofitting.
                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #232
                                                                                                                                                                                                                                                                                F,A
                                                                                                                                                                                                                                                                                Net Area Shift due to Retrofit Status Switching (sf / Year)
                                                                                                                                                                                                                                                                                Net Area Shift due to Retrofit Status Switching[Cohort] = SUM(
                                                                                                                                                                                                                                                                                Net Area Shift by System[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                Description: Shift in area between energy sources due to houses switching sources.
                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #233
                                                                                                                                                                                                                                                                                F,A
                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting (Houses / Year)
                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] = (
                                                                                                                                                                                                                                                                                Indicated Homes Retrofitting[ Cohort, Heating and Cooling System]- Housing[ Cohort, Heating and Cooling System,Open to Retrofitting])/ Time to Decide to Retrofit
                                                                                                                                                                                                                                                                                Description: Homes that are in the process of deciding to retrofit.
                                                                                                                                                                                                                                                                                Present In 3 Views: Used By
                                                                                                                                                                                                                                                                                • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                                                                                                                • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                                                                                                • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #234
                                                                                                                                                                                                                                                                                F,A
                                                                                                                                                                                                                                                                                Net U Value Change from Retrofitting Home Shifts (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, U Value by Grouping[ Cohort, Heating and Cooling System,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                                                                                                Description: Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #235
                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                No Turnover Switch (dmnl )
                                                                                                                                                                                                                                                                                = 0
                                                                                                                                                                                                                                                                                Description: Switch for having no turnover in housing stock-- i.e., no housing demolitions or constructions.
                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                • Demolitions Homes that are destroyed every year.
                                                                                                                                                                                                                                                                                • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #237
                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                Noise Correlation Time 1 (Year)
                                                                                                                                                                                                                                                                                = 4
                                                                                                                                                                                                                                                                                Description: The correlation time constant for Pink Noise.
                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                • White Noise 1 White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #240
                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                Noise Standard Deviation 1 (Dimensionless)
                                                                                                                                                                                                                                                                                = 0
                                                                                                                                                                                                                                                                                Description: The standard deviation of the pink noise process.
                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #243
                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                Noise Start Time 1 (Year)
                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                Description: Start time for the random input.
                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #245
                                                                                                                                                                                                                                                                                A,T
                                                                                                                                                                                                                                                                                Oil COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                Oil COP TABLE([(2020,0)-(2050,1)],(2020,0.835),(2030,0.84),(2050,0.84))

                                                                                                                                                                                                                                                                                Description: Efficiency of oil systems over time. Taken as the average of projected efficiency for reference distillate boilers and furnaces, from MassDEP's Energy Pathways for Deep Decarbonization Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #246
                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                Optimal Cooling Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                Optimal Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                Expected Cooling Energy Price* Optimal Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                Description: The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #247
                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                                                                                                                                Description: The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #248
                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                Optimal Energy Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                Optimal Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                Optimal Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Optimal Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                Description: Total energy cost if optimal U value is achieved.
                                                                                                                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #249
                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                Optimal Energy Use (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]+ Optimal Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                Description: Average energy use to heat and cool per house if U is optimal.
                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #250
                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                  Optimal Heating Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                  Optimal Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                  Expected Heating Energy Price[ Heating and Cooling System]* Optimal Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                  Description: Average heating cost if U value is optimal.
                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #251
                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                  Optimal Heating Energy Use (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                  Optimal Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                  Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                  Description: The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #252
                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                  Optimal U Across All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                  = SUM(
                                                                                                                                                                                                                                                                                  Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort!, Heating and Cooling System!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!]/ Total Housing Stock)
                                                                                                                                                                                                                                                                                  Description: The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #255
                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                    Optimal U Value for Existing Homes (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                    Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                    U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]< Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System],IF THEN ELSE( Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]> Marginal Cost at Binding U Value without EEHIC[ Cohort, Heating and Cooling System], Optimal U Value with No EEHIC Proportional Subsidy[ Cohort, Heating and Cooling System], U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]))
                                                                                                                                                                                                                                                                                    Description: This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
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                                                                                                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #256
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                                                                                                                                                                                                                                                                                    Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                    Optimal U Value with No EEHIC Proportional Subsidy[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                    Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                                                                                                                    Description: Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #257
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                                                                                                                                                                                                                                                                                    Peak Cooling Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                    = SUM(
                                                                                                                                                                                                                                                                                    Peak Load from Heat Pumps on Hottest Days per Group[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                    Description: Annual load from heat pumps providing heating on the coldest day, across all groups.
                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #258
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                                                                                                                                                                                                                                                                                      Peak Heating Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                      = SUM(
                                                                                                                                                                                                                                                                                      Peak Load from Heat Pumps on Coldest Days per Group[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                      Description: Annual load from heat pumps providing heating on the coldest days, across all groups.
                                                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #259
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                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)
                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Heat Pump Heating and Cooling,Retrofitting Status] =
                                                                                                                                                                                                                                                                                        Housing[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* HDD on Coldest Day/ Heat Pump COP on Coldest Days/( kBTU per kWH* Days per Year)
                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Fossil Fuel Heating,Retrofitting Status] = 0
                                                                                                                                                                                                                                                                                        Description: The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #260
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                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)
                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Hottest Days per Group[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                        Housing[ Cohort, Heating and Cooling System, Retrofitting Status]* U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* CDD on Coldest Day/ Cooling System Efficiency[ Heating and Cooling System]/( kBTU per kWH* Days per Year)
                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Hottest Days per Group[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                                                                                                                                        Description: The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #261
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                                                                                                                                                                                                                                                                                        Peak Load from Non Heating or Cooling Sources (kWH / Day )
                                                                                                                                                                                                                                                                                        = 18344.8*1000*0.461799
                                                                                                                                                                                                                                                                                        Description: The peak load coming from non-heating sources, like other household uses, commercial uses, industrial uses, etc. Approximated as the average peak load in September, October, April, and May of 2022 and 2023 from New England ISO data, since there is little heating or cooling demand in those swing months. We multiply by 0.46 as Massachusetts has 46% of New England's population and we assume demand is proportional to population.Data source: https://www.iso-ne.com/isoexpress/web/reports/load-and-demand/-/tree/net-ener-peak-load
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                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #262
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                                                                                                                                                                                                                                                                                          Perceived Cost of Not Retrofitting (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                          Perceived Cost of Not Retrofitting[Cohort,Heating and Cooling System] = (1-
                                                                                                                                                                                                                                                                                          Weight on Upfront Cost)* Total Cost of Ownership of Average Home[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                          Description: Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                          • Affinity of Not Retrofitting The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #263
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                                                                                                                                                                                                                                                                                          Perceived Cost of Retrofitting (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                          Perceived Cost of Retrofitting[Cohort,Heating and Cooling System] = (1-
                                                                                                                                                                                                                                                                                          Weight on Upfront Cost)* Total Cost of Ownership of Retrofitted Homes[ Cohort, Heating and Cooling System]+ Weight on Upfront Cost* Amoritized Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                          Description: Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #264
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                                                                                                                                                                                                                                                                                          Pounds per Ton (lb CO2 / tCO2)
                                                                                                                                                                                                                                                                                          = 2204.6
                                                                                                                                                                                                                                                                                          Description: The number of pounds in a metric ton.
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                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #267
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                                                                                                                                                                                                                                                                                          Present Value of Operating Costs (Dollar / (House) )
                                                                                                                                                                                                                                                                                          Present Value of Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                          Present Value of Cooling Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]+ Present Value of Heating Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]
                                                                                                                                                                                                                                                                                          Present Value of Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Present Value of Cooling Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]+ Present Value of Heating Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]
                                                                                                                                                                                                                                                                                          Description: Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
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                                                                                                                                                                                                                                                                                          • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #268
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                                                                                                                                                                                                                                                                                          Present Value Replacement Cost (Dollar / House)
                                                                                                                                                                                                                                                                                          Present Value Replacement Cost[Heating and Cooling System] =
                                                                                                                                                                                                                                                                                          Cost of Cooling System Replacement[ Heating and Cooling System]/( Average Lifetime of Cooling Technology[ Heating and Cooling System]* Discount Rate)+ Cost of Heating System Replacement[ Heating and Cooling System]/( Average Lifetime of Heating Technology[ Heating and Cooling System]* Discount Rate)
                                                                                                                                                                                                                                                                                          Present Value Replacement Cost[Heat Pump Heating and Cooling] = Cost of Cooling System Replacement[ Heat Pump Heating and Cooling]/( Average Lifetime of Cooling Technology[ Heat Pump Heating and Cooling]* Discount Rate)
                                                                                                                                                                                                                                                                                          Present Value Replacement Cost[No AC Cooling] = 0
                                                                                                                                                                                                                                                                                          Description: Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
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                                                                                                                                                                                                                                                                                          • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #269
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                                                                                                                                                                                                                                                                                          Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                                                                                                          = 2023
                                                                                                                                                                                                                                                                                          Description: Time at which the proportional subsidy will take effect from the Energy Efficiency Home Improvement Credit.Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #270
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                                                                                                                                                                                                                                                                                          Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                                          = 1
                                                                                                                                                                                                                                                                                          Description: Turns proportional subsidy's effect on retrofit cost on/off.
                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #274
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                                                                                                                                                                                                                                                                                          Pulse Time 1 (Year)
                                                                                                                                                                                                                                                                                          = 5
                                                                                                                                                                                                                                                                                          Description: Time at which the pulse in Input occurs.
                                                                                                                                                                                                                                                                                          Present In 1 View:
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                                                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #277
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                                                                                                                                                                                                                                                                                          Ramp End Time 1 (Year)
                                                                                                                                                                                                                                                                                          = 1e+09
                                                                                                                                                                                                                                                                                          Description: End time for the ramp input.
                                                                                                                                                                                                                                                                                          Present In 1 View:
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                                                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #280
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                                                                                                                                                                                                                                                                                          Ramp Start Time 1 (Year)
                                                                                                                                                                                                                                                                                          = 5
                                                                                                                                                                                                                                                                                          Description: Start time for the ramp input.
                                                                                                                                                                                                                                                                                          Present In 1 View:
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                                                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #282
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                                                                                                                                                                                                                                                                                          Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )
                                                                                                                                                                                                                                                                                          = 30000
                                                                                                                                                                                                                                                                                          Description: The reference value of lifetime heating and cooling combinations when people calculate affinity of each combo. Hand calibrated to roughly match heat pump sales in https://www.masssave.com/en/about/news-and-events/news/mass-save-sponsors-announce-record-number-of-heat-pump-installations-across-massachusetts
                                                                                                                                                                                                                                                                                          Present In 1 View:
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                                                                                                                                                                                                                                                                                          • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #284
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                                                                                                                                                                                                                                                                                          Reference Retrofit Cost (Dollar / (House * Year) )
                                                                                                                                                                                                                                                                                          = 8740
                                                                                                                                                                                                                                                                                          Description: Perceived cost of home heating to which households compare the perceived cost of retrofitting to when deciding to retrofit.Taken from average retrofit cost in Less et al. (2021)'s dataset, shown on page 17: https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #286
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                                                                                                                                                                                                                                                                                          Retrofit Delay (Year )
                                                                                                                                                                                                                                                                                          = 2
                                                                                                                                                                                                                                                                                          Description: Time to retrofit. Assumed to be on average six months.
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                                                                                                                                                                                                                                                                                          • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                                                                                                          • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #288
                                                                                                                                                                                                                                                                                          F,A
                                                                                                                                                                                                                                                                                          Retrofitting (House * kBTU / (sf * F* Year) / Year)
                                                                                                                                                                                                                                                                                          Retrofitting[Cohort,Heating and Cooling System] = MAX(0,
                                                                                                                                                                                                                                                                                          Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]*( U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]- Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])/ Retrofit Delay)
                                                                                                                                                                                                                                                                                          Description: Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #287
                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                          Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                          Retrofitting[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                          Description: The total amount of retrofits across all cohorts and heating/cooling systems.
                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #290
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                                                                                                                                                                                                                                                                                            Sensitivity of Affinity to Cost (dmnl )
                                                                                                                                                                                                                                                                                            = 10
                                                                                                                                                                                                                                                                                            Description: Sensitivity of affinity to each heating and cooling combination having higher cost. The higher this, the fewer houses will convert to more expensive combinations.Calculated by hand calibration-- value ensures that amount of heat pumps sold 2020 - 2024 begins at about 10K and goes to about 20K in 2024, in accordance with MassSave data from https://www.masssave.com/en/about/news-and-events/news/mass-save-sponsors-announce-record-number-of-heat-pump-installations-across-massachusetts
                                                                                                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                                                                                                            Used By
                                                                                                                                                                                                                                                                                            • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #292
                                                                                                                                                                                                                                                                                            C
                                                                                                                                                                                                                                                                                            Sensitivity of Retrofits to Cost (dmnl )
                                                                                                                                                                                                                                                                                            = 10
                                                                                                                                                                                                                                                                                            Description: Sensitivity of affinity (and fraction of houses retrofitting) to NPV of retrofitting.
                                                                                                                                                                                                                                                                                            Present In 2 Views:
                                                                                                                                                                                                                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #294
                                                                                                                                                                                                                                                                                            C
                                                                                                                                                                                                                                                                                            Sine Amplitude 1 (Dimensionless)
                                                                                                                                                                                                                                                                                            = 0
                                                                                                                                                                                                                                                                                            Description: Amplitude of sine wave in customer orders (fraction of mean).
                                                                                                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                                                                                                            Used By
                                                                                                                                                                                                                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #297
                                                                                                                                                                                                                                                                                            C
                                                                                                                                                                                                                                                                                            Sine Period 1 (Year)
                                                                                                                                                                                                                                                                                            = 50
                                                                                                                                                                                                                                                                                            Description: Period of sine wave. Set initially to 50 weeks (1 year).
                                                                                                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                                                                                                            Used By
                                                                                                                                                                                                                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #299
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Soft Costs of Retrofitting (Dollar / Home)
                                                                                                                                                                                                                                                                                            =
                                                                                                                                                                                                                                                                                            Average Income* Homeowner Hours Spent Retrofitting
                                                                                                                                                                                                                                                                                            Description: The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                            • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #301
                                                                                                                                                                                                                                                                                            C
                                                                                                                                                                                                                                                                                            Step Time 1 (Year)
                                                                                                                                                                                                                                                                                            = 5
                                                                                                                                                                                                                                                                                            Description: Time for the step input.
                                                                                                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                                                                                                            Used By
                                                                                                                                                                                                                                                                                            • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #303
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Subsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                            = MAX(0,
                                                                                                                                                                                                                                                                                            Unsubsidized Cost of Heat Pumps- Expected Subsidy for Heat Pumps)
                                                                                                                                                                                                                                                                                            Description: The upfront cost of heat pump once subsidies are taken into account.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                            • Cost of Cooling System Replacement The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                                                                                                            • Cost of Heating System Replacement The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #305
                                                                                                                                                                                                                                                                                            C
                                                                                                                                                                                                                                                                                            System Switching SWITCH (dmnl )
                                                                                                                                                                                                                                                                                            = 1
                                                                                                                                                                                                                                                                                            Description: Switch for allowing houses to switch heating and cooling systems. If 1, they can switch.
                                                                                                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                                                                                                            Used By
                                                                                                                                                                                                                                                                                            • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #307
                                                                                                                                                                                                                                                                                            C
                                                                                                                                                                                                                                                                                            Time to Decide to Retrofit (Year )
                                                                                                                                                                                                                                                                                            = 3
                                                                                                                                                                                                                                                                                            Description: Time to decide to retrofit.
                                                                                                                                                                                                                                                                                            Present In 1 View:
                                                                                                                                                                                                                                                                                            Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #310
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Area (sf)
                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                            Area[ Cohort!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                            Description: The total area across all housing.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #311
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Cooling Cost (Dollar / Year)
                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                            Average Cooling Cost[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                            Description: The total amount of money spent on cooling homes, per year.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #312
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Cooling Energy Use (kBTU/ Year)
                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                            Average Cooling Energy Use[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                            Description: The total amount of energy spent on cooling homes.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #313
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Cost of Ownership of Average Home (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                            Total Cost of Ownership of Average Home[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                            Average Energy Costs for Retrofitting Home[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                            Description: Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                            • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #314
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                            Total Cost of Ownership of Retrofitted Homes[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                            Amoritized Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]+ Average Energy Costs if Retrofitted[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                            Description: The total cost of ownership of owning a home that has been retrofitted to the optimal U.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                            • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #315
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Energy Use (kBTU / Year)
                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                            Energy Use by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                            Description: The total energy use for all homes in the model.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #316
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Heat Pump Sales (House / Year)
                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                            Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump Only]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Gas]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Oil])
                                                                                                                                                                                                                                                                                            Description: Number of houses buying heat pumps every year.
                                                                                                                                                                                                                                                                                            Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #317
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Heating Cost (Dollar / Year)
                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                            Average Heating Cost[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                            Description: The total amount of money spent on heating homes.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #318
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Heating Energy Use (kBTU/ Year)
                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                            Average Heating Energy Use[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                            Description: The total amount of energy spent on heating per year.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #319
                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                            Total Housing Starts (House/ Year)
                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                            Housing Starts[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                            Description: The total housing starts across all cohorts and sources.
                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #321
                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                              Total Initial Homes (Houses )
                                                                                                                                                                                                                                                                                              = 20
                                                                                                                                                                                                                                                                                              Description: Total number of houses, including those retrofitting or not. Number taken from Census's list of households in MA in 2022: https://www.census.gov/quickfacts/fact/table/MA/PST045222
                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #322
                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                Total Initial Housing Starts (Houses / Year )
                                                                                                                                                                                                                                                                                                = 0.5
                                                                                                                                                                                                                                                                                                Description: Total number of houses that are built per year, across all systems.
                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #323
                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                Total Present Value of Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                Total Present Value of Cost[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                Present Value of Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]+ Present Value Replacement Cost[ Heating and Cooling System]+ Cost of Bad Air Conditioning[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                Total Present Value of Cost[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Present Value of Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]+ Present Value Replacement Cost[ Heating and Cooling System]+ Cost of Bad Air Conditioning[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                Description: Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #327
                                                                                                                                                                                                                                                                                                L
                                                                                                                                                                                                                                                                                                Total U Value (House * kBTU / (Year * F * sf) )
                                                                                                                                                                                                                                                                                                Total U Value[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                                                                                                                                                                Increase in U Value from Housing Starts[ Cohort, Heating and Cooling System]- Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System])- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Not Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Not Open to Retrofitting])) dt + Initial U Value[ Cohort, Heating and Cooling System,Not Open to Retrofitting]
                                                                                                                                                                                                                                                                                                Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] = ((( Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System]- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Open to Retrofitting])))- Retrofitting[ Cohort, Heating and Cooling Systemdt + Initial U Value[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                                                                                                                Description: Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #324
                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                Total U Value Across All Groupings (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                = SUM(
                                                                                                                                                                                                                                                                                                Total U Value by Cohort[ Cohort!])
                                                                                                                                                                                                                                                                                                Description: Total U value across all groupings of households.
                                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #325
                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                Total U Value by Cohort (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                Total U Value by Cohort[Cohort] = SUM(
                                                                                                                                                                                                                                                                                                Total U Value[ Cohort, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                Description: Total U Value within each cohort.
                                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #326
                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                Total U Value by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                                                Total U Value[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                Description: The total U value by heating and cooling system
                                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #328
                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))
                                                                                                                                                                                                                                                                                                U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06:AND: Expected EEHIC Proportional Subsidy Rate for Retrofits>1e-06, Reference U Value*(( Sensitivity of Marginal Cost to U Value-1)*((( Expected EEHIC Maximum Subsidy for Retrofits- Expected EEHIC Proportional Subsidy Rate for Retrofits* Expected Fixed Cost)/( U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]* Expected EEHIC Proportional Subsidy Rate for Retrofits* Expected Reference Marginal Cost* Average Area[ Cohort,Open to Retrofitting]))-(1/(- Sensitivity of Marginal Cost to U Value+1))*(( U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]/ Reference U Value)^(- Sensitivity of Marginal Cost to U Value+1)))^(1/(- Sensitivity of Marginal Cost to U Value+1))),0)
                                                                                                                                                                                                                                                                                                Description: This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                                                • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #329
                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                                                                                                                                                Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                                                                                                                Present In 8 Views: Used By
                                                                                                                                                                                                                                                                                                • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                                                • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                                                                                                                • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                                                                                                                • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                                • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                                                                                                                • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                                                                                                                Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #330
                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                U Value Increase from Source Switching (kBTU*House/(Year*Year*sf*F))
                                                                                                                                                                                                                                                                                                U Value Increase from Source Switching[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                                                U Value Shift from Source Switching[ Cohort!, Heating and Cooling System!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                Description: The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #331
                                                                                                                                                                                                                                                                                                F,A
                                                                                                                                                                                                                                                                                                U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                U Value Loss from Demolition[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Demolitions[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                Description: Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #333
                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                U Value of Retrofitting Homes (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                U Value of Retrofitting Homes[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                                                                                                                Description: The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #334
                                                                                                                                                                                                                                                                                                L
                                                                                                                                                                                                                                                                                                U Value Retrofitted Away (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                = SUM(
                                                                                                                                                                                                                                                                                                Retrofitting[ Cohort!, Heating and Cooling System!]) dt + 0.0
                                                                                                                                                                                                                                                                                                Description: Total amount of U value that has been retrofitted away.
                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #335
                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                  U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                  U Value Shift from Source Switching[Cohort,Heat Pump Heating and Cooling,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                  Houses Switching Sources[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]
                                                                                                                                                                                                                                                                                                  U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] = Houses Switching Sources[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Fossil Fuel Heating, Retrofitting Status]
                                                                                                                                                                                                                                                                                                  Description: The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                  Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                  • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                  • U Value Increase from Source Switching The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #336
                                                                                                                                                                                                                                                                                                  A,T
                                                                                                                                                                                                                                                                                                  Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)
                                                                                                                                                                                                                                                                                                  Unsubsidized Cost of Heat Pump Over Time TABLE([(2020,5000)-(2050,10000)],(2020,22000),(2030,20483.7 ),(2040,18967.3),(2050,17448.6))

                                                                                                                                                                                                                                                                                                  Description: The cost of installing and buying a heat pump over time. Initial value taken from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then assume that ratio of future prices to initial is the same as average of reference and ductless heat pumps in MassDEP's Energy Pathways Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download. (That is, I took the ratio of the initial price to the initial price in that report, then I multiplied that ratio times all projections of future heat pump prices). I was unable to use the MassDEP report's prices directly, because they are based on national estimates from NREL, and MA is typically a more expensive state. In particular, the MassDEP projections say that heat pumps cost only $9K, but MassSave subsidy is $10K!Assumes rates of change are linear between projected points.
                                                                                                                                                                                                                                                                                                  Present In 1 View:
                                                                                                                                                                                                                                                                                                  Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #337
                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                  Unsubsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                  Unsubsidized Cost of Heat Pump Over Time TABLE( Time)
                                                                                                                                                                                                                                                                                                  Description: The unsubsidized cost of heat pumps, instantiated at each time.
                                                                                                                                                                                                                                                                                                  Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #340
                                                                                                                                                                                                                                                                                                  C
                                                                                                                                                                                                                                                                                                  Weight on Upfront Cost (dmnl )
                                                                                                                                                                                                                                                                                                  = 0.5
                                                                                                                                                                                                                                                                                                  Description: How much homeowners weigh upfront (amoritized) costs of retrofits as opposed to the total cost of ownership due to being more perceptive of short-term costs.
                                                                                                                                                                                                                                                                                                  Present In 2 Views:
                                                                                                                                                                                                                                                                                                  Used By
                                                                                                                                                                                                                                                                                                  • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                  • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #342
                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                  White Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                  Noise Standard Deviation 1*((24* Noise Correlation Time 1/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                                                                                                                                                                                                                                  Description: White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                  • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                  Top (Type) Level (14 Variables)
                                                                                                                                                                                                                                                                                                  Group
                                                                                                                                                                                                                                                                                                  Type
                                                                                                                                                                                                                                                                                                  Variable Name And Description
                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #21
                                                                                                                                                                                                                                                                                                  L
                                                                                                                                                                                                                                                                                                  Area (sf)
                                                                                                                                                                                                                                                                                                  Area[Cohort,Not Open to Retrofitting] = (
                                                                                                                                                                                                                                                                                                  Area of New Homes[ Cohort]- Net Area Shift due to Retrofit Status Switching[ Cohort])- Area Removal[ Cohort,Not Open to Retrofitting] dt + Initial Area[ Cohort]*(1.0- Fraction Retrofitting by Cohort[ Cohort])
                                                                                                                                                                                                                                                                                                  Area[Preexisting Cohorts,Not Open to Retrofitting] = (- Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts])- Area Removal[ Preexisting Cohorts,Not Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]*(1.0- Fraction Retrofitting by Cohort[ Preexisting Cohorts])
                                                                                                                                                                                                                                                                                                  Area[Cohort,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Cohort]- Area Removal[ Cohort,Open to Retrofitting] dt + Initial Area[ Cohort]* Fraction Retrofitting by Cohort[ Cohort]
                                                                                                                                                                                                                                                                                                  Area[Preexisting Cohorts,Open to Retrofitting] = Net Area Shift due to Retrofit Status Switching[ Preexisting Cohorts]- Area Removal[ Preexisting Cohorts,Open to Retrofitting] dt + Initial Area[ Preexisting Cohorts]* Fraction Retrofitting by Cohort[ Preexisting Cohorts]
                                                                                                                                                                                                                                                                                                  Description: "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                  Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                  • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                                                                                                                  • Total Area The total area across all housing.
                                                                                                                                                                                                                                                                                                  Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #24
                                                                                                                                                                                                                                                                                                  L
                                                                                                                                                                                                                                                                                                  Autocorrelated Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                  Change in AC Noise dt + 0.0
                                                                                                                                                                                                                                                                                                  Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                  • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                  • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #22
                                                                                                                                                                                                                                                                                                  L
                                                                                                                                                                                                                                                                                                  Autocorrelated Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                  Change in AC Noise 0 dt + 0.0
                                                                                                                                                                                                                                                                                                  Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                  • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                  • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #23
                                                                                                                                                                                                                                                                                                  L
                                                                                                                                                                                                                                                                                                  Autocorrelated Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                  Change in AC Noise 1 dt + 0.0
                                                                                                                                                                                                                                                                                                  Description: First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                  • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                  • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                  .housingagingchain v18 #65
                                                                                                                                                                                                                                                                                                  L
                                                                                                                                                                                                                                                                                                  Code U (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                  = -
                                                                                                                                                                                                                                                                                                  Decrease in Code U dt + Initial Code U Value
                                                                                                                                                                                                                                                                                                  Description: U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                                                                                                                  Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                  • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                  • Decrease in Code U The change in code U from policy.
                                                                                                                                                                                                                                                                                                  • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #77
                                                                                                                                                                                                                                                                                                  L
                                                                                                                                                                                                                                                                                                  Cumulative Emissions (tCO2)
                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                  Emissions dt + 0.0
                                                                                                                                                                                                                                                                                                  Description: The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #78
                                                                                                                                                                                                                                                                                                    L
                                                                                                                                                                                                                                                                                                    Cumulative Federal Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                    =
                                                                                                                                                                                                                                                                                                    Annual Federal Subsidies dt + 0.0
                                                                                                                                                                                                                                                                                                    Description: The amount of money the federal government spends on subsidies for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #79
                                                                                                                                                                                                                                                                                                      L
                                                                                                                                                                                                                                                                                                      Cumulative MA Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                      =
                                                                                                                                                                                                                                                                                                      Annual MA Subsidies dt + 0.0
                                                                                                                                                                                                                                                                                                      Description: The amount of subsidies that the Massachusetts state government has given out for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #80
                                                                                                                                                                                                                                                                                                        L
                                                                                                                                                                                                                                                                                                        Cumulative Subsidies for Heat Pumps (Dollar)
                                                                                                                                                                                                                                                                                                        =
                                                                                                                                                                                                                                                                                                        Annual Heat Pump Subsidy dt + 0.0
                                                                                                                                                                                                                                                                                                        Description: The total amount of dollars spent on subsidizing heat pumps throughout the model's run.
                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                        • Cumulative Subsidies The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #82
                                                                                                                                                                                                                                                                                                        L
                                                                                                                                                                                                                                                                                                        Cumulative Subsidy for Retrofits (Dollar)
                                                                                                                                                                                                                                                                                                        =
                                                                                                                                                                                                                                                                                                        Annual Retrofit Subsidy dt + 0.0
                                                                                                                                                                                                                                                                                                        Description: The total amount spent on retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                        • Cumulative Subsidies The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #174
                                                                                                                                                                                                                                                                                                        L
                                                                                                                                                                                                                                                                                                        Housing (House)
                                                                                                                                                                                                                                                                                                        Housing[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                                                                                                                                                                        Housing Starts[ Cohort, Heating and Cooling System]- Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])- Demolitions[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Not Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Not Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Not Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                        Housing[Cohort,Heating and Cooling System,Open to Retrofitting] = (( Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]- Demolitions[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System!,Open to Retrofitting, Heating and Cooling System])))-(SUM( Houses Switching Sources[ Cohort, Heating and Cooling System,Open to Retrofitting, Heating and Cooling System!])) dt + Initial Homes Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                        Description: Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                        Present In 7 Views: Used By Feedback Loops: 5 (29.4%) (+) 3  [2,4] (-) 2  [2,2]
                                                                                                                                                                                                                                                                                                        .housingagingchain v8 #309
                                                                                                                                                                                                                                                                                                        L
                                                                                                                                                                                                                                                                                                        Total Age (House * Year)
                                                                                                                                                                                                                                                                                                        Total Age[Cohort,Not Open to Retrofitting] = (
                                                                                                                                                                                                                                                                                                        Aging[ Cohort,Not Open to Retrofitting]- Net Age Shift from Retrofitting Status Shifting[ Cohort])- Age Removal[ Cohort,Not Open to Retrofitting] dt + Initial Age[ Cohort,Not Open to Retrofitting]
                                                                                                                                                                                                                                                                                                        Total Age[Cohort,Open to Retrofitting] = ( Net Age Shift from Retrofitting Status Shifting[ Cohort]+ Aging[ Cohort,Open to Retrofitting])- Age Removal[ Cohort,Open to Retrofitting] dt + Initial Age[ Cohort,Open to Retrofitting]
                                                                                                                                                                                                                                                                                                        Description: "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                        Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                        • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                                                                                                                                                                        • Average Age in All Housing Average age of houses, regardless of cohort
                                                                                                                                                                                                                                                                                                        Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #327
                                                                                                                                                                                                                                                                                                        L
                                                                                                                                                                                                                                                                                                        Total U Value (House * kBTU / (Year * F * sf) )
                                                                                                                                                                                                                                                                                                        Total U Value[Cohort,Heating and Cooling System,Not Open to Retrofitting] = (((
                                                                                                                                                                                                                                                                                                        Increase in U Value from Housing Starts[ Cohort, Heating and Cooling System]- Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System])- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Not Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Not Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Not Open to Retrofitting])) dt + Initial U Value[ Cohort, Heating and Cooling System,Not Open to Retrofitting]
                                                                                                                                                                                                                                                                                                        Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] = ((( Net U Value Change from Retrofitting Home Shifts[ Cohort, Heating and Cooling System]- U Value Loss from Demolition[ Cohort, Heating and Cooling System,Open to Retrofitting])+(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System!, Heating and Cooling System,Open to Retrofitting])))-(SUM( U Value Shift from Source Switching[ Cohort, Heating and Cooling System, Heating and Cooling System!,Open to Retrofitting])))- Retrofitting[ Cohort, Heating and Cooling Systemdt + Initial U Value[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                                                                                                                        Description: Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                        Present In 2 Views: Used By Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #334
                                                                                                                                                                                                                                                                                                        L
                                                                                                                                                                                                                                                                                                        U Value Retrofitted Away (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                        = SUM(
                                                                                                                                                                                                                                                                                                        Retrofitting[ Cohort!, Heating and Cooling System!]) dt + 0.0
                                                                                                                                                                                                                                                                                                        Description: Total amount of U value that has been retrofitted away.
                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          Top (Type) Smooth (13 Variables) (13/173)
                                                                                                                                                                                                                                                                                                          Group
                                                                                                                                                                                                                                                                                                          Type
                                                                                                                                                                                                                                                                                                          Variable Name And Description
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #111
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          Cooling Energy Price, Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                                                                                                                          Description: Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                                                                                                                          Present In 4 Views: Used By
                                                                                                                                                                                                                                                                                                          • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                                                                                                                          • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                                                                          • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                                                                                                                          • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #112
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          Implemented EEHIC Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                          Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays.
                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                          • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                                                          • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #113
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          Implemented EEHIC Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                                                                                                                          Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                          • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                                                          • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                          • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #114
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected Fixed Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                          = SMOOTH(
                                                                                                                                                                                                                                                                                                          Fixed Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                                                                                                                          Description: Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                          • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                                                                                                                          • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #115
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected Heating Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                          Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                                                                                                                                                                                                                                                                          Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                                                                                                                          Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                                                                                                                          Present In 6 Views: Used By
                                                                                                                                                                                                                                                                                                          • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                                                                                                                          • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                                                                                                                          • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                                                                                                                          • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #116
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          IRA Implemented Subsidy Proportional Rate for Heat Pumps, Delay in Changing Subsidy Expectations)* Proportional IRA Subsidy Switch for Heat Pumps
                                                                                                                                                                                                                                                                                                          Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #118
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          Implemented MassSave Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                          Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #119
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          Implemented MassSave Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                                                                                                                          Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                          Present In 4 Views: Used By
                                                                                                                                                                                                                                                                                                          • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                          • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                                                                                                                          • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                          • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                          • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #120
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          Implemented IRA Maximum Proportional Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                          Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #121
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                                                                                                                          = SMOOTH(
                                                                                                                                                                                                                                                                                                          Reference Marginal Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                                                                                                                          Description: Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                                                                                                                          Present In 4 Views: Used By
                                                                                                                                                                                                                                                                                                          • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                          • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                                                          • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                          • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                          • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                          • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                          • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #148
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          HOMES Expected Higher Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          HOMES Implemented High Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                          Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #149
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          HOMES Implemented Lower Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                          Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                          Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #217
                                                                                                                                                                                                                                                                                                          SM,A
                                                                                                                                                                                                                                                                                                          MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                          = SMOOTH3(
                                                                                                                                                                                                                                                                                                          MassSave Implemented Lump Sum Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                          Description: Expected lump sum subsidy that lowers subsidized retrofit costs from the state, taking into account information delays.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          Top (Type) Delay (0 Variables) (0/0)
                                                                                                                                                                                                                                                                                                          Group
                                                                                                                                                                                                                                                                                                          Type
                                                                                                                                                                                                                                                                                                          Variable Name And Description
                                                                                                                                                                                                                                                                                                          Top (Type) Level Initial (7 Variables)
                                                                                                                                                                                                                                                                                                          Group
                                                                                                                                                                                                                                                                                                          Type
                                                                                                                                                                                                                                                                                                          Variable Name And Description
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #132
                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                          Fraction Retrofitting by Cohort (dmnl)
                                                                                                                                                                                                                                                                                                          Fraction Retrofitting by Cohort[Cohort] = ZIDZ(SUM(
                                                                                                                                                                                                                                                                                                          Housing[ Cohort, Heating and Cooling System!,Open to Retrofitting]),SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!]))
                                                                                                                                                                                                                                                                                                          Description: Fraction that are retrofitting, only by cohort.
                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                          • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #184
                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                          Initial Age (House * Year)
                                                                                                                                                                                                                                                                                                          Initial Age[Cohort,Retrofitting Status] = INITIAL(0)
                                                                                                                                                                                                                                                                                                          Initial Age[Preexisting Cohorts,Retrofitting Status] = (
                                                                                                                                                                                                                                                                                                          Cohort Duration*(ELMCOUNT( Preexisting Cohorts)- Preexisting Cohorts+1))* Housing by Cohort and Retrofitting Status[ Preexisting Cohorts, Retrofitting Status]
                                                                                                                                                                                                                                                                                                          Description: The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #185
                                                                                                                                                                                                                                                                                                          LI,C
                                                                                                                                                                                                                                                                                                          Initial Area (sf)
                                                                                                                                                                                                                                                                                                          Initial Area[Cohort] = 10
                                                                                                                                                                                                                                                                                                          Description: Total initial area across all houses, by cohort (assuming that average area is the same across systems).
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #188
                                                                                                                                                                                                                                                                                                          LI,C
                                                                                                                                                                                                                                                                                                          Initial Code U Value (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                          = 0.003
                                                                                                                                                                                                                                                                                                          Description: The initial value of code U. For initial paper, assume that this is between initial optimal U (nearly 0) and average U (0.006).
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v5 testing #192
                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                          Initial Homes Not Retrofitting (House)
                                                                                                                                                                                                                                                                                                          Initial Homes Not Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Initial Homes Not Retrofitting[Preexisting Cohorts,Heating and Cooling System] = (1-
                                                                                                                                                                                                                                                                                                          Initial Fraction of Homes Retrofitting)* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                          Description: Initial homes not open to retrofitting.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v5 testing #193
                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                          Initial Homes Retrofitting (Houses)
                                                                                                                                                                                                                                                                                                          Initial Homes Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Initial Homes Retrofitting[Preexisting Cohorts,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                          Initial Fraction of Homes Retrofitting* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                          Description: Homes that are open to retrofitting initially.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #197
                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                          Initial U Value (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                          Initial U Value[Cohort,Heating and Cooling System,Retrofitting Status] = 0
                                                                                                                                                                                                                                                                                                          Initial U Value[Preexisting Cohorts,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                          Initial Average U Value[ Preexisting Cohorts]* Housing[ Preexisting Cohorts, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                          Description: Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          Top (Type) Initial (1 Variables)
                                                                                                                                                                                                                                                                                                          Group
                                                                                                                                                                                                                                                                                                          Type
                                                                                                                                                                                                                                                                                                          Variable Name And Description
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #184
                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                          Initial Age (House * Year)
                                                                                                                                                                                                                                                                                                          Initial Age[Cohort,Retrofitting Status] = INITIAL(0)
                                                                                                                                                                                                                                                                                                          Initial Age[Preexisting Cohorts,Retrofitting Status] = (
                                                                                                                                                                                                                                                                                                          Cohort Duration*(ELMCOUNT( Preexisting Cohorts)- Preexisting Cohorts+1))* Housing by Cohort and Retrofitting Status[ Preexisting Cohorts, Retrofitting Status]
                                                                                                                                                                                                                                                                                                          Description: The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          Top (Type) Constant (121 Variables)
                                                                                                                                                                                                                                                                                                          Group
                                                                                                                                                                                                                                                                                                          Type
                                                                                                                                                                                                                                                                                                          Variable Name And Description
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #9
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Aging per Year (Year / Year)
                                                                                                                                                                                                                                                                                                          = 1
                                                                                                                                                                                                                                                                                                          Description: Number of years a house ages per year (which must be one), used to ensure dimensional consistency and make the model clearer
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Aging Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #11
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Amoritization Period (Year )
                                                                                                                                                                                                                                                                                                          = 20
                                                                                                                                                                                                                                                                                                          Description: Time period over which incurred retrofit cost is amoritized; should be related to lifetime of a home.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #52
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Average Income (Dollar / Hour / House )
                                                                                                                                                                                                                                                                                                          = 55
                                                                                                                                                                                                                                                                                                          Description: The average income of single family homeowners in Massachusetts. Calculated from 2020 EIA RECS data for MA SFH, where each individual was assigned the average income of their reported income bracket, other than those making more than $150K/year, who were assigned $175,000. Hourly wage calculated by assuming working 8 hours a day, 5 days a week, for 50 weeks in a year.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Soft Costs of Retrofitting The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #54
                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                          Average Lifetime of Cooling Technology (Years)
                                                                                                                                                                                                                                                                                                          Average Lifetime of Cooling Technology[Heat Pump Heating and Cooling] = 12.5
                                                                                                                                                                                                                                                                                                          Average Lifetime of Cooling Technology[Central AC Cooling] = 12.5
                                                                                                                                                                                                                                                                                                          Average Lifetime of Cooling Technology[Window AC Cooling] = 9
                                                                                                                                                                                                                                                                                                          Average Lifetime of Cooling Technology[No AC Cooling] =
                                                                                                                                                                                                                                                                                                          NAREPLACEMENT
                                                                                                                                                                                                                                                                                                          Description: The average lifetime of each cooling system.Central AC data from: https://www.energy.gov/energysaver/central-air-conditioningWindow AC data from: https://www.consumerreports.org/air-conditioner/is-it-time-to-get-a-new-window-air-conditioner-a1532530762/
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                                                                          • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #55
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Average Lifetime of Heating Technology (Year)
                                                                                                                                                                                                                                                                                                          Average Lifetime of Heating Technology[Heat Pump Heating and Cooling] = 12.5
                                                                                                                                                                                                                                                                                                          Average Lifetime of Heating Technology[Gas Heating] = 20
                                                                                                                                                                                                                                                                                                          Average Lifetime of Heating Technology[Oil Heating] = 20
                                                                                                                                                                                                                                                                                                          Description: The average lifetime of each heating system.Heat pump data from: https://glascohvac.com/heating/heat-pumps/long-heat-pump-last/Gas data from: https://www.carrier.com/residential/en/us/products/furnaces/how-long-does-a-furnaces-last/Oil data from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                                                                          • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #57
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Average Time To Consider Switching (Year )
                                                                                                                                                                                                                                                                                                          = 15
                                                                                                                                                                                                                                                                                                          Description: The average time it takes for a house to consider switching their heating and cooling system.
                                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #61
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          CDD on Coldest Day (F )
                                                                                                                                                                                                                                                                                                          = 17.1
                                                                                                                                                                                                                                                                                                          Description: The total CDD from hottest day.Data from https://www.degreedays.net/ for KOWD, weather station nearest to centre of population for MA, Natick. Calculated by finding CDDs from the past three years (February 2021 - January 2024), finding the highest CDD in each year, and averaging them. Following industry standard, used 65°F as set point.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #66
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Cohort Duration (Year )
                                                                                                                                                                                                                                                                                                          = 10
                                                                                                                                                                                                                                                                                                          Description: The width (duration) of each cohort.
                                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                                                                                                                                          • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #67
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Cooling Degree Days (F )
                                                                                                                                                                                                                                                                                                          = 1029
                                                                                                                                                                                                                                                                                                          Description: The difference between temperature setpoint (65 F) and outside temperature for heating. Typically called cooling degree days, but units are solely in terms of fahrenheit.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. Use set point of 65°F, in line with industry standard, as at that temperature little heating or cooling is necessary.
                                                                                                                                                                                                                                                                                                          Present In 3 Views:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                          • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                          • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                                                                          • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #68
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Cooling Emissions Factor (lb CO2 / kBTU)
                                                                                                                                                                                                                                                                                                          = 614/3414.43
                                                                                                                                                                                                                                                                                                          Description: Amount of CO2 emitted from using one kBTU to cool a home. Emissions factor is common, and is for electricity.Taken from: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/download
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #69
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Cooling Energy Price Step Height 1 (Dimensionless )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: Height of step input to customer orders, as fraction of initial value.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #73
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Cost of Bad Air Conditioning (Dollar / House )
                                                                                                                                                                                                                                                                                                          Cost of Bad Air Conditioning[Window AC Cooling] = 80000
                                                                                                                                                                                                                                                                                                          Cost of Bad Air Conditioning[No AC Cooling] = 100000
                                                                                                                                                                                                                                                                                                          Description: Willingness of Window AC users and those without AC to pay for central AC or heat pumps due to those technologies' inability to heat homes and their noisiness.Chosen to be sufficiently high that very few or no houses choose to keep window AC or no AC.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #76
                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems (Dollar / House)
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Heat Pump Only] =
                                                                                                                                                                                                                                                                                                          Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]+ Cost of Heating System Replacement[Gas and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heat Pump and Gas] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Heat Pump Only]+ Cost of Heating System Replacement[Heat Pump Only]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Heat Pump and Gas]+ Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Central AC,Retrofitting Status,Gas and Central AC] = Total Present Value of Cost[ Cohort,Gas and Central AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Gas and Window or No AC,Retrofitting Status,Gas and Central AC] = Cost of Cooling System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort, Gas and Window or No AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Gas,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Heat Pump and Gas, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump Only,Retrofitting Status,Oil and Central AC] = Cost of Heating System Replacement[Oil and Central AC]+ Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Gas and Central AC] = Cost of Heating System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Heat Pump and Oil] = Cost of Heating System Replacement[Heat Pump and Oil]+ Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Heat Pump and Oil]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Central AC,Retrofitting Status,Oil and Central AC] = Total Present Value of Cost[ Cohort,Oil and Central AC, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heat Pump Only] = Cost of Heating System Replacement[Heat Pump Only]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Gas and Central AC] = Cost of Heating System Replacement[Gas and Central AC]+ Cost of Cooling System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Gas and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Heat Pump and Oil] = Cost of Heating System Replacement[Heat Pump and Oil]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Heat Pump and Oil]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Oil and Window or No AC,Retrofitting Status,Oil and Central AC] = Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort, Oil and Window or No AC, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump Only] = Total Present Value of Cost[ Cohort,Heat Pump Only, Retrofitting Status,Heat Pump Only]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Gas] = Cost of Heating System Replacement[Gas and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Heat Pump and Gas]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Oil and Central AC] = Cost of Cooling System Replacement[Oil and Central AC]+ Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Oil and Central AC]
                                                                                                                                                                                                                                                                                                          Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Oil] = Total Present Value of Cost[ Cohort,Heat Pump and Oil, Retrofitting Status,Heat Pump and Oil]
                                                                                                                                                                                                                                                                                                          Description: Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #83
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Days per Year (Day / Year )
                                                                                                                                                                                                                                                                                                          = 365
                                                                                                                                                                                                                                                                                                          Description: The number of days each year. Used to convert yearly measures to daily ones.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #85
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Delay in Changing Subsidy Expectations (Year )
                                                                                                                                                                                                                                                                                                          = 0.5
                                                                                                                                                                                                                                                                                                          Description: Delay in perceiving any changes to subsidies. Assumed to be the same for both subsidies.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #86
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Delay in Forming Expectations of Energy Price (Year )
                                                                                                                                                                                                                                                                                                          = 1
                                                                                                                                                                                                                                                                                                          Description: Delay in perceiving changes in energy price.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                                                                                                                          • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #87
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Delay in Forming Expectations of Retrofit Costs (Year )
                                                                                                                                                                                                                                                                                                          = 1.5
                                                                                                                                                                                                                                                                                                          Description: Delay in perceiving changes in fixed retrofit cost and reference marginal cost. Assumed to be the same for both types of costs.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
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                                                                                                                                                                                                                                                                                                          • Expected Fixed Cost Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                                                                                                                          • Expected Reference Marginal Cost Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #88
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Demolition Hazard Rate (1 / Year )
                                                                                                                                                                                                                                                                                                          = 0.01
                                                                                                                                                                                                                                                                                                          Description: Proportion of homes demolished every year. Value is assumed to be equal across both retrofitting and non-retrofitting homes. Heuristically chosen so total housing stock grows at net 1%/year.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #90
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Discount Rate (1 / Year )
                                                                                                                                                                                                                                                                                                          = 0.05
                                                                                                                                                                                                                                                                                                          Description: Discount rate for discounting energy savings cash flows.Average and bounds from demand-side discount rate from MassDEP's analysis of pathways for net zero (pg. 103): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadhttps://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                                                                                                                          Present In 4 Views:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                                                                                                                          • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                          • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                                                                          • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                          • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #92
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          EEHIC Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                                                                                                                          = 1200
                                                                                                                                                                                                                                                                                                          Description: The maximum proportional subsidy that will be offered from Energy Efficient Home Improvement Credit, regardless of that subsidy's discount. Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #93
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                          = 0.3
                                                                                                                                                                                                                                                                                                          Description: Proportion of total retrofit cost that will be credited with the Energy Efficiency Home Improvement Credit.Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                                                                                                                          Present In 1 View:
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                                                                                                                                                                                                                                                                                                          • Implemented EEHIC Subsidy Proportional Rate for Retrofits The implemented proportional subsidy rate for retrofits from the IRA, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #94
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          EEHIC Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                                                                                                                          = 2033
                                                                                                                                                                                                                                                                                                          Description: The year in which the EEHIC is phased out. If final time, then has no ending data.Source: https://www.irs.gov/credits-deductions/energy-efficient-home-improvement-credit
                                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #95
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                                                                                                                                                                                                                                                                                                          Effect of Air Leakage from Window AC on Efficiency (dmnl)
                                                                                                                                                                                                                                                                                                          = 0.9*10/11
                                                                                                                                                                                                                                                                                                          Description: A window air conditioner typically does not perfectly cover its intended cavity, leading to more air leakage and therefore reducing efficiency.Taken from: https://www.energy.gov/sites/prod/files/2014/08/f18/ba_innovations_1-2-5_window_ac.pdf
                                                                                                                                                                                                                                                                                                          Present In 1 View:
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                                                                                                                                                                                                                                                                                                          • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #100
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                                                                                                                                                                                                                                                                                                          Energy Price Exponential Growth Rate (1/Year )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: The exogenous growth fraction for the test input.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #99
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Energy Price Exponential Growth Rate 1 (1/Year )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: The exogenous growth fraction for the test input.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #102
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Energy Price Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: The quantity to be injected to customer orders, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
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                                                                                                                                                                                                                                                                                                          • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #101
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Energy Price Pulse Quantity 1 (Dimensionless*Year)
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: Pulse value, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #104
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Energy Price Ramp Slope (1/Year )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #103
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Energy Price Ramp Slope 1 (1/Year )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #105
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Energy Price Step Height (Dimensionless )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: Height of step input to customer orders, as fraction of initial value.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v5 testing #128
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Fixed Cost (Dollar / House )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: Fixed cost of retrofitting, due to permitting, finding contractors, etc. This is not taken into account in the marginal cost of retrofitting, and this model assumes that households have not yet paid a fixed cost when deciding to retrofit. This cost only applies to existing housing.Set this equal to 0, because almost all costs for retrofits seem to be variable (except for permitting, which isn't usually used), and there's no data to suggest otherwise.
                                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Expected Fixed Cost Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #135
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                                                                                                                                                                                                                                                                                                          Fractional Decrease in Code U (1 / Year )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: Fractional decrease in code per year. Exogenous and set by policymakers in the real world. For initial paper, assume that code U is constant.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #137
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          HDD on Coldest Day (F )
                                                                                                                                                                                                                                                                                                          = 55.2333
                                                                                                                                                                                                                                                                                                          Description: The total HDD from coldest day.Data from https://www.degreedays.net/ for KOWD, weather station nearest to centre of population for MA, Natick. Calculated by finding HDDs from the past three years (February 2021 - January 2024), finding the highest HDD in each year, and averaging them. Following industry standard, used set point of 65°F.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #139
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Heat Pump COP on Coldest Days (dmnl )
                                                                                                                                                                                                                                                                                                          = 2.16438
                                                                                                                                                                                                                                                                                                          Description: The heat pump COP on coolest day of the year.Taken from NYSERDA/MassCEC study on heat pump performance on 41 heat pumps: https://e4thefuture.org/wp-content/uploads/2022/06/Residential-ccASHP-Building-Electrification_060322.pdf (pg. 24). Regressed COP on temperature and its square. Using daily data on HDD (set point 65°F) for 2021-2023 from degreedays.net, calculated temperature of coldest day on average. Plugged that into regression model to find COP on coldest day.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #141
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Heating Degree Days (F )
                                                                                                                                                                                                                                                                                                          = 5026
                                                                                                                                                                                                                                                                                                          Description: The difference between temperature setpoint (65 F) and outside temperature.Data from degreedays.net, using the weather station for Norwood Memorial Airport, the closest weather station to the center of MA's population, Natick. In line with industry standard, use set point of 65°F, as thattemperature little heating or cooling is needed.
                                                                                                                                                                                                                                                                                                          Present In 3 Views:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                                                          • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                          • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                                                                                                                          • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #142
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Heating Emissions Factors (lb CO2 / kBTU)
                                                                                                                                                                                                                                                                                                          Heating Emissions Factors[Heat Pump Heating and Cooling] = 684/3414.43
                                                                                                                                                                                                                                                                                                          Heating Emissions Factors[Gas Heating] = 116.65/1000
                                                                                                                                                                                                                                                                                                          Heating Emissions Factors[Oil Heating] = 163.45/1000
                                                                                                                                                                                                                                                                                                          Description: The pounds of CO2 emitted per kBTU of heating energy provided, for each heating fuel.Data for heat pumps (electricity) is: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/downloadRest is from: https://www.eia.gov/environment/emissions/co2_vol_mass.phpIn line with that source, I assume that each heat pump will add to the grid and is not part of base demand, and so the marginal emissions from producing electricity from heat pumps will be constant at the value as it will come from natural gas generators (explanation of which is from here: https://willbrownsberger.com/how-green-will-the-power-be/
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #146
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Homeowner Hours Spent Retrofitting (Hour )
                                                                                                                                                                                                                                                                                                          = 750
                                                                                                                                                                                                                                                                                                          Description: The amount of hours a homeowners spends retrofitting their home themselves, i.e., the hours spent deciding to retrofit, supervising audits, moving out of the home as necessary, etc. No hard data on this, calibrated so that the initial fraction of homes willing to retrofit is 10%.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Soft Costs of Retrofitting The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #147
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          HOMES Cut Off for Savings (dmnl )
                                                                                                                                                                                                                                                                                                          = 0.35
                                                                                                                                                                                                                                                                                                          Description: The percent energy savings needed to get the higher subsidy amount from the Home Owner Managing Energy Savings rebate. Taken from: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #150
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          HOMES High Subsidy Amount (Dollar / House )
                                                                                                                                                                                                                                                                                                          = 4000
                                                                                                                                                                                                                                                                                                          Description: The subsidy from the home owner managing energy savings rebate for retrofits saving more than 35% of energy.Source: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #153
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          HOMES Lower Subsidy Amount (Dollar / House )
                                                                                                                                                                                                                                                                                                          = 2000
                                                                                                                                                                                                                                                                                                          Description: The lump sum subsidy given for retrofits that save less than 35% of their energy from the Home Owner Managing Energy Savings tax credit.Source: https://www.nrdc.org/bio/lauren-urbanek/theres-no-better-time-consider-home-energy-upgrades#: :text=The%20HOMES%20Rebate%20Program%20provides,or%20from%20measured%20energy%20savings.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • HOMES Implemented Lower Subsidy Lump sum subsidy that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #154
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          HOMES Subsidy Final Year (Year)
                                                                                                                                                                                                                                                                                                          = 2032
                                                                                                                                                                                                                                                                                                          Description: Final year of Home Owner Managing Energy Savings rebate, assumed to be the same as that of the EEHIC.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #155
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          HOMES Subsidy Implementation Year (Year )
                                                                                                                                                                                                                                                                                                          = 2025
                                                                                                                                                                                                                                                                                                          Description: The year in which the lump sum subsidy will activate.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #166
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Housing Fractional Growth Rate (1 / Year )
                                                                                                                                                                                                                                                                                                          = 0.02
                                                                                                                                                                                                                                                                                                          Description: The annual growth rate in housing. Heuristically chosen so that total housing stock grows at net 1%/year.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #168
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Housing Starts Exponential Growth Rate (1/Year )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: The exogenous growth fraction for the test input.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #170
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Housing Starts Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: The quantity to be injected to customer orders, as a fraction of the base value of Input.For example, to pulse in a quantity equal to 50% of the current value of input, set to.50.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #171
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Housing Starts Ramp Slope (1/Year )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: Slope of the ramp input, as a fraction of the base value (per week).
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #172
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Housing Starts Step Height (Dimensionless )
                                                                                                                                                                                                                                                                                                          = 0
                                                                                                                                                                                                                                                                                                          Description: Height of step input to customer orders, as fraction of initial value.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #180
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Increase in Area per Year (sf / Year / House )
                                                                                                                                                                                                                                                                                                          = 10.76
                                                                                                                                                                                                                                                                                                          Description: The exogenous increase in area per year, found by regressing area on year house was built in RECS 2020 data for MA SFG.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #185
                                                                                                                                                                                                                                                                                                          LI,C
                                                                                                                                                                                                                                                                                                          Initial Area (sf)
                                                                                                                                                                                                                                                                                                          Initial Area[Cohort] = 10
                                                                                                                                                                                                                                                                                                          Description: Total initial area across all houses, by cohort (assuming that average area is the same across systems).
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #186
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Initial Average Area of Housing Starts (sf / House )
                                                                                                                                                                                                                                                                                                          = 2347
                                                                                                                                                                                                                                                                                                          Description: Initial average area of housing starts. Taken from average area of MA SFH homes built from 2015 to 2020, from EIA RECS data.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #187
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Initial Average U Value (kBTU/(Year*sf*F))
                                                                                                                                                                                                                                                                                                          Initial Average U Value[Cohort] = 0.19235
                                                                                                                                                                                                                                                                                                          Description: The initial average U, equal to the average U value of MA SFH in 2022, from EIA RECS.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #188
                                                                                                                                                                                                                                                                                                          LI,C
                                                                                                                                                                                                                                                                                                          Initial Code U Value (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                          = 0.003
                                                                                                                                                                                                                                                                                                          Description: The initial value of code U. For initial paper, assume that this is between initial optimal U (nearly 0) and average U (0.006).
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #189
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Initial Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                          = 0.062
                                                                                                                                                                                                                                                                                                          Description: The price to cool a home per BTU. This is the price of electricity as all cooling systems, as air conditioning systems, use electricity.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Cooling Energy Price Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #190
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Initial Fraction of Homes Retrofitting (dmnl )
                                                                                                                                                                                                                                                                                                          = 0.1
                                                                                                                                                                                                                                                                                                          Description: Initial fraction of homes open to retrofitting. Heuristically chosen to be 0.1 to match low level of retrofitting that current occurs.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v5 testing #191
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Initial Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                                                                                                                                          Initial Heating Energy Price[Heat Pump Heating and Cooling] = 0.062
                                                                                                                                                                                                                                                                                                          Initial Heating Energy Price[Gas Heating] = 0.0142
                                                                                                                                                                                                                                                                                                          Initial Heating Energy Price[Oil Heating] = 0.017
                                                                                                                                                                                                                                                                                                          Description: Price of energy used in each technology: heat pump, central AC, window AC, no AC, gas, and oil. For heat pumps and air conditioners, this is electricity.Data from (using annual 2020 data for MA):electricity: https://www.eia.gov/electricity/data/browser/#/topic/7?agg=1,0&geo=vvvvvvvvvvvvo&endsec=8&freq=M&start=200101&ctype=linechart&ltype=pin&rtype=s&pin=&rse=0&maptype=0,natural gas:https://www.eia.gov/dnav/ng/ng_pri_sum_a_EPG0_PRS_DMcf_a.htmheating oil: https://www.eia.gov/petroleum/heatingoilpropane/
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By
                                                                                                                                                                                                                                                                                                          • Heating Energy Price The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v5 testing #192
                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                          Initial Homes Not Retrofitting (House)
                                                                                                                                                                                                                                                                                                          Initial Homes Not Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Initial Homes Not Retrofitting[Preexisting Cohorts,Heating and Cooling System] = (1-
                                                                                                                                                                                                                                                                                                          Initial Fraction of Homes Retrofitting)* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                          Description: Initial homes not open to retrofitting.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v5 testing #193
                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                          Initial Homes Retrofitting (Houses)
                                                                                                                                                                                                                                                                                                          Initial Homes Retrofitting[Cohort,Heating and Cooling System] = 0
                                                                                                                                                                                                                                                                                                          Initial Homes Retrofitting[Preexisting Cohorts,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                          Initial Fraction of Homes Retrofitting* Initial Housing[ Preexisting Cohorts, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                          Description: Homes that are open to retrofitting initially.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #195
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Initial Housing (House)
                                                                                                                                                                                                                                                                                                          Initial Housing[Cohort,Heating and Cooling System] = 2.2e+06
                                                                                                                                                                                                                                                                                                          Description: The total number of houses that begin in each cohort and heating and cooling source. Taken from CIN file.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #197
                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                          Initial U Value (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                          Initial U Value[Cohort,Heating and Cooling System,Retrofitting Status] = 0
                                                                                                                                                                                                                                                                                                          Initial U Value[Preexisting Cohorts,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                          Initial Average U Value[ Preexisting Cohorts]* Housing[ Preexisting Cohorts, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                          Description: Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                          • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #204
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )
                                                                                                                                                                                                                                                                                                          = 2032
                                                                                                                                                                                                                                                                                                          Description: The year in which the subsidy is phased out. If final time, then has no ending date.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #205
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )
                                                                                                                                                                                                                                                                                                          = 2000
                                                                                                                                                                                                                                                                                                          Description: The maximum proportional subsidy for heat pumps that will be offered, regardless of the subsidy rate. For instance, if the proportional subsidy is 50% but the maximum is $1000, then for a retrofit project that costs $3000 only a $1000 subsidy will be given.Taken from: https://www.energystar.gov/about/federal-tax-credits
                                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #206
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                                                                                                                          = 2023
                                                                                                                                                                                                                                                                                                          Description: Time at which the proportional subsidy will take effect from the Inflation Reduction Act, from https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #207
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                                                          = 0.3
                                                                                                                                                                                                                                                                                                          Description: Proportion of total heat pump cost that will be credited as part of a proportional subsidy.Taken from: https://www.energystar.gov/about/federal-tax-credits
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #208
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          kBTU per kWH (kBTU / kWH )
                                                                                                                                                                                                                                                                                                          = 3.41214
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #214
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                          = 0.75
                                                                                                                                                                                                                                                                                                          Description: Proportion of total retrofit cost that will be credited as part of a proportional subsidy. Theoretically, this can vary between current housing and housing under construction.Based off Mass Save data: https://www.masssave.com/en/residential/rebates-and-incentives/insulation-and-windows/insulation-and-air-sealing
                                                                                                                                                                                                                                                                                                          Present In 2 Views:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #220
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )
                                                                                                                                                                                                                                                                                                          = 10000
                                                                                                                                                                                                                                                                                                          Description: The total amount of money offered by the lump sum subsidy.Taken from: https://www.masssave.com/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #221
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)
                                                                                                                                                                                                                                                                                                          = 2200
                                                                                                                                                                                                                                                                                                          Description: The year in which the state's subsidy for heat pumps is phased out.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #222
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                                                                                                                          = 2020
                                                                                                                                                                                                                                                                                                          Description: The year in which the state's lump sum subsidy for heat pumps will activate.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #223
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          MassSave Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                                                                                                                          = 1e+07
                                                                                                                                                                                                                                                                                                          Description: The maximum proportional subsidy that will be offered, regardless of that subsidy's discount. For instance, if the proportional subsidy is 50% but the maximum is $1000, then for a retrofit project that costs $3000 only a $1000 subsidy will be given.If very large, then no maximum subsidy given.
                                                                                                                                                                                                                                                                                                          Present In 1 View:
                                                                                                                                                                                                                                                                                                          Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #225
                                                                                                                                                                                                                                                                                                          C
                                                                                                                                                                                                                                                                                                          Maximum Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                          = 10
                                                                                                                                                                                                                                                                                                          Description: Shifts x-axis for graph of optimal retrofit amount as a function of energy price.
                                                                                                                                                                                                                                                                                                          Present In 0 Views:
                                                                                                                                                                                                                                                                                                            Used By
                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #227
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Months per Year (Month / Year )
                                                                                                                                                                                                                                                                                                              = 12
                                                                                                                                                                                                                                                                                                              Description: The number of months per year.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #235
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              No Turnover Switch (dmnl )
                                                                                                                                                                                                                                                                                                              = 0
                                                                                                                                                                                                                                                                                                              Description: Switch for having no turnover in housing stock-- i.e., no housing demolitions or constructions.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                              • Demolitions Homes that are destroyed every year.
                                                                                                                                                                                                                                                                                                              • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              .housingagingchain v8 #238
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Noise Correlation Time (Year)
                                                                                                                                                                                                                                                                                                              = 4
                                                                                                                                                                                                                                                                                                              Description: The correlation time constant for Pink Noise.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                              • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                              • White Noise White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              .housingagingchain v8 #236
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Noise Correlation Time 0 (Year)
                                                                                                                                                                                                                                                                                                              = 4
                                                                                                                                                                                                                                                                                                              Description: The correlation time constant for Pink Noise.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                              • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                              • White Noise 0 White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #237
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Noise Correlation Time 1 (Year)
                                                                                                                                                                                                                                                                                                              = 4
                                                                                                                                                                                                                                                                                                              Description: The correlation time constant for Pink Noise.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                              • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                              • White Noise 1 White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              .housingagingchain v8 #241
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Noise Standard Deviation (Dimensionless)
                                                                                                                                                                                                                                                                                                              = 0
                                                                                                                                                                                                                                                                                                              Description: The standard deviation of the pink noise process.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                              • White Noise White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              .housingagingchain v8 #239
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Noise Standard Deviation 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                              = 0
                                                                                                                                                                                                                                                                                                              Description: The standard deviation of the pink noise process.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #240
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Noise Standard Deviation 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                              = 0
                                                                                                                                                                                                                                                                                                              Description: The standard deviation of the pink noise process.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              .housingagingchain v8 #244
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Noise Start Time (Year)
                                                                                                                                                                                                                                                                                                              = 5
                                                                                                                                                                                                                                                                                                              Description: Start time for the random input.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                              • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              .housingagingchain v8 #242
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Noise Start Time 0 (Year)
                                                                                                                                                                                                                                                                                                              = 5
                                                                                                                                                                                                                                                                                                              Description: Start time for the random input.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                              • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #243
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Noise Start Time 1 (Year)
                                                                                                                                                                                                                                                                                                              = 5
                                                                                                                                                                                                                                                                                                              Description: Start time for the random input.
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                              • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #261
                                                                                                                                                                                                                                                                                                              C
                                                                                                                                                                                                                                                                                                              Peak Load from Non Heating or Cooling Sources (kWH / Day )
                                                                                                                                                                                                                                                                                                              = 18344.8*1000*0.461799
                                                                                                                                                                                                                                                                                                              Description: The peak load coming from non-heating sources, like other household uses, commercial uses, industrial uses, etc. Approximated as the average peak load in September, October, April, and May of 2022 and 2023 from New England ISO data, since there is little heating or cooling demand in those swing months. We multiply by 0.46 as Massachusetts has 46% of New England's population and we assume demand is proportional to population.Data source: https://www.iso-ne.com/isoexpress/web/reports/load-and-demand/-/tree/net-ener-peak-load
                                                                                                                                                                                                                                                                                                              Present In 1 View:
                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #264
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Pounds per Ton (lb CO2 / tCO2)
                                                                                                                                                                                                                                                                                                                = 2204.6
                                                                                                                                                                                                                                                                                                                Description: The number of pounds in a metric ton.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #269
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                                                                                                                                = 2023
                                                                                                                                                                                                                                                                                                                Description: Time at which the proportional subsidy will take effect from the Energy Efficiency Home Improvement Credit.Source: https://www.nrdc.org/stories/consumer-guide-inflation-reduction-act
                                                                                                                                                                                                                                                                                                                Present In 2 Views:
                                                                                                                                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #270
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                                                                = 1
                                                                                                                                                                                                                                                                                                                Description: Turns proportional subsidy's effect on retrofit cost on/off.
                                                                                                                                                                                                                                                                                                                Present In 2 Views:
                                                                                                                                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                .housingagingchain v15 #271
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Proportional MassSave Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                                                                                                                                = 2020
                                                                                                                                                                                                                                                                                                                Description: Time at which the proportional subsidy will take effect.
                                                                                                                                                                                                                                                                                                                Present In 2 Views:
                                                                                                                                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                .housingagingchain v15 #272
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Proportional Subsidy Switch for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                = 1
                                                                                                                                                                                                                                                                                                                Description: Turns proportional subsidy's effect on retrofit cost on/off.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #275
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Pulse Time (Year)
                                                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                                                Description: Time at which the pulse in Input occurs.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #273
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Pulse Time 0 (Year)
                                                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                                                Description: Time at which the pulse in Input occurs.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #274
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Pulse Time 1 (Year)
                                                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                                                Description: Time at which the pulse in Input occurs.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #278
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Ramp End Time (Year)
                                                                                                                                                                                                                                                                                                                = 1e+09
                                                                                                                                                                                                                                                                                                                Description: End time for the ramp input.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #276
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Ramp End Time 0 (Year)
                                                                                                                                                                                                                                                                                                                = 1e+09
                                                                                                                                                                                                                                                                                                                Description: End time for the ramp input.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #277
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Ramp End Time 1 (Year)
                                                                                                                                                                                                                                                                                                                = 1e+09
                                                                                                                                                                                                                                                                                                                Description: End time for the ramp input.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #281
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Ramp Start Time (Year)
                                                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                                                Description: Start time for the ramp input.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #279
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Ramp Start Time 0 (Year)
                                                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                                                Description: Start time for the ramp input.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #280
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Ramp Start Time 1 (Year)
                                                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                                                Description: Start time for the ramp input.
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #282
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )
                                                                                                                                                                                                                                                                                                                = 30000
                                                                                                                                                                                                                                                                                                                Description: The reference value of lifetime heating and cooling combinations when people calculate affinity of each combo. Hand calibrated to roughly match heat pump sales in https://www.masssave.com/en/about/news-and-events/news/mass-save-sponsors-announce-record-number-of-heat-pump-installations-across-massachusetts
                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testing #283
                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )
                                                                                                                                                                                                                                                                                                                = 12.88
                                                                                                                                                                                                                                                                                                                Description: The marginal cost of retrofitting at the reference EUI. In particular, the marginal cost of retrofitting at some EUI is Reference U *( (Reference U / U) ^ Sensitivity )This was calculated by setting sensitivity of marginal cost equal to 1.25, and finding the MC where a 31% reduction in U value from the reference costs a total of 4.95 / (1 - 0.21) dollars per square foot. The sensitivity value is explained in the sensitivity variable. Less et al. (2021, pg. 17-18) note that in their project database, the median cost per square foot for retrofits after subsidies was $4.95, while subsidies accounted for 21% of the total project cost for the median project. The median cost reduced energy use by 28% - 33% (of which I took the average), and I use the lower bound value to account for the fact that energy savings may occur not only due to increase in U value.Obviously all of this is extraordinarily rough.Less et al. (2021): https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #284
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                                                                                                                                                                                                                                                                                                                Reference Retrofit Cost (Dollar / (House * Year) )
                                                                                                                                                                                                                                                                                                                = 8740
                                                                                                                                                                                                                                                                                                                Description: Perceived cost of home heating to which households compare the perceived cost of retrofitting to when deciding to retrofit.Taken from average retrofit cost in Less et al. (2021)'s dataset, shown on page 17: https://eta-publications.lbl.gov/sites/default/files/final_walker_-_the_cost_of_decarbonization_and_energy.pdf
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                                                                                                                                                                                                                                                                                                                .housingagingchain v9 #285
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                                                                                                                                                                                                                                                                                                                Reference U Value (kBTU / (sf * Year * F) )
                                                                                                                                                                                                                                                                                                                = 0.006
                                                                                                                                                                                                                                                                                                                Description: Reference U Value to ensure base of exponent in marginally optimal U value is dimensionless. This must be equal to or greater than code U value.Value taken as the average of U values of single family homes in MA in 2020 for our sample.
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                                                                                                                                                                                                                                                                                                                • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                                • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                                                                • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                                • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                                • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                                • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #286
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                                                                                                                                                                                                                                                                                                                Retrofit Delay (Year )
                                                                                                                                                                                                                                                                                                                = 2
                                                                                                                                                                                                                                                                                                                Description: Time to retrofit. Assumed to be on average six months.
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                                                                                                                                                                                                                                                                                                                • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                                                                                                                                • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #290
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                                                                                                                                                                                                                                                                                                                Sensitivity of Affinity to Cost (dmnl )
                                                                                                                                                                                                                                                                                                                = 10
                                                                                                                                                                                                                                                                                                                Description: Sensitivity of affinity to each heating and cooling combination having higher cost. The higher this, the fewer houses will convert to more expensive combinations.Calculated by hand calibration-- value ensures that amount of heat pumps sold 2020 - 2024 begins at about 10K and goes to about 20K in 2024, in accordance with MassSave data from https://www.masssave.com/en/about/news-and-events/news/mass-save-sponsors-announce-record-number-of-heat-pump-installations-across-massachusetts
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                                                                                                                                                                                                                                                                                                                • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
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                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testing #291
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                                                                                                                                                                                                                                                                                                                Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                                                                                                                                                                                                                                                = 3.25
                                                                                                                                                                                                                                                                                                                Description: Measures the sensitivity of marginal retrofit costs as a function of optimal U value. In particular, marginal Retrofit Cost is equal to Constant * (U Value retrofitted away ^ Convexity). This must be greater than 1.This is taken from pg. 69 of Caswell (2022), where she calculates the total retrofit cost curve as a function of percent savings as having an exponent of 2.25. Because this is the total retrofit cost curve, the exponent for the marginal cost is -2.25 - 1. Because percent savings is inversely proportional to U, the exponent in the total cost curve will be the negation of 2.25, which is ensured in the marginal cost curve formulation in other variables.
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                                                                                                                                                                                                                                                                                                                • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                                • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                                                                • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                                • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                                • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                                • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #292
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                                                                                                                                                                                                                                                                                                                Sensitivity of Retrofits to Cost (dmnl )
                                                                                                                                                                                                                                                                                                                = 10
                                                                                                                                                                                                                                                                                                                Description: Sensitivity of affinity (and fraction of houses retrofitting) to NPV of retrofitting.
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                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #295
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                                                                                                                                                                                                                                                                                                                Sine Amplitude (Dimensionless)
                                                                                                                                                                                                                                                                                                                = 0
                                                                                                                                                                                                                                                                                                                Description: Amplitude of sine wave in customer orders (fraction of mean).
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                                                                                                                                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #293
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                                                                                                                                                                                                                                                                                                                Sine Amplitude 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                = 0
                                                                                                                                                                                                                                                                                                                Description: Amplitude of sine wave in customer orders (fraction of mean).
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                                                                                                                                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #294
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                                                                                                                                                                                                                                                                                                                Sine Amplitude 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                = 0
                                                                                                                                                                                                                                                                                                                Description: Amplitude of sine wave in customer orders (fraction of mean).
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                                                                                                                                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #298
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                                                                                                                                                                                                                                                                                                                Sine Period (Year)
                                                                                                                                                                                                                                                                                                                = 50
                                                                                                                                                                                                                                                                                                                Description: Period of sine wave in customer demand. Set initially to 50 weeks (1 year).
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                                                                                                                                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #296
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                                                                                                                                                                                                                                                                                                                Sine Period 0 (Year)
                                                                                                                                                                                                                                                                                                                = 50
                                                                                                                                                                                                                                                                                                                Description: Period of sine wave in customer demand. Set initially to 50 weeks (1 year).
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                                                                                                                                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #297
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                                                                                                                                                                                                                                                                                                                Sine Period 1 (Year)
                                                                                                                                                                                                                                                                                                                = 50
                                                                                                                                                                                                                                                                                                                Description: Period of sine wave. Set initially to 50 weeks (1 year).
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                                                                                                                                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #302
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                                                                                                                                                                                                                                                                                                                Step Time (Year)
                                                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                                                Description: Time for the step input.
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                                                                                                                                                                                                                                                                                                                • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #300
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                                                                                                                                                                                                                                                                                                                Step Time 0 (Year)
                                                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                                                Description: Time for the step input.
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                                                                                                                                                                                                                                                                                                                • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #301
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                                                                                                                                                                                                                                                                                                                Step Time 1 (Year)
                                                                                                                                                                                                                                                                                                                = 5
                                                                                                                                                                                                                                                                                                                Description: Time for the step input.
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                                                                                                                                                                                                                                                                                                                • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #305
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                                                                                                                                                                                                                                                                                                                System Switching SWITCH (dmnl )
                                                                                                                                                                                                                                                                                                                = 1
                                                                                                                                                                                                                                                                                                                Description: Switch for allowing houses to switch heating and cooling systems. If 1, they can switch.
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                                                                                                                                                                                                                                                                                                                • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #307
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                                                                                                                                                                                                                                                                                                                Time to Decide to Retrofit (Year )
                                                                                                                                                                                                                                                                                                                = 3
                                                                                                                                                                                                                                                                                                                Description: Time to decide to retrofit.
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                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #321
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                                                                                                                                                                                                                                                                                                                Total Initial Homes (Houses )
                                                                                                                                                                                                                                                                                                                = 20
                                                                                                                                                                                                                                                                                                                Description: Total number of houses, including those retrofitting or not. Number taken from Census's list of households in MA in 2022: https://www.census.gov/quickfacts/fact/table/MA/PST045222
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                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #322
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                                                                                                                                                                                                                                                                                                                  Total Initial Housing Starts (Houses / Year )
                                                                                                                                                                                                                                                                                                                  = 0.5
                                                                                                                                                                                                                                                                                                                  Description: Total number of houses that are built per year, across all systems.
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                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #340
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                                                                                                                                                                                                                                                                                                                  Weight on Upfront Cost (dmnl )
                                                                                                                                                                                                                                                                                                                  = 0.5
                                                                                                                                                                                                                                                                                                                  Description: How much homeowners weigh upfront (amoritized) costs of retrofits as opposed to the total cost of ownership due to being more perceptive of short-term costs.
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                                                                                                                                                                                                                                                                                                                  • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                                  • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
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                                                                                                                                                                                                                                                                                                                  .Control #126
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                                                                                                                                                                                                                                                                                                                  FINAL TIME (Year)
                                                                                                                                                                                                                                                                                                                  = 2050
                                                                                                                                                                                                                                                                                                                  Description: The final time for the simulation.
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                                                                                                                                                                                                                                                                                                                  .Control #196
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                                                                                                                                                                                                                                                                                                                  INITIAL TIME (Year)
                                                                                                                                                                                                                                                                                                                  = 2020
                                                                                                                                                                                                                                                                                                                  Description: The initial time for the simulation.
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                                                                                                                                                                                                                                                                                                                  • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                                                                                                                                                  • Average Area of Housing Starts The average area of housing starts.
                                                                                                                                                                                                                                                                                                                  • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                  • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                  • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
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                                                                                                                                                                                                                                                                                                                  .Control #306
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                                                                                                                                                                                                                                                                                                                  TIME STEP (Year )
                                                                                                                                                                                                                                                                                                                  = 0.03125
                                                                                                                                                                                                                                                                                                                  Description: The time step for the simulation.
                                                                                                                                                                                                                                                                                                                  Present In 1 View:
                                                                                                                                                                                                                                                                                                                  Used By
                                                                                                                                                                                                                                                                                                                  • Input Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                  • Input 0 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                  • Input 1 Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                  • SAVEPER The frequency with which output is stored.
                                                                                                                                                                                                                                                                                                                  • White Noise White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                                  • White Noise 0 White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                                  • White Noise 1 White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  Top (Type) Flow (24 Variables)
                                                                                                                                                                                                                                                                                                                  Group
                                                                                                                                                                                                                                                                                                                  Type
                                                                                                                                                                                                                                                                                                                  Variable Name And Description
                                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #8
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Age Removal (House * Year /Year)
                                                                                                                                                                                                                                                                                                                  Age Removal[Cohort,Retrofitting Status] = SUM(
                                                                                                                                                                                                                                                                                                                  Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])* Average Age[ Cohort, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                  Description: Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #10
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Aging (House * Year / Year)
                                                                                                                                                                                                                                                                                                                  Aging[Cohort,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                  Aging per Year*SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                                                                                                                                                                                                                                  Description: Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #13
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Annual Federal Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Federal Annual Heat Pump Subsidy+ Federal Annual Retrofit Subsidy
                                                                                                                                                                                                                                                                                                                  Description: The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Cumulative Federal Subsidy The amount of money the federal government spends on subsidies for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #14
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Federal Annual Heat Pump Subsidy+ Massachusetts Annual Heat Pumps Subsidy
                                                                                                                                                                                                                                                                                                                  Description: The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #16
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Annual MA Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Massachusetts Annual Retrofit Subsidy+ Massachusetts Annual Heat Pumps Subsidy
                                                                                                                                                                                                                                                                                                                  Description: The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Cumulative MA Subsidy The amount of subsidies that the Massachusetts state government has given out for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #17
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Federal Annual Retrofit Subsidy+ Massachusetts Annual Retrofit Subsidy
                                                                                                                                                                                                                                                                                                                  Description: The subsidies for retrofits paid out every year.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #19
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Area of New Homes (sf / Year)
                                                                                                                                                                                                                                                                                                                  Area of New Homes[Cohort] =
                                                                                                                                                                                                                                                                                                                  Average Area of Housing Starts*SUM( Housing Starts[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                  Description: The total Area added by the construction of new homes, by cohort.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #20
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Area Removal (sf /Year)
                                                                                                                                                                                                                                                                                                                  Area Removal[Cohort,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                  Average Area[ Cohort, Retrofitting Status]*SUM( Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                                                                                                                                                                                                                                  Description: Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #64
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Change in AC Noise (1/Year)
                                                                                                                                                                                                                                                                                                                  = (
                                                                                                                                                                                                                                                                                                                  White Noise- Autocorrelated Noise)/ Noise Correlation Time
                                                                                                                                                                                                                                                                                                                  Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Autocorrelated Noise First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #62
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Change in AC Noise 0 (1/Year)
                                                                                                                                                                                                                                                                                                                  = (
                                                                                                                                                                                                                                                                                                                  White Noise 0- Autocorrelated Noise 0)/ Noise Correlation Time 0
                                                                                                                                                                                                                                                                                                                  Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Autocorrelated Noise 0 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #63
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Change in AC Noise 1 (1/Year)
                                                                                                                                                                                                                                                                                                                  = (
                                                                                                                                                                                                                                                                                                                  White Noise 1- Autocorrelated Noise 1)/ Noise Correlation Time 1
                                                                                                                                                                                                                                                                                                                  Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Autocorrelated Noise 1 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v18 #84
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Decrease in Code U (kBTU / (sf * Year * F) / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Code U* Fractional Decrease in Code U
                                                                                                                                                                                                                                                                                                                  Description: The change in code U from policy.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #89
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Demolitions (House / Year)
                                                                                                                                                                                                                                                                                                                  Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                  Demolition Hazard Rate* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]*(1- No Turnover Switch)
                                                                                                                                                                                                                                                                                                                  Description: Homes that are destroyed every year.
                                                                                                                                                                                                                                                                                                                  Present In 3 Views: Used By
                                                                                                                                                                                                                                                                                                                  • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                  • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                  • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                                  • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #98
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Emissions (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                  = SUM(
                                                                                                                                                                                                                                                                                                                  Emissions by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                  Description: The total amount of emissions across all housing groups.
                                                                                                                                                                                                                                                                                                                  Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                  • Average Emissions The average CO2 emissions for a household, not disaggregated into any grouping.
                                                                                                                                                                                                                                                                                                                  • Cumulative Emissions The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #160
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Houses Switching Sources (House / Year)
                                                                                                                                                                                                                                                                                                                  Houses Switching Sources[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                  Fraction of Houses Switching[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                                                                                                                                                                                  Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Fraction of Houses Switching[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Fossil Fuel Heating, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                                                                                                                                                                                  Description: The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                                                  Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #173
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Housing Starts (Houses / Year)
                                                                                                                                                                                                                                                                                                                  Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                  Housing Fractional Growth Rate*SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])* Active Cohort Indicator[ Cohort]*(1- No Turnover Switch)
                                                                                                                                                                                                                                                                                                                  Description: Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                                                                  Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [2,2] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v18 #181
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                  Increase in U Value from Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                  Housing Starts[ Cohort, Heating and Cooling System]* U Value of Housing Starts[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                  Description: New U value from new homes being built.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #230
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Net Age Shift from Retrofitting Status Shifting (House * Year / Year)
                                                                                                                                                                                                                                                                                                                  Net Age Shift from Retrofitting Status Shifting[Cohort] = SUM(
                                                                                                                                                                                                                                                                                                                  Net Age Shift by System[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                  Description: Shift in age within each cohort due to houses becoming open or closed to retrofitting.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #232
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Net Area Shift due to Retrofit Status Switching (sf / Year)
                                                                                                                                                                                                                                                                                                                  Net Area Shift due to Retrofit Status Switching[Cohort] = SUM(
                                                                                                                                                                                                                                                                                                                  Net Area Shift by System[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                  Description: Shift in area between energy sources due to houses switching sources.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #233
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Net Change in Homes Retrofitting (Houses / Year)
                                                                                                                                                                                                                                                                                                                  Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] = (
                                                                                                                                                                                                                                                                                                                  Indicated Homes Retrofitting[ Cohort, Heating and Cooling System]- Housing[ Cohort, Heating and Cooling System,Open to Retrofitting])/ Time to Decide to Retrofit
                                                                                                                                                                                                                                                                                                                  Description: Homes that are in the process of deciding to retrofit.
                                                                                                                                                                                                                                                                                                                  Present In 3 Views: Used By
                                                                                                                                                                                                                                                                                                                  • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                                  • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                                                                                                                                                  • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                                                                                                                                  • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #234
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Net U Value Change from Retrofitting Home Shifts (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                  Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                  Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, U Value by Grouping[ Cohort, Heating and Cooling System,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                                                                                                                                  Description: Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #288
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Retrofitting (House * kBTU / (sf * F* Year) / Year)
                                                                                                                                                                                                                                                                                                                  Retrofitting[Cohort,Heating and Cooling System] = MAX(0,
                                                                                                                                                                                                                                                                                                                  Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]*( U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]- Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])/ Retrofit Delay)
                                                                                                                                                                                                                                                                                                                  Description: Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #331
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                  U Value Loss from Demolition[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                  U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Demolitions[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                  Description: Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #335
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                  U Value Shift from Source Switching[Cohort,Heat Pump Heating and Cooling,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                  Houses Switching Sources[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                  U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] = Houses Switching Sources[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Fossil Fuel Heating, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                  Description: The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                                  Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                  • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                  • U Value Increase from Source Switching The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  Top (Type) Auxiliary (202 Variables)
                                                                                                                                                                                                                                                                                                                  Group
                                                                                                                                                                                                                                                                                                                  Type
                                                                                                                                                                                                                                                                                                                  Variable Name And Description
                                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #0
                                                                                                                                                                                                                                                                                                                  C
                                                                                                                                                                                                                                                                                                                  Active Cohort Indicator (dmnl)
                                                                                                                                                                                                                                                                                                                  Active Cohort Indicator[Cohort] = IF THEN ELSE(INTEGER((
                                                                                                                                                                                                                                                                                                                  Time- INITIAL TIME)/ Cohort Duration)+1= Cohort-ELMCOUNT( Preexisting Cohorts),1,0)
                                                                                                                                                                                                                                                                                                                  Active Cohort Indicator[Preexisting Cohorts] = 0
                                                                                                                                                                                                                                                                                                                  Description: The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #1
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Actual EEHIC Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                  Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] = MIN(
                                                                                                                                                                                                                                                                                                                  Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]* Implemented EEHIC Subsidy Proportional Rate for Retrofits, Implemented EEHIC Maximum Subsidy for Retrofits)
                                                                                                                                                                                                                                                                                                                  Description: The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #2
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Actual HOMES Subsidy for Retrofits (Dollar/ Home)
                                                                                                                                                                                                                                                                                                                  Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                  Energy Savings[ Cohort, Heating and Cooling System]< HOMES Cut Off for Savings, HOMES Implemented Lower Subsidy, HOMES Implemented High Subsidy)
                                                                                                                                                                                                                                                                                                                  Description: The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #3
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Actual MassSave Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                  Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] = MIN(
                                                                                                                                                                                                                                                                                                                  Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]* Implemented MassSave Subsidy Proportional Rate for Retrofits, Implemented MassSave Maximum Subsidy for Retrofits)
                                                                                                                                                                                                                                                                                                                  Description: The actual subsidy offered for retrofits by MassSave, not the expected value.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v15 #4
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Additional Cost of Building to U Value (Dollar / sf)
                                                                                                                                                                                                                                                                                                                  Additional Cost of Building to U Value[Cohort,Heating and Cooling System] = ((1-
                                                                                                                                                                                                                                                                                                                  Expected MassSave Proportional Subsidy Rate for Retrofits)* Expected Reference Marginal Cost/(1- Sensitivity of Marginal Cost to U Value))*((( Reference U Value/ Code U)^ Sensitivity of Marginal Cost to U Value)* Code U-(( Reference U Value/ Optimal U for New Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value))* Optimal U for New Homes[ Cohort, Heating and Cooling System])- Expected Lump Sum Subsidy Intensity[New Housing]
                                                                                                                                                                                                                                                                                                                  Description: Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #5
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Affinity of Heating and Cooling Systems (dmnl)
                                                                                                                                                                                                                                                                                                                  Affinity of Heating and Cooling Systems[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                  Cost of Switching Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]>0,exp(- Sensitivity of Affinity to Cost* Cost of Switching Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Reference Lifetime Cost of Heating and Cooling Systems),0)
                                                                                                                                                                                                                                                                                                                  Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = IF THEN ELSE( Cost of Switching Heating and Cooling Systems[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]>0,exp(- Sensitivity of Affinity to Cost* Cost of Switching Heating and Cooling Systems[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]/ Reference Lifetime Cost of Heating and Cooling Systems),0)
                                                                                                                                                                                                                                                                                                                  Description: The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #6
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Affinity of Not Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                  Affinity of Not Retrofitting[Cohort,Heating and Cooling System] = exp(-
                                                                                                                                                                                                                                                                                                                  Sensitivity of Retrofits to Cost* Perceived Cost of Not Retrofitting[ Cohort, Heating and Cooling System]/ Reference Retrofit Cost)
                                                                                                                                                                                                                                                                                                                  Description: The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v4 testing #7
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Affinity of Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                  Affinity of Retrofitting[Cohort,Heating and Cooling System] = exp(-
                                                                                                                                                                                                                                                                                                                  Sensitivity of Retrofits to Cost* Perceived Cost of Retrofitting[ Cohort, Heating and Cooling System]/ Reference Retrofit Cost)
                                                                                                                                                                                                                                                                                                                  Description: Affinity of retrofitting, where utility value is equal to its NPV.
                                                                                                                                                                                                                                                                                                                  Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                  • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #8
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Age Removal (House * Year /Year)
                                                                                                                                                                                                                                                                                                                  Age Removal[Cohort,Retrofitting Status] = SUM(
                                                                                                                                                                                                                                                                                                                  Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])* Average Age[ Cohort, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                  Description: Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v8 #10
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Aging (House * Year / Year)
                                                                                                                                                                                                                                                                                                                  Aging[Cohort,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                  Aging per Year*SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                                                                                                                                                                                                                                  Description: Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  .housingagingchain v15 #12
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                  Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                  Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]/ Amoritization Period
                                                                                                                                                                                                                                                                                                                  Description: The incurred total retrofit cost amoritized over the specified amoritization period.
                                                                                                                                                                                                                                                                                                                  Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #13
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Annual Federal Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Federal Annual Heat Pump Subsidy+ Federal Annual Retrofit Subsidy
                                                                                                                                                                                                                                                                                                                  Description: The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Cumulative Federal Subsidy The amount of money the federal government spends on subsidies for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #14
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Federal Annual Heat Pump Subsidy+ Massachusetts Annual Heat Pumps Subsidy
                                                                                                                                                                                                                                                                                                                  Description: The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #15
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Annual Load from Heat Pumps (kBTU / Year)
                                                                                                                                                                                                                                                                                                                  = SUM(
                                                                                                                                                                                                                                                                                                                  Energy Use by Grouping[ Cohort!, Heat Pump Heating and Cooling!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                  Description: The load on the electric grid from servicing heating and cooling demand from heat pumps, across the whole year.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #16
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Annual MA Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Massachusetts Annual Retrofit Subsidy+ Massachusetts Annual Heat Pumps Subsidy
                                                                                                                                                                                                                                                                                                                  Description: The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                  • Cumulative MA Subsidy The amount of subsidies that the Massachusetts state government has given out for heat pumps and retrofits since the beginning of the model's run.
                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #17
                                                                                                                                                                                                                                                                                                                  F,A
                                                                                                                                                                                                                                                                                                                  Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Federal Annual Retrofit Subsidy+ Massachusetts Annual Retrofit Subsidy
                                                                                                                                                                                                                                                                                                                  Description: The subsidies for retrofits paid out every year.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #18
                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                  Annual Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                  Annual Heat Pump Subsidy+ Annual Retrofit Subsidy
                                                                                                                                                                                                                                                                                                                  Description: The amount of subsidies spent on heat pumps and retrofits every year.
                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                    .housingagingchain v8 #19
                                                                                                                                                                                                                                                                                                                    F,A
                                                                                                                                                                                                                                                                                                                    Area of New Homes (sf / Year)
                                                                                                                                                                                                                                                                                                                    Area of New Homes[Cohort] =
                                                                                                                                                                                                                                                                                                                    Average Area of Housing Starts*SUM( Housing Starts[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                    Description: The total Area added by the construction of new homes, by cohort.
                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                    • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                    .housingagingchain v8 #20
                                                                                                                                                                                                                                                                                                                    F,A
                                                                                                                                                                                                                                                                                                                    Area Removal (sf /Year)
                                                                                                                                                                                                                                                                                                                    Area Removal[Cohort,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                    Average Area[ Cohort, Retrofitting Status]*SUM( Demolitions[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                                                                                                                                                                                                                                    Description: Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                    • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                    .housingagingchain v8 #26
                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                    Average Age (Year)
                                                                                                                                                                                                                                                                                                                    Average Age[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                                                                                                                                                                                                                                    Total Age[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                                                                                                                                                                                                                                    Description: The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                    • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                    • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                                                                                                                                                    Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                    .housingagingchain v8 #25
                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                    Average Age in All Housing (Year)
                                                                                                                                                                                                                                                                                                                    = ZIDZ(SUM(
                                                                                                                                                                                                                                                                                                                    Total Age[ Cohort!, Retrofitting Status!]), Total Housing Stock)
                                                                                                                                                                                                                                                                                                                    Description: Average age of houses, regardless of cohort
                                                                                                                                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #29
                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                      Average Area (sf / House)
                                                                                                                                                                                                                                                                                                                      Average Area[Cohort,Retrofitting Status] = ZIDZ(
                                                                                                                                                                                                                                                                                                                      Area[ Cohort, Retrofitting Status], Housing by Cohort and Retrofitting Status[ Cohort, Retrofitting Status])
                                                                                                                                                                                                                                                                                                                      Description: Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                                                                                                                                      Present In 7 Views: Used By
                                                                                                                                                                                                                                                                                                                      • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                      • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                                      • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                                                                                                                                                                                      • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                                                                      • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                      • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                                                                      • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                                                                                                                                      • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                      • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                                                                                                                                      • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                                                                                                                                      • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                      • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                      • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                      • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                      • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                      • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                                                                                                                                      Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                      .housingagingchain v8 #27
                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                      Average Area in All Housing (sf/ House)
                                                                                                                                                                                                                                                                                                                      = ZIDZ(
                                                                                                                                                                                                                                                                                                                      Total Area, Total Housing Stock)
                                                                                                                                                                                                                                                                                                                      Description: The average are of all houses, regardless of what group they're in.
                                                                                                                                                                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #28
                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                      Average Area of Housing Starts (sf / House)
                                                                                                                                                                                                                                                                                                                      =
                                                                                                                                                                                                                                                                                                                      Increase in Area per Year*( Time- INITIAL TIME)+ Initial Average Area of Housing Starts
                                                                                                                                                                                                                                                                                                                      Description: The average area of housing starts.
                                                                                                                                                                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #31
                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                      Average Cooling Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                      Average Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                      Expected Cooling Energy Price* Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                      Description: The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #30
                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                      Average Cooling Cost Across All Homes (Dollar / House/ Year)
                                                                                                                                                                                                                                                                                                                      =
                                                                                                                                                                                                                                                                                                                      Total Cooling Cost/SUM( Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                      Description: The average cost to cool a home, for all cohorts and systems.
                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #33
                                                                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                                                                        Average Cooling Energy Use (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                        Average Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                        U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                        Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                                                                                                                                                                        Description: The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                                        Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #32
                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                        Average Cooling Energy Use Across All Homes (kBTU / Year / House)
                                                                                                                                                                                                                                                                                                                        = ZIDZ(
                                                                                                                                                                                                                                                                                                                        Total Cooling Energy Use, Total Housing Stock)
                                                                                                                                                                                                                                                                                                                        Description: The amount of energy an average home spends on cooling, regardless of cohort, retrofit status, etc.
                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #34
                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                          Average Daily Load from Heat Pumps (kBTU / Day)
                                                                                                                                                                                                                                                                                                                          =
                                                                                                                                                                                                                                                                                                                          Annual Load from Heat Pumps/ Days per Year
                                                                                                                                                                                                                                                                                                                          Description: The average load on the electric grid from heat pumps, per day.
                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #39
                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                            Average Emissions (tCO2 / House / Year)
                                                                                                                                                                                                                                                                                                                            = ZIDZ(
                                                                                                                                                                                                                                                                                                                            Emissions, Total Housing Stock)
                                                                                                                                                                                                                                                                                                                            Description: The average CO2 emissions for a household, not disaggregated into any grouping.
                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #35
                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                              Average Emissions by Grouping (tCO2 / (Year * House))
                                                                                                                                                                                                                                                                                                                              Average Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                              Average Emissions from Cooling by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Emissions from Heating by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                              Description: The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #36
                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                              Average Emissions by Heating and Cooling System (tCO2 / Year / House)
                                                                                                                                                                                                                                                                                                                              Average Emissions by Heating and Cooling System[Heating and Cooling System] = ZIDZ(
                                                                                                                                                                                                                                                                                                                              Emissions by Heating and Cooling System[ Heating and Cooling System], Housing by Heating and Cooling System[ Heating and Cooling System])
                                                                                                                                                                                                                                                                                                                              Description: The average CO2 emissions for each house, by heating and cooling system.
                                                                                                                                                                                                                                                                                                                              Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #37
                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                Average Emissions from Cooling by Grouping (tCO2 / (House * Year))
                                                                                                                                                                                                                                                                                                                                Average Emissions from Cooling by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Cooling Emissions Factor/ Pounds per Ton
                                                                                                                                                                                                                                                                                                                                Description: The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status.
                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #38
                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                Average Emissions from Heating by Grouping (tCO2 / (House * Year))
                                                                                                                                                                                                                                                                                                                                Average Emissions from Heating by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Heating Emissions Factors[ Heating and Cooling System]/ Pounds per Ton
                                                                                                                                                                                                                                                                                                                                Description: Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc.
                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #40
                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                Average Energy Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                Average Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                Average Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                Description: The average cost of both heating and cooling a home, by grouping.
                                                                                                                                                                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                .housingagingchain v15 #41
                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                Average Energy Costs for Retrofitting Home (Dollar / Year / House)
                                                                                                                                                                                                                                                                                                                                Average Energy Costs for Retrofitting Home[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                Average Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                                                                                                                                                Description: Heating costs for each home open to retrofitting, annually, if no further retrofit measures are undertaken.
                                                                                                                                                                                                                                                                                                                                Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                • Total Cost of Ownership of Average Home Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #42
                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                Average Energy Costs if Retrofitted (Dollar/(Year*House))
                                                                                                                                                                                                                                                                                                                                Average Energy Costs if Retrofitted[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                Optimal Energy Cost[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                                                                                                                                                Description: Energy costs per year for each retrofitting house if homes retrofit to the optimal U value.
                                                                                                                                                                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #45
                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                Average Energy Use (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                Average Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]+ Average Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                Description: Average energy use to both heat and cool a home.
                                                                                                                                                                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #43
                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                Average Energy Use by Heating and Cooling System (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                Average Energy Use by Heating and Cooling System[Heating and Cooling System] = ZIDZ(SUM(
                                                                                                                                                                                                                                                                                                                                Energy Use by Grouping[ Cohort!, Heating and Cooling System, Retrofitting Status!]),SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!]))
                                                                                                                                                                                                                                                                                                                                Description: The average energy use for each home by heating and cooling system.
                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #44
                                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                                  Average Energy Use in All Housing (kBTU / Year / House)
                                                                                                                                                                                                                                                                                                                                  =
                                                                                                                                                                                                                                                                                                                                  Total Energy Use/ Total Housing Stock
                                                                                                                                                                                                                                                                                                                                  Description: The average energy use across all stocks.
                                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #46
                                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                                  Average EUI by Grouping (kBTU / (sf * Year))
                                                                                                                                                                                                                                                                                                                                  Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = XIDZ(
                                                                                                                                                                                                                                                                                                                                  Average Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status], Average Area[ Cohort, Retrofitting Status], NAREPLACEMENT)
                                                                                                                                                                                                                                                                                                                                  Description: The average energy use intensity by grouping
                                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #47
                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                    Average EUI in All Housing (kBTU / (sf * Year))
                                                                                                                                                                                                                                                                                                                                    =
                                                                                                                                                                                                                                                                                                                                    Average Energy Use in All Housing/ Average Area in All Housing
                                                                                                                                                                                                                                                                                                                                    Description: The average energy use intensity across all housing.
                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                      .housingagingchain v5 testing #49
                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                      Average Heating Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                      Average Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                      Expected Heating Energy Price[ Heating and Cooling System]* Average Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                      Description: The costs per year to heat one house.
                                                                                                                                                                                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #48
                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                      Average Heating Cost Across All Homes (Dollar / Year / House)
                                                                                                                                                                                                                                                                                                                                      = ZIDZ(
                                                                                                                                                                                                                                                                                                                                      Total Heating Cost,SUM( Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!]))
                                                                                                                                                                                                                                                                                                                                      Description: The average amount a home spends on heating, regardless of cohort or heating and cooling system.
                                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #51
                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                        Average Heating Energy Use (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                        Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                        U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                        Description: The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                        Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #50
                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                        Average Heating Energy Use Across All Homes (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                        = ZIDZ(
                                                                                                                                                                                                                                                                                                                                        Total Heating Energy Use, Total Housing Stock)
                                                                                                                                                                                                                                                                                                                                        Description: The average heating energy use per home, regardless of cohort, system,etc.
                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #53
                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                          Average Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                          Indicated Homes Retrofitting[ Cohort!, Heating and Cooling System!])/ Total Housing Stock
                                                                                                                                                                                                                                                                                                                                          Description: The average fraction of homes that will retrofit retrofitting after decision delayacross all housing.
                                                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #56
                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                            Average Subsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                                                                            Housing[ Cohort!, Heating and Cooling System!,Open to Retrofitting]* Subsidized Retrofit Cost[ Cohort!, Heating and Cooling System!])/SUM( Housing[ Cohort!, Heating and Cooling System!,Open to Retrofitting])
                                                                                                                                                                                                                                                                                                                                            Description: The average subsidized retrofit cost across all houses.
                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #58
                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                              Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                              Average U Value by Heating and Cooling System[Heating and Cooling System] = ZIDZ(
                                                                                                                                                                                                                                                                                                                                              Total U Value by Heating and Cooling System[ Heating and Cooling System], Housing by Heating and Cooling System[ Heating and Cooling System])
                                                                                                                                                                                                                                                                                                                                              Description: The U value of the average house using each heating and cooling system.
                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testing #59
                                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                                Average U Value in All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                = ZIDZ(
                                                                                                                                                                                                                                                                                                                                                Total U Value Across All Groupings, Total Housing Stock)
                                                                                                                                                                                                                                                                                                                                                Description: The average U Value over the entire housing stock, not disaggregated by any groupings.
                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #60
                                                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                                                  Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                  Average U Value of Houses Switching Into Sources[Heating and Cooling System] = XIDZ(
                                                                                                                                                                                                                                                                                                                                                  U Value Increase from Source Switching[ Heating and Cooling System], Houses Switching Into Sources[ Heating and Cooling System], NAREPLACEMENT)
                                                                                                                                                                                                                                                                                                                                                  Description: The average U value of houses switching into each source, for each source.
                                                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                    .housingagingchain v8 #64
                                                                                                                                                                                                                                                                                                                                                    F,A
                                                                                                                                                                                                                                                                                                                                                    Change in AC Noise (1/Year)
                                                                                                                                                                                                                                                                                                                                                    = (
                                                                                                                                                                                                                                                                                                                                                    White Noise- Autocorrelated Noise)/ Noise Correlation Time
                                                                                                                                                                                                                                                                                                                                                    Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                    • Autocorrelated Noise First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                                                    .housingagingchain v8 #62
                                                                                                                                                                                                                                                                                                                                                    F,A
                                                                                                                                                                                                                                                                                                                                                    Change in AC Noise 0 (1/Year)
                                                                                                                                                                                                                                                                                                                                                    = (
                                                                                                                                                                                                                                                                                                                                                    White Noise 0- Autocorrelated Noise 0)/ Noise Correlation Time 0
                                                                                                                                                                                                                                                                                                                                                    Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                    • Autocorrelated Noise 0 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #63
                                                                                                                                                                                                                                                                                                                                                    F,A
                                                                                                                                                                                                                                                                                                                                                    Change in AC Noise 1 (1/Year)
                                                                                                                                                                                                                                                                                                                                                    = (
                                                                                                                                                                                                                                                                                                                                                    White Noise 1- Autocorrelated Noise 1)/ Noise Correlation Time 1
                                                                                                                                                                                                                                                                                                                                                    Description: Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                    • Autocorrelated Noise 1 First-order autocorrelated noise. Provides a realistic noise input to models in which the next random shock depends in part on the previous shocks. The user can specify the correlation time. The mean is 0 and the standard deviation is specifiedby the user.
                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #70
                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                    Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                    =
                                                                                                                                                                                                                                                                                                                                                    Initial Cooling Energy Price* Input 1
                                                                                                                                                                                                                                                                                                                                                    Description: Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                                                                                                                                                                                    Present In 3 Views: Used By
                                                                                                                                                                                                                                                                                                                                                    • Expected Cooling Energy Price Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #71
                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                    Cooling Energy Use Under Alternatives (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Not Open to Retrofitting,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                    U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Traditional Cooling,Not Open to Retrofitting,Heating and Cooling System] = U Value by Grouping[ Cohort, Traditional Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] = 0
                                                                                                                                                                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                    Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Fossil Fuel Heating,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                    Description: The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #72
                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                    Cooling System Efficiency (dmnl)
                                                                                                                                                                                                                                                                                                                                                    Cooling System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                                                                                                                                                                    Heat Pump Cooling COP TABLE( Time)
                                                                                                                                                                                                                                                                                                                                                    Cooling System Efficiency[Central AC Cooling] = 2.93
                                                                                                                                                                                                                                                                                                                                                    Cooling System Efficiency[Window AC Cooling] = 2.49* Effect of Air Leakage from Window AC on Efficiency
                                                                                                                                                                                                                                                                                                                                                    Cooling System Efficiency[No AC Cooling] = NAREPLACEMENT
                                                                                                                                                                                                                                                                                                                                                    Description: The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                                                                                                                    Present In 4 Views: Used By
                                                                                                                                                                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #74
                                                                                                                                                                                                                                                                                                                                                    C
                                                                                                                                                                                                                                                                                                                                                    Cost of Cooling System Replacement (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                    Cost of Cooling System Replacement[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                                                                                                                                                                    Subsidized Cost of Heat Pumps
                                                                                                                                                                                                                                                                                                                                                    Cost of Cooling System Replacement[Central AC Cooling] = 5800
                                                                                                                                                                                                                                                                                                                                                    Cost of Cooling System Replacement[Window AC Cooling] = 1600
                                                                                                                                                                                                                                                                                                                                                    Cost of Cooling System Replacement[No AC Cooling] = 0
                                                                                                                                                                                                                                                                                                                                                    Description: The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #75
                                                                                                                                                                                                                                                                                                                                                    C
                                                                                                                                                                                                                                                                                                                                                    Cost of Heating System Replacement (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                    Cost of Heating System Replacement[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                                                                                                                                                                    Subsidized Cost of Heat Pumps
                                                                                                                                                                                                                                                                                                                                                    Cost of Heating System Replacement[Gas Heating] = 10000
                                                                                                                                                                                                                                                                                                                                                    Cost of Heating System Replacement[Oil Heating] = 7450
                                                                                                                                                                                                                                                                                                                                                    Description: The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #81
                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                    Cumulative Subsidies (Dollar)
                                                                                                                                                                                                                                                                                                                                                    =
                                                                                                                                                                                                                                                                                                                                                    Cumulative Subsidy for Retrofits+ Cumulative Subsidies for Heat Pumps
                                                                                                                                                                                                                                                                                                                                                    Description: The amount spent on subsidies for both heat pumps and retrofits by both since state and federal governments the beginning of the model run.
                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                      .housingagingchain v18 #84
                                                                                                                                                                                                                                                                                                                                                      F,A
                                                                                                                                                                                                                                                                                                                                                      Decrease in Code U (kBTU / (sf * Year * F) / Year)
                                                                                                                                                                                                                                                                                                                                                      =
                                                                                                                                                                                                                                                                                                                                                      Code U* Fractional Decrease in Code U
                                                                                                                                                                                                                                                                                                                                                      Description: The change in code U from policy.
                                                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                      • Code U U of house that is built to standard code.For initial paper, assume that it's constant at a level in between average U and optimal U.
                                                                                                                                                                                                                                                                                                                                                      Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #89
                                                                                                                                                                                                                                                                                                                                                      F,A
                                                                                                                                                                                                                                                                                                                                                      Demolitions (House / Year)
                                                                                                                                                                                                                                                                                                                                                      Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                      Demolition Hazard Rate* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]*(1- No Turnover Switch)
                                                                                                                                                                                                                                                                                                                                                      Description: Homes that are destroyed every year.
                                                                                                                                                                                                                                                                                                                                                      Present In 3 Views: Used By
                                                                                                                                                                                                                                                                                                                                                      • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                                                      • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                                                      • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                                                                      • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                                                                      Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #91
                                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                                      EEHIC Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                      EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = MIN(
                                                                                                                                                                                                                                                                                                                                                      Proportional Subsidy Switch for Retrofits* Expected EEHIC Proportional Subsidy Rate for Retrofits* Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status], Expected EEHIC Maximum Subsidy for Retrofits)
                                                                                                                                                                                                                                                                                                                                                      Description: The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #98
                                                                                                                                                                                                                                                                                                                                                      F,A
                                                                                                                                                                                                                                                                                                                                                      Emissions (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                                                      = SUM(
                                                                                                                                                                                                                                                                                                                                                      Emissions by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                      Description: The total amount of emissions across all housing groups.
                                                                                                                                                                                                                                                                                                                                                      Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                      • Average Emissions The average CO2 emissions for a household, not disaggregated into any grouping.
                                                                                                                                                                                                                                                                                                                                                      • Cumulative Emissions The total amount of CO2 emitted into the atmosphere during the course of the model's run.
                                                                                                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #96
                                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                                      Emissions by Grouping (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                                                      Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                      Housing[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Emissions by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                      Description: The total emissions for the most disaggregated grouping in the model.
                                                                                                                                                                                                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #97
                                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                                      Emissions by Heating and Cooling System (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                                                      Emissions by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                                                                                                      Emissions by Grouping[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                      Description: The total amount of emissions for houses by Heating and Cooling System.
                                                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #106
                                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                                      Energy Savings (dmnl)
                                                                                                                                                                                                                                                                                                                                                      Energy Savings[Cohort,Heating and Cooling System] = MAX(0,ABS(ZIDZ((
                                                                                                                                                                                                                                                                                                                                                      Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]- U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]), U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting])))
                                                                                                                                                                                                                                                                                                                                                      Description: The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                                                                                                                                                                      Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #107
                                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                                      Energy Use by Gas Houses (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                      = SUM(
                                                                                                                                                                                                                                                                                                                                                      Energy Use by Grouping[ Cohort!,Gas and Central AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Gas and Window AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Gas and No AC, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                      Description: The total amount of energy for heating and cooling used by homes which primarily use gas to heat their homes.
                                                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #108
                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                        Energy Use by Grouping (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                        Energy Use by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                        Average Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]* Housing[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                        Description: The total amount of energy used for heating and cooling in each group.
                                                                                                                                                                                                                                                                                                                                                        Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #109
                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                        Energy Use by Heat Pump Houses (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                        = SUM(
                                                                                                                                                                                                                                                                                                                                                        Energy Use by Grouping[ Cohort!,Heat Pump Only, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Heat Pump and Gas, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Heat Pump and Oil, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                        Description: The amount of energy used for heating and cooling by homes which primarily use heat pumps to heat their home.
                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #110
                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                          Energy Use by Oil Houses (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                                          Energy Use by Grouping[ Cohort!,Oil and Central AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Oil and Window AC, Retrofitting Status!])+SUM( Energy Use by Grouping[ Cohort!,Oil and No AC, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                          Description: The total amount of energy for heating and cooling used by homes primarily using oil to heat their home.
                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #111
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                            = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                            Cooling Energy Price, Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                                                                                                                                                                            Description: Energy price for one kBTU of cooling used to calculate optimal U value. Third order exponential smoothing of cooling energy price.
                                                                                                                                                                                                                                                                                                                                                            Present In 4 Views: Used By
                                                                                                                                                                                                                                                                                                                                                            • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                                                                                                                                                                            • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                                                                                                                            • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                                                                                                                                                                            • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #112
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                            = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                            Implemented EEHIC Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                                                                            Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays.
                                                                                                                                                                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                            • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                                                                                                            • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #113
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                            = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                            Implemented EEHIC Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                                                                                                                                                                            Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                            • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                                                                                                            • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                                                                            • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v15 #114
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected Fixed Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                            = SMOOTH(
                                                                                                                                                                                                                                                                                                                                                            Fixed Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                                                                                                                                                                            Description: Fixed cost used in calculating optimal EUI. Third order exponential smoothing of fixed cost.
                                                                                                                                                                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                            • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                            • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v15 #115
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected Heating Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                            Expected Heating Energy Price[Heating and Cooling System] = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                            Heating Energy Price[ Heating and Cooling System], Delay in Forming Expectations of Energy Price)
                                                                                                                                                                                                                                                                                                                                                            Description: Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                                                                                                                                                                            Present In 6 Views: Used By
                                                                                                                                                                                                                                                                                                                                                            • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                                                                                                                                                                            • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                                                                                                                                                                            • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                                                                                                                                                                            • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #116
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                            = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                            IRA Implemented Subsidy Proportional Rate for Heat Pumps, Delay in Changing Subsidy Expectations)* Proportional IRA Subsidy Switch for Heat Pumps
                                                                                                                                                                                                                                                                                                                                                            Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v15 #117
                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                            Expected Lump Sum Subsidy Intensity (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                            Expected Lump Sum Subsidy Intensity[Retrofit Cost] =
                                                                                                                                                                                                                                                                                                                                                            HOMES Expected Lower Lump Sum Subsidy/ Average Area of Housing Starts
                                                                                                                                                                                                                                                                                                                                                            Description: Lump sum subsidy for retrofits per square foot.
                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                            • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v15 #118
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                            = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                            Implemented MassSave Maximum Subsidy for Retrofits, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                                                                            Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v15 #119
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                            = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                            Implemented MassSave Subsidy Proportional Rate for Retrofits, Delay in Changing Subsidy Expectations)* Proportional Subsidy Switch for Retrofits
                                                                                                                                                                                                                                                                                                                                                            Description: Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                                                                            Present In 4 Views: Used By
                                                                                                                                                                                                                                                                                                                                                            • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                                                                            • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                                                                                                                                                                            • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                                                                            • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                                                                            • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #120
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                            = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                            Implemented IRA Maximum Proportional Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                                                                            Description: Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v15 #121
                                                                                                                                                                                                                                                                                                                                                            SM,A
                                                                                                                                                                                                                                                                                                                                                            Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                                                                                                                                                                            = SMOOTH(
                                                                                                                                                                                                                                                                                                                                                            Reference Marginal Cost, Delay in Forming Expectations of Retrofit Costs)
                                                                                                                                                                                                                                                                                                                                                            Description: Reference marginal cost used in calculating optimal U value. Third order exponential smoothing of reference marginal cost.
                                                                                                                                                                                                                                                                                                                                                            Present In 4 Views: Used By
                                                                                                                                                                                                                                                                                                                                                            • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                                                                            • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                                                                                                            • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                                                                            • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                                                                            • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                                                                            • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                                                            • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #122
                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                            Expected Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                            =
                                                                                                                                                                                                                                                                                                                                                            MassSave Expected Lump Sum Subsidy for Heat Pumps+ IRA Expected Proportional Subsidy for Heat Pumps
                                                                                                                                                                                                                                                                                                                                                            Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidies.
                                                                                                                                                                                                                                                                                                                                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v15 #123
                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                            Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                            Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                            Energy Savings[ Cohort, Heating and Cooling System]>= HOMES Cut Off for Savings, HOMES Expected Higher Subsidy, HOMES Expected Lower Lump Sum Subsidy)+ MassSave Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]+ EEHIC Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                            Description: Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                                                                                                                                                                                                                                                                                                                            Present In 4 Views: Used By
                                                                                                                                                                                                                                                                                                                                                            • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #124
                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                            Federal Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                            =
                                                                                                                                                                                                                                                                                                                                                            Total Heat Pump Sales* IRA Actual Subsidy for Heat Pumps
                                                                                                                                                                                                                                                                                                                                                            Description: The amount of subsidies the federal government spends on heat pumps through the Inflation Reduction Act every year.
                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                            • Annual Federal Subsidies The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year.
                                                                                                                                                                                                                                                                                                                                                            • Annual Heat Pump Subsidy The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #125
                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                            Federal Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                            = SUM((
                                                                                                                                                                                                                                                                                                                                                            Actual EEHIC Subsidy for Retrofits[ Cohort!, Heating and Cooling System!]+ Actual HOMES Subsidy for Retrofits[ Cohort!, Heating and Cooling System!])* Houses Retrofitting per Year[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                            Description: The amount of federal subsidies spent by the federal government, through the IRA.
                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v5 testing #127
                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                            Fixed Cost per Unit Area (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                            Fixed Cost per Unit Area[Cohort] = ZIDZ(
                                                                                                                                                                                                                                                                                                                                                            Expected Fixed Cost, Average Area[ Cohort,Open to Retrofitting])
                                                                                                                                                                                                                                                                                                                                                            Description: The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                            • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #129
                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                            Fraction of Houses in Each Heating and Cooling System (dmnl)
                                                                                                                                                                                                                                                                                                                                                            Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] = XIDZ(
                                                                                                                                                                                                                                                                                                                                                            Housing by Heating and Cooling System[ Heating and Cooling System], Total Housing Stock, NAREPLACEMENT)
                                                                                                                                                                                                                                                                                                                                                            Description: The fraction of houses using each heating and cooling system
                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                              .housingagingchain v5 testing #130
                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                              Fraction of Houses Switching (dmnl)
                                                                                                                                                                                                                                                                                                                                                              Fraction of Houses Switching[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                              Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                              Fraction of Houses Switching[Cohort,Gas Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Gas Heating, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                              Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] = Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System]/SUM( Affinity of Heating and Cooling Systems[ Cohort, Oil Heating, Retrofitting Status, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                              Description: Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                                                                                                                                                              Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                              • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #131
                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                              Fraction of Housing by Heating and Cooling System (dmnl)
                                                                                                                                                                                                                                                                                                                                                              Fraction of Housing by Heating and Cooling System[Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                              Housing by Heating and Cooling System[ Heating and Cooling System]/ Total Housing Stock
                                                                                                                                                                                                                                                                                                                                                              Description: The fraction of the total housing stock using each heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #134
                                                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                                                Fraction Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                =
                                                                                                                                                                                                                                                                                                                                                                Housing by Retrofitting Status[Open to Retrofitting]/( Housing by Retrofitting Status[Not Open to Retrofitting]+ Housing by Retrofitting Status[Open to Retrofitting])
                                                                                                                                                                                                                                                                                                                                                                Description: Proportion of housing that is open to retrofitting, across all cohorts and systems.
                                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #132
                                                                                                                                                                                                                                                                                                                                                                  LI,A
                                                                                                                                                                                                                                                                                                                                                                  Fraction Retrofitting by Cohort (dmnl)
                                                                                                                                                                                                                                                                                                                                                                  Fraction Retrofitting by Cohort[Cohort] = ZIDZ(SUM(
                                                                                                                                                                                                                                                                                                                                                                  Housing[ Cohort, Heating and Cooling System!,Open to Retrofitting]),SUM( Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!]))
                                                                                                                                                                                                                                                                                                                                                                  Description: Fraction that are retrofitting, only by cohort.
                                                                                                                                                                                                                                                                                                                                                                  Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                  • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #133
                                                                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                                                                  Fraction Retrofitting by System and Cohort (dmnl)
                                                                                                                                                                                                                                                                                                                                                                  Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] = ZIDZ(
                                                                                                                                                                                                                                                                                                                                                                  Housing[ Cohort, Heating and Cooling System,Open to Retrofitting],SUM( Housing[ Cohort, Heating and Cooling System, Retrofitting Status!]))
                                                                                                                                                                                                                                                                                                                                                                  Description: The fraction of houses that are retrofitting, by heating/cooling system and cohort.
                                                                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                    .housingagingchain v5 testing #143
                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                    Heating Energy Price (Dollar / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                    Heating Energy Price[Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                    Initial Heating Energy Price[ Heating and Cooling System]* Input 0
                                                                                                                                                                                                                                                                                                                                                                    Description: The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                                                                                                                                                                                    Present In 6 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                    • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #144
                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                    Heating Energy Use Under Alternatives (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                    Heating Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Not Open to Retrofitting,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                    U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                    Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Not Open to Retrofitting,Heating and Cooling System] = U Value by Grouping[ Cohort, Fossil Fuel Heating,Not Open to Retrofitting]* Average Area[ Cohort,Not Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                    Heating Energy Use Under Alternatives[Cohort,Heat Pump Heating and Cooling,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Heat Pump Heating and Cooling,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                    Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] = MIN( U Value by Grouping[ Cohort, Fossil Fuel Heating,Open to Retrofitting], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])* Average Area[ Cohort,Open to Retrofitting]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                    Description: The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #145
                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                    Heating System Efficiency (dmnl)
                                                                                                                                                                                                                                                                                                                                                                    Heating System Efficiency[Heat Pump Heating and Cooling] =
                                                                                                                                                                                                                                                                                                                                                                    Heat Pump Heating COP TABLE( Time)
                                                                                                                                                                                                                                                                                                                                                                    Heating System Efficiency[Gas Heating] = Gas COP TABLE( Time)
                                                                                                                                                                                                                                                                                                                                                                    Heating System Efficiency[Oil Heating] = Oil COP TABLE( Time)
                                                                                                                                                                                                                                                                                                                                                                    Description: The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                                                                                                                    Present In 3 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #148
                                                                                                                                                                                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                                                                                                                                                                                    HOMES Expected Higher Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                                    HOMES Implemented High Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                                                                                    Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                    .housingagingchain v15 #149
                                                                                                                                                                                                                                                                                                                                                                    SM,A
                                                                                                                                                                                                                                                                                                                                                                    HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                    = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                                    HOMES Implemented Lower Subsidy, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                                                                                    Description: Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays.
                                                                                                                                                                                                                                                                                                                                                                    Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #151
                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                    HOMES Implemented High Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                    Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES High Subsidy Amount,0)
                                                                                                                                                                                                                                                                                                                                                                    Description: Implemented higher subsidy from the HOMES rebate program.
                                                                                                                                                                                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                    • Actual HOMES Subsidy for Retrofits The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                                                                                                                                                                                                                                                                                                                                    • HOMES Expected Higher Subsidy Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. This is for homes that save more than 35% of energy
                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                    .housingagingchain v15 #152
                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                    HOMES Implemented Lower Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                    = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                    Time>= HOMES Subsidy Implementation Year:AND: Time<= HOMES Subsidy Final Year, HOMES Lower Subsidy Amount,0)
                                                                                                                                                                                                                                                                                                                                                                    Description: Lump sum subsidy that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                                                                                                                                                                                                                    Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #156
                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                    Houses Considering Switching System (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                    Houses Considering Switching System[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                    Housing[ Cohort, Heating and Cooling System, Retrofitting Status]/ Average Time To Consider Switching
                                                                                                                                                                                                                                                                                                                                                                    Description: The number of houses per year considering switching their heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                    • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #158
                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                    Houses Retrofitting (Houses)
                                                                                                                                                                                                                                                                                                                                                                    Houses Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                    Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                                                                                                                                                                                    Description: Total amount of houses retrofitting in each cohort and heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #157
                                                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                                                      Houses Retrofitting per Year (House / Year)
                                                                                                                                                                                                                                                                                                                                                                      Houses Retrofitting per Year[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                      Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]< U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting], Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]/ Retrofit Delay,0)
                                                                                                                                                                                                                                                                                                                                                                      Description: The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #159
                                                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                                                      Houses Switching Into Sources (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                      Houses Switching Into Sources[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                                                                                                                      Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!, Heating and Cooling System])
                                                                                                                                                                                                                                                                                                                                                                      Description: The number of houses switching into each Heating and Cooling System, cohort, and retrofitting group due to system switching.
                                                                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #160
                                                                                                                                                                                                                                                                                                                                                                      F,A
                                                                                                                                                                                                                                                                                                                                                                      Houses Switching Sources (House / Year)
                                                                                                                                                                                                                                                                                                                                                                      Houses Switching Sources[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                      Fraction of Houses Switching[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                                                                                                                                                                                                                                      Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Fraction of Houses Switching[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* Houses Considering Switching System[ Cohort, Fossil Fuel Heating, Retrofitting Status]* System Switching SWITCH
                                                                                                                                                                                                                                                                                                                                                                      Description: The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                                                                                                      Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #163
                                                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                                                      Housing by Cohort (House)
                                                                                                                                                                                                                                                                                                                                                                      Housing by Cohort[Cohort] = SUM(
                                                                                                                                                                                                                                                                                                                                                                      Housing[ Cohort, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                      Description: Number of houses per cohort
                                                                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #161
                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                        Housing by Cohort and Heating and Cooling System (Houses)
                                                                                                                                                                                                                                                                                                                                                                        Housing by Cohort and Heating and Cooling System[Cohort,Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                                                                                                                        Housing[ Cohort, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                        Description: Housing by heating and cooling system and cohort, irrespective of retrofit status.
                                                                                                                                                                                                                                                                                                                                                                        Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #162
                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                        Housing by Cohort and Retrofitting Status (House)
                                                                                                                                                                                                                                                                                                                                                                        Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] = SUM(
                                                                                                                                                                                                                                                                                                                                                                        Housing[ Cohort, Heating and Cooling System!, Retrofitting Status])
                                                                                                                                                                                                                                                                                                                                                                        Description: Amount of housing by retrofit status and cohort.
                                                                                                                                                                                                                                                                                                                                                                        Present In 3 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                        • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                                                                                                                                                                                                                                        • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                                                                                                                                                                                        • Housing by Retrofitting Status Amount of housing by retrofitting status, across all cohorts and systems.
                                                                                                                                                                                                                                                                                                                                                                        • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #164
                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                        Housing by Heating and Cooling System (House)
                                                                                                                                                                                                                                                                                                                                                                        Housing by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                                                                                                                        Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                        Description: Number of houses by energy source across all cohorts.
                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #165
                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                        Housing by Retrofitting Status (House)
                                                                                                                                                                                                                                                                                                                                                                        Housing by Retrofitting Status[Retrofitting Status] = SUM(
                                                                                                                                                                                                                                                                                                                                                                        Housing by Cohort and Retrofitting Status[ Cohort!, Retrofitting Status])
                                                                                                                                                                                                                                                                                                                                                                        Description: Amount of housing by retrofitting status, across all cohorts and systems.
                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                        • Fraction Retrofitting Proportion of housing that is open to retrofitting, across all cohorts and systems.
                                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #173
                                                                                                                                                                                                                                                                                                                                                                        F,A
                                                                                                                                                                                                                                                                                                                                                                        Housing Starts (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                        Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                        Housing Fractional Growth Rate*SUM( Housing[ Cohort!, Heating and Cooling System, Retrofitting Status!])* Active Cohort Indicator[ Cohort]*(1- No Turnover Switch)
                                                                                                                                                                                                                                                                                                                                                                        Description: Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                                                                                                                        Present In 3 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [2,2] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #167
                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                        Housing Starts Across Cohorts ()
                                                                                                                                                                                                                                                                                                                                                                        = SUM(
                                                                                                                                                                                                                                                                                                                                                                        Housing Starts In Each Cohort[ Cohort!])
                                                                                                                                                                                                                                                                                                                                                                        Description: Housing starts across all cohorts.
                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #169
                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                          Housing Starts In Each Cohort (House / Year)
                                                                                                                                                                                                                                                                                                                                                                          Housing Starts In Each Cohort[Cohort] = SUM(
                                                                                                                                                                                                                                                                                                                                                                          Housing Starts[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                                          Description: Housing starts across heating and cooling systems.
                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #175
                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                          Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                          = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                          Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: Time<= EEHIC Subsidy for Retrofits Final Year, EEHIC Maximum Subsidy for Retrofits,0)
                                                                                                                                                                                                                                                                                                                                                                          Description: Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #176
                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                          Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                          = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                          Time>= Proportional EEHIC Subsidy Implementation Year for Retrofits:AND: EEHIC Subsidy for Retrofits Final Year>= Time, EEHIC Proportional Subsidy Rate for Retrofits,0)
                                                                                                                                                                                                                                                                                                                                                                          Description: The implemented proportional subsidy rate for retrofits from the IRA, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #177
                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                          Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                          = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                          Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: Time<= IRA Lump Sum Subsidy for Heat Pumps Final Year, IRA Maximum Proportional Subsidy for Heat Pumps,0)
                                                                                                                                                                                                                                                                                                                                                                          Description: Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #178
                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                          Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                          = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                          Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: Time<= MassSave Subsidy for Retrofits Final Year, MassSave Maximum Subsidy for Retrofits,0)
                                                                                                                                                                                                                                                                                                                                                                          Description: Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year.
                                                                                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #179
                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                          Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                          = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                          Time>= Proportional MassSave Subsidy Implementation Year for Retrofits:AND: MassSave Subsidy for Retrofits Final Year>= Time, Mass Save Proportional Subsidy Rate for Retrofits,0)
                                                                                                                                                                                                                                                                                                                                                                          Description: The implemented proportional subsidy rate from the state, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy discount afterwards.
                                                                                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          .housingagingchain v18 #181
                                                                                                                                                                                                                                                                                                                                                                          F,A
                                                                                                                                                                                                                                                                                                                                                                          Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                          Increase in U Value from Housing Starts[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                          Housing Starts[ Cohort, Heating and Cooling System]* U Value of Housing Starts[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                          Description: New U value from new homes being built.
                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                          • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #182
                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                          Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                          Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                          Affinity of Retrofitting[ Cohort, Heating and Cooling System]/( Affinity of Retrofitting[ Cohort, Heating and Cooling System]+ Affinity of Not Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                                                                                                                                                                                          Description: Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #183
                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                          Indicated Homes Retrofitting (House)
                                                                                                                                                                                                                                                                                                                                                                          Indicated Homes Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                          Indicated Fraction of Homes Retrofitting[ Cohort, Heating and Cooling System]* Housing by Cohort and Heating and Cooling System[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                          Description: Number of homes that, once delays are taken into account, will be open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          .housingagingchain v8 #184
                                                                                                                                                                                                                                                                                                                                                                          LI,A
                                                                                                                                                                                                                                                                                                                                                                          Initial Age (House * Year)
                                                                                                                                                                                                                                                                                                                                                                          Initial Age[Cohort,Retrofitting Status] = INITIAL(0)
                                                                                                                                                                                                                                                                                                                                                                          Initial Age[Preexisting Cohorts,Retrofitting Status] = (
                                                                                                                                                                                                                                                                                                                                                                          Cohort Duration*(ELMCOUNT( Preexisting Cohorts)- Preexisting Cohorts+1))* Housing by Cohort and Retrofitting Status[ Preexisting Cohorts, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                                          Description: The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                          • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                          . #194
                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                          Initial Housing Starts (House/Year)
                                                                                                                                                                                                                                                                                                                                                                          Initial Housing Starts[Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                          Total Initial Housing Starts/ELMCOUNT( Heating and Cooling System)
                                                                                                                                                                                                                                                                                                                                                                          Description: Initial value of housing starts, initialized at 10 total houses.
                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v8 #200
                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                            Input (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                            = 1+STEP(
                                                                                                                                                                                                                                                                                                                                                                            Housing Starts Step Height, INITIAL TIME+ Step Time)+( Housing Starts Pulse Quantity/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time, TIME STEP)+RAMP( Housing Starts Ramp Slope, INITIAL TIME+ Ramp Start Time, INITIAL TIME+ Ramp End Time)+(STEP(1, INITIAL TIME)*(exp( Housing Starts Exponential Growth Rate*( Time- INITIAL TIME))-1))+ Sine Amplitude*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period)+STEP(1, INITIAL TIME+ Noise Start Time)* Autocorrelated Noise
                                                                                                                                                                                                                                                                                                                                                                            Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              .housingagingchain v8 #198
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Input 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                              = 1+STEP(
                                                                                                                                                                                                                                                                                                                                                                              Energy Price Step Height, INITIAL TIME+ Step Time 0)+( Energy Price Pulse Quantity/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time 0, TIME STEP)+RAMP( Energy Price Ramp Slope, INITIAL TIME+ Ramp Start Time 0, INITIAL TIME+ Ramp End Time 0)+(STEP(1, INITIAL TIME)*(exp( Energy Price Exponential Growth Rate*( Time- INITIAL TIME))-1))+ Sine Amplitude 0*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period 0)+STEP(1, INITIAL TIME+ Noise Start Time 0)* Autocorrelated Noise 0
                                                                                                                                                                                                                                                                                                                                                                              Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                              • Heating Energy Price The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #199
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Input 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                              = 1+STEP(
                                                                                                                                                                                                                                                                                                                                                                              Cooling Energy Price Step Height 1, INITIAL TIME+ Step Time 1)+( Energy Price Pulse Quantity 1/ TIME STEP)*PULSE( INITIAL TIME+ Pulse Time 1, TIME STEP)+RAMP( Energy Price Ramp Slope 1, INITIAL TIME+ Ramp Start Time 1, INITIAL TIME+ Ramp End Time 1)+(STEP(1, INITIAL TIME)*(exp( Energy Price Exponential Growth Rate 1*( Time- INITIAL TIME))-1))+ Sine Amplitude 1*SIN(2*3.14159*( Time- INITIAL TIME)/ Sine Period 1)+STEP(1, INITIAL TIME+ Noise Start Time 1)* Autocorrelated Noise 1
                                                                                                                                                                                                                                                                                                                                                                              Description: Input is a dimensionless variable which provides a variety of test input patterns, including a step,pulse, sine wave, and random noise.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                              • Cooling Energy Price Price of cooling a home (through air conditioning), subject to the test input.
                                                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #201
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              IRA Actual Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                              = MIN(
                                                                                                                                                                                                                                                                                                                                                                              IRA Implemented Subsidy Proportional Rate for Heat Pumps* Unsubsidized Cost of Heat Pumps, Implemented IRA Maximum Proportional Subsidy for Heat Pumps)
                                                                                                                                                                                                                                                                                                                                                                              Description: The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #202
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                              = MIN(
                                                                                                                                                                                                                                                                                                                                                                              Proportional IRA Subsidy Switch for Heat Pumps* Expected IRA Proportional Subsidy Rate for Heat Pumps* Unsubsidized Cost of Heat Pumps, Expected Maximum IRA Proportional Subsidy for Heat Pumps)
                                                                                                                                                                                                                                                                                                                                                                              Description: The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #203
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                                              = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                              Time>= IRA Proportional Subsidy Implementation Year for Heat Pumps:AND: IRA Lump Sum Subsidy for Heat Pumps Final Year>= Time, IRA Proportional Subsidy Rate for Heat Pumps,0)
                                                                                                                                                                                                                                                                                                                                                                              Description: The implemented proportional subsidy rate, taking into account whether a proportional subsidy has been implemented. Equal to zero before implementation year and proportional subsidy rate afterwards.
                                                                                                                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #209
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)
                                                                                                                                                                                                                                                                                                                                                                              Lifetime Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                              Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]/ Discount Rate
                                                                                                                                                                                                                                                                                                                                                                              Description: The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                              • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                              • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                                                                                              • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #210
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                              Marginal Cooling Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                              Expected Cooling Energy Price* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                              Description: The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #211
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))
                                                                                                                                                                                                                                                                                                                                                                              Marginal Cost at Binding U Value without EEHIC[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                              Expected Reference Marginal Cost*(ZIDZ( Reference U Value, U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]))^ Sensitivity of Marginal Cost to U Value
                                                                                                                                                                                                                                                                                                                                                                              Description: This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                              • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              .housingagingchain v15 #212
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)
                                                                                                                                                                                                                                                                                                                                                                              Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                              Marginal Cooling Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]+ Marginal Heating Cost Reduction from Retrofitting[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                              Description: Total cost reductions from retrofitting away one unit of U value for existing homes, including reductions in both heating and cooling costs.
                                                                                                                                                                                                                                                                                                                                                                              Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                              • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                                                                                                                                                                                              • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              .housingagingchain v5 testing #213
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                              Marginal Heating Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                              Expected Heating Energy Price[ Heating and Cooling System]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                              Description: The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #215
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                              =
                                                                                                                                                                                                                                                                                                                                                                              Total Heat Pump Sales* MassSave Implemented Lump Sum Subsidy for Heat Pumps
                                                                                                                                                                                                                                                                                                                                                                              Description: The actual subsidy provided for purchase of heat pumps by Massachusetts, as opposed to what the subsidy expected by homeowners is.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                              • Annual Heat Pump Subsidy The amount of money the government spends to subsidize heat pumps, including state and federal government.
                                                                                                                                                                                                                                                                                                                                                                              • Annual MA Subsidies The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps.
                                                                                                                                                                                                                                                                                                                                                                              Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #216
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Massachusetts Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                              = SUM(
                                                                                                                                                                                                                                                                                                                                                                              Houses Retrofitting per Year[ Cohort!, Heating and Cooling System!]* Actual MassSave Subsidy for Retrofits[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                                              Description: Amount of money Massachusetts spends on MassSave subsidies for retrofits, yearly.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #217
                                                                                                                                                                                                                                                                                                                                                                              SM,A
                                                                                                                                                                                                                                                                                                                                                                              MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                              = SMOOTH3(
                                                                                                                                                                                                                                                                                                                                                                              MassSave Implemented Lump Sum Subsidy for Heat Pumps, Delay in Changing Subsidy Expectations)
                                                                                                                                                                                                                                                                                                                                                                              Description: Expected lump sum subsidy that lowers subsidized retrofit costs from the state, taking into account information delays.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              .housingagingchain v15 #218
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              MassSave Expected Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                              MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] = MIN(
                                                                                                                                                                                                                                                                                                                                                                              Proportional Subsidy Switch for Retrofits* Expected MassSave Proportional Subsidy Rate for Retrofits* Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status], Expected MassSave Maximum Subsidy for Retrofits)
                                                                                                                                                                                                                                                                                                                                                                              Description: The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #219
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                              = MIN(
                                                                                                                                                                                                                                                                                                                                                                              Unsubsidized Cost of Heat Pumps,IF THEN ELSE( Time>= MassSave Lump Sum Subsidy Implementation Year for Heat Pumps:AND: Time<= MassSave Lump Sum Subsidy for Heat Pumps Final Year, MassSave Lump Sum Subsidy Amount for Heat Pumps,0))
                                                                                                                                                                                                                                                                                                                                                                              Description: Lump sum subsidy from MassSave that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year.
                                                                                                                                                                                                                                                                                                                                                                              Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #224
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              MassSave Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                                                                                                                                                                                              =
                                                                                                                                                                                                                                                                                                                                                                              FINAL TIME
                                                                                                                                                                                                                                                                                                                                                                              Description: The year in which the subsidy is phased out. If final time, then has no ending data.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                              HeatPumpModel_v31 #226
                                                                                                                                                                                                                                                                                                                                                                              A
                                                                                                                                                                                                                                                                                                                                                                              Monthly Total Heat Pump Sales (Houses/ Month)
                                                                                                                                                                                                                                                                                                                                                                              =
                                                                                                                                                                                                                                                                                                                                                                              Total Heat Pump Sales/ Months per Year
                                                                                                                                                                                                                                                                                                                                                                              Description: The number of homes buying heat pumps, every year.
                                                                                                                                                                                                                                                                                                                                                                              Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #229
                                                                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                                                                Net Age Shift by System (Year * House / Year)
                                                                                                                                                                                                                                                                                                                                                                                Net Age Shift by System[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, Average Age[ Cohort,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], Average Age[ Cohort,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                                                                                                                                                                                                Description: The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #230
                                                                                                                                                                                                                                                                                                                                                                                F,A
                                                                                                                                                                                                                                                                                                                                                                                Net Age Shift from Retrofitting Status Shifting (House * Year / Year)
                                                                                                                                                                                                                                                                                                                                                                                Net Age Shift from Retrofitting Status Shifting[Cohort] = SUM(
                                                                                                                                                                                                                                                                                                                                                                                Net Age Shift by System[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                                                Description: Shift in age within each cohort due to houses becoming open or closed to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8 #231
                                                                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                                                                Net Area Shift by System (sf / Year)
                                                                                                                                                                                                                                                                                                                                                                                Net Area Shift by System[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, Average Area[ Cohort,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], Average Area[ Cohort,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                                                                                                                                                                                                Description: The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #232
                                                                                                                                                                                                                                                                                                                                                                                F,A
                                                                                                                                                                                                                                                                                                                                                                                Net Area Shift due to Retrofit Status Switching (sf / Year)
                                                                                                                                                                                                                                                                                                                                                                                Net Area Shift due to Retrofit Status Switching[Cohort] = SUM(
                                                                                                                                                                                                                                                                                                                                                                                Net Area Shift by System[ Cohort, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                                                Description: Shift in area between energy sources due to houses switching sources.
                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 1  [4,4] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #233
                                                                                                                                                                                                                                                                                                                                                                                F,A
                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] = (
                                                                                                                                                                                                                                                                                                                                                                                Indicated Homes Retrofitting[ Cohort, Heating and Cooling System]- Housing[ Cohort, Heating and Cooling System,Open to Retrofitting])/ Time to Decide to Retrofit
                                                                                                                                                                                                                                                                                                                                                                                Description: Homes that are in the process of deciding to retrofit.
                                                                                                                                                                                                                                                                                                                                                                                Present In 3 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                                • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                                                                                                • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                                                                                                                                                                                                • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 2 (11.8%) (+) 1  [4,4] (-) 1  [2,2]
                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #234
                                                                                                                                                                                                                                                                                                                                                                                F,A
                                                                                                                                                                                                                                                                                                                                                                                Net U Value Change from Retrofitting Home Shifts (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System]>0, U Value by Grouping[ Cohort, Heating and Cooling System,Not Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System], U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]* Net Change in Homes Retrofitting[ Cohort, Heating and Cooling System])
                                                                                                                                                                                                                                                                                                                                                                                Description: Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #246
                                                                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                Expected Cooling Energy Price* Optimal Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                                                Description: The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #247
                                                                                                                                                                                                                                                                                                                                                                                C
                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status]* Cooling Degree Days/ Cooling System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                                                                                                                                                                                                                                Description: The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #248
                                                                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                                                                Optimal Energy Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                Optimal Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Cost[ Cohort, Heating and Cooling System, Retrofitting Status]+ Optimal Heating Cost[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                                                Description: Total energy cost if optimal U value is achieved.
                                                                                                                                                                                                                                                                                                                                                                                Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #249
                                                                                                                                                                                                                                                                                                                                                                                A
                                                                                                                                                                                                                                                                                                                                                                                Optimal Energy Use (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]+ Optimal Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                                                Description: Average energy use to heat and cool per house if U is optimal.
                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                  Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #250
                                                                                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                                                                                  Optimal Heating Cost (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                  Optimal Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                  Expected Heating Energy Price[ Heating and Cooling System]* Optimal Heating Energy Use[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                                                  Description: Average heating cost if U value is optimal.
                                                                                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #251
                                                                                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                                                                                  Optimal Heating Energy Use (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                  Optimal Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                  Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System]* Average Area[ Cohort, Retrofitting Status]* Heating Degree Days/ Heating System Efficiency[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                  Description: The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                  HeatPumpModel_v31 #252
                                                                                                                                                                                                                                                                                                                                                                                  A
                                                                                                                                                                                                                                                                                                                                                                                  Optimal U Across All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                  = SUM(
                                                                                                                                                                                                                                                                                                                                                                                  Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort!, Heating and Cooling System!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!]/ Total Housing Stock)
                                                                                                                                                                                                                                                                                                                                                                                  Description: The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                                                                                                                                                                                                                  Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                    .housingagingchain v18 #253
                                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                                    Optimal U for New Homes (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                    Optimal U for New Homes[Cohort,Heating and Cooling System] = ((
                                                                                                                                                                                                                                                                                                                                                                                    Expected Reference Marginal Cost/( Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]/ Discount Rate))^(1/ Sensitivity of Marginal Cost to U Value))* Reference U Value*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)
                                                                                                                                                                                                                                                                                                                                                                                    Description: The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                                                                                                    Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                                                                                                    • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #255
                                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                                    Optimal U Value for Existing Homes (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                    Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                                    U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]< Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System], Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System],IF THEN ELSE( Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System]> Marginal Cost at Binding U Value without EEHIC[ Cohort, Heating and Cooling System], Optimal U Value with No EEHIC Proportional Subsidy[ Cohort, Heating and Cooling System], U Value at Which EEHIC Cap Binds[ Cohort, Heating and Cooling System]))
                                                                                                                                                                                                                                                                                                                                                                                    Description: This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                    .housingagingchain v4 testing #254
                                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                    Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                    Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)*(1- Expected EEHIC Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                                                                                                                                                                                                                    Description: Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                                                                                                    Present In 8 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                    • Optimal U Across All Housing The average optimal U value across all cohorts and all energy sources. Weigh optimal U by share of housing so that houses which haven't been built yet don't factor into the average.
                                                                                                                                                                                                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #256
                                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                                    Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                    Optimal U Value with No EEHIC Proportional Subsidy[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                    Reference U Value*( Expected Reference Marginal Cost*(1- Expected MassSave Proportional Subsidy Rate for Retrofits)/ Lifetime Marginal Cost Reductions from Retrofitting[ Cohort, Heating and Cooling System])^(1/ Sensitivity of Marginal Cost to U Value)
                                                                                                                                                                                                                                                                                                                                                                                    Description: Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #257
                                                                                                                                                                                                                                                                                                                                                                                    A
                                                                                                                                                                                                                                                                                                                                                                                    Peak Cooling Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                    = SUM(
                                                                                                                                                                                                                                                                                                                                                                                    Peak Load from Heat Pumps on Hottest Days per Group[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                    Description: Annual load from heat pumps providing heating on the coldest day, across all groups.
                                                                                                                                                                                                                                                                                                                                                                                    Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                      Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                      HeatPumpModel_v31 #258
                                                                                                                                                                                                                                                                                                                                                                                      A
                                                                                                                                                                                                                                                                                                                                                                                      Peak Heating Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                      = SUM(
                                                                                                                                                                                                                                                                                                                                                                                      Peak Load from Heat Pumps on Coldest Days per Group[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                      Description: Annual load from heat pumps providing heating on the coldest days, across all groups.
                                                                                                                                                                                                                                                                                                                                                                                      Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #259
                                                                                                                                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Heat Pump Heating and Cooling,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                        Housing[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* HDD on Coldest Day/ Heat Pump COP on Coldest Days/( kBTU per kWH* Days per Year)
                                                                                                                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Fossil Fuel Heating,Retrofitting Status] = 0
                                                                                                                                                                                                                                                                                                                                                                                        Description: The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #260
                                                                                                                                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Hottest Days per Group[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                        Housing[ Cohort, Heating and Cooling System, Retrofitting Status]* U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Average Area[ Cohort, Retrofitting Status]* CDD on Coldest Day/ Cooling System Efficiency[ Heating and Cooling System]/( kBTU per kWH* Days per Year)
                                                                                                                                                                                                                                                                                                                                                                                        Peak Load from Heat Pumps on Hottest Days per Group[Cohort,No AC Cooling,Retrofitting Status] = 0
                                                                                                                                                                                                                                                                                                                                                                                        Description: The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #262
                                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                                        Perceived Cost of Not Retrofitting (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                        Perceived Cost of Not Retrofitting[Cohort,Heating and Cooling System] = (1-
                                                                                                                                                                                                                                                                                                                                                                                        Weight on Upfront Cost)* Total Cost of Ownership of Average Home[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                        Description: Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                        • Affinity of Not Retrofitting The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
                                                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #263
                                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                                        Perceived Cost of Retrofitting (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                        Perceived Cost of Retrofitting[Cohort,Heating and Cooling System] = (1-
                                                                                                                                                                                                                                                                                                                                                                                        Weight on Upfront Cost)* Total Cost of Ownership of Retrofitted Homes[ Cohort, Heating and Cooling System]+ Weight on Upfront Cost* Amoritized Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                        Description: Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                                                                                                        Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                        .housingagingchain v5 testing #265
                                                                                                                                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Cooling Operating Costs (Dollars / (House))
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Cooling Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = (
                                                                                                                                                                                                                                                                                                                                                                                        Expected Cooling Energy Price* Cooling Energy Use Under Alternatives[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Cooling Technology[ Heating and Cooling System]))
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Cooling Operating Costs[Cohort,Traditional Cooling,Retrofitting Status,Heating and Cooling System] = ( Expected Cooling Energy Price* Cooling Energy Use Under Alternatives[ Cohort, Traditional Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Cooling Technology[ Heating and Cooling System]))
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Cooling Operating Costs[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] = 0
                                                                                                                                                                                                                                                                                                                                                                                        Description: The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                        • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                        .housingagingchain v5 testing #266
                                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Heating Operating Costs (Dollar / (House))
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Heating Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] = (
                                                                                                                                                                                                                                                                                                                                                                                        Expected Heating Energy Price[ Heating and Cooling System]* Heating Energy Use Under Alternatives[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Heating Technology[ Heating and Cooling System]))
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Heating Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = ( Expected Heating Energy Price[ Heating and Cooling System]* Heating Energy Use Under Alternatives[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]/ Discount Rate)*(1-exp(- Discount Rate* Average Lifetime of Heating Technology[ Heating and Cooling System]))
                                                                                                                                                                                                                                                                                                                                                                                        Description: The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                        • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #267
                                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Operating Costs (Dollar / (House) )
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Operating Costs[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Cooling Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]+ Present Value of Heating Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                        Present Value of Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Present Value of Cooling Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]+ Present Value of Heating Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                        Description: Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                        • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #268
                                                                                                                                                                                                                                                                                                                                                                                        C
                                                                                                                                                                                                                                                                                                                                                                                        Present Value Replacement Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                        Present Value Replacement Cost[Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                        Cost of Cooling System Replacement[ Heating and Cooling System]/( Average Lifetime of Cooling Technology[ Heating and Cooling System]* Discount Rate)+ Cost of Heating System Replacement[ Heating and Cooling System]/( Average Lifetime of Heating Technology[ Heating and Cooling System]* Discount Rate)
                                                                                                                                                                                                                                                                                                                                                                                        Present Value Replacement Cost[Heat Pump Heating and Cooling] = Cost of Cooling System Replacement[ Heat Pump Heating and Cooling]/( Average Lifetime of Cooling Technology[ Heat Pump Heating and Cooling]* Discount Rate)
                                                                                                                                                                                                                                                                                                                                                                                        Present Value Replacement Cost[No AC Cooling] = 0
                                                                                                                                                                                                                                                                                                                                                                                        Description: Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                        • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                                                                                                        Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #288
                                                                                                                                                                                                                                                                                                                                                                                        F,A
                                                                                                                                                                                                                                                                                                                                                                                        Retrofitting (House * kBTU / (sf * F* Year) / Year)
                                                                                                                                                                                                                                                                                                                                                                                        Retrofitting[Cohort,Heating and Cooling System] = MAX(0,
                                                                                                                                                                                                                                                                                                                                                                                        Housing[ Cohort, Heating and Cooling System,Open to Retrofitting]*( U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]- Optimal U Value for Existing Homes if no EEHIC Cap[ Cohort, Heating and Cooling System])/ Retrofit Delay)
                                                                                                                                                                                                                                                                                                                                                                                        Description: Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                                                                                        HeatPumpModel_v31 #287
                                                                                                                                                                                                                                                                                                                                                                                        A
                                                                                                                                                                                                                                                                                                                                                                                        Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
                                                                                                                                                                                                                                                                                                                                                                                        = SUM(
                                                                                                                                                                                                                                                                                                                                                                                        Retrofitting[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                                                        Description: The total amount of retrofits across all cohorts and heating/cooling systems.
                                                                                                                                                                                                                                                                                                                                                                                        Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #299
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Soft Costs of Retrofitting (Dollar / Home)
                                                                                                                                                                                                                                                                                                                                                                                          =
                                                                                                                                                                                                                                                                                                                                                                                          Average Income* Homeowner Hours Spent Retrofitting
                                                                                                                                                                                                                                                                                                                                                                                          Description: The "hassle cost" of retrofitting a home, that is not due to economic costs but rather from the time and hassle spent on a homeowner retrofitting (such as having to move out). This is calculated as the opportunity cost of all the time spent retrofitting, using the average hourly income for MA SFH homeowners.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                          • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #303
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Subsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                          = MAX(0,
                                                                                                                                                                                                                                                                                                                                                                                          Unsubsidized Cost of Heat Pumps- Expected Subsidy for Heat Pumps)
                                                                                                                                                                                                                                                                                                                                                                                          Description: The upfront cost of heat pump once subsidies are taken into account.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                          • Cost of Cooling System Replacement The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                                                                                                                                                                                                          • Cost of Heating System Replacement The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          .housingagingchain v15 #304
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Subsidized Retrofit Cost (Dollar /House)
                                                                                                                                                                                                                                                                                                                                                                                          Subsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                          Unsubsidized Retrofit Cost[ Cohort, Heating and Cooling System]- Expected Subsidy for Retrofits[ Cohort, Heating and Cooling System,Open to Retrofitting]+ Soft Costs of Retrofitting
                                                                                                                                                                                                                                                                                                                                                                                          Description: The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #310
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Area (sf)
                                                                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                                                                          Area[ Cohort!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                          Description: The total area across all housing.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #311
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Cooling Cost (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                                                                          Average Cooling Cost[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                          Description: The total amount of money spent on cooling homes, per year.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #312
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Cooling Energy Use (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                                                                          Average Cooling Energy Use[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                          Description: The total amount of energy spent on cooling homes.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #313
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Cost of Ownership of Average Home (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                          Total Cost of Ownership of Average Home[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                          Average Energy Costs for Retrofitting Home[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                          Description: Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                                          • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #314
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                          Total Cost of Ownership of Retrofitted Homes[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                          Amoritized Subsidized Retrofit Cost[ Cohort, Heating and Cooling System]+ Average Energy Costs if Retrofitted[ Cohort, Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                          Description: The total cost of ownership of owning a home that has been retrofitted to the optimal U.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                          • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                                                                                                          Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #315
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Energy Use (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                                                                          Energy Use by Grouping[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                          Description: The total energy use for all homes in the model.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #316
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Heat Pump Sales (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                                                                          Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump Only]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Gas]+ Houses Switching Sources[ Cohort!, Heating and Cooling System!, Retrofitting Status!,Heat Pump and Oil])
                                                                                                                                                                                                                                                                                                                                                                                          Description: Number of houses buying heat pumps every year.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #317
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Heating Cost (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                                                                          Average Heating Cost[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                          Description: The total amount of money spent on heating homes.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #318
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Heating Energy Use (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                                                                          Average Heating Energy Use[ Cohort!, Heating and Cooling System!, Retrofitting Status!]* Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                          Description: The total amount of energy spent on heating per year.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                          HeatPumpModel_v31 #319
                                                                                                                                                                                                                                                                                                                                                                                          A
                                                                                                                                                                                                                                                                                                                                                                                          Total Housing Starts (House/ Year)
                                                                                                                                                                                                                                                                                                                                                                                          = SUM(
                                                                                                                                                                                                                                                                                                                                                                                          Housing Starts[ Cohort!, Heating and Cooling System!])
                                                                                                                                                                                                                                                                                                                                                                                          Description: The total housing starts across all cohorts and sources.
                                                                                                                                                                                                                                                                                                                                                                                          Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v4 testing #320
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            Total Housing Stock (House)
                                                                                                                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                                                                                                                            Housing[ Cohort!, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                            Description: Total number of houses across all cohorts, heating/cooling systems, and retrofitting status.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #323
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            Total Present Value of Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                            Total Present Value of Cost[Cohort,Heat Pump Heating and Cooling,Retrofitting Status,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                            Present Value of Operating Costs[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]+ Present Value Replacement Cost[ Heating and Cooling System]+ Cost of Bad Air Conditioning[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                            Total Present Value of Cost[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] = Present Value of Operating Costs[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]+ Present Value Replacement Cost[ Heating and Cooling System]+ Cost of Bad Air Conditioning[ Heating and Cooling System]
                                                                                                                                                                                                                                                                                                                                                                                            Description: Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                            • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #324
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            Total U Value Across All Groupings (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                            = SUM(
                                                                                                                                                                                                                                                                                                                                                                                            Total U Value by Cohort[ Cohort!])
                                                                                                                                                                                                                                                                                                                                                                                            Description: Total U value across all groupings of households.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #325
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            Total U Value by Cohort (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                            Total U Value by Cohort[Cohort] = SUM(
                                                                                                                                                                                                                                                                                                                                                                                            Total U Value[ Cohort, Heating and Cooling System!, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                            Description: Total U Value within each cohort.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #326
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                            Total U Value by Heating and Cooling System[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                                                                                                                                            Total U Value[ Cohort!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                            Description: The total U value by heating and cooling system
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #328
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                            U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                                            U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06:AND: Expected EEHIC Proportional Subsidy Rate for Retrofits>1e-06, Reference U Value*(( Sensitivity of Marginal Cost to U Value-1)*((( Expected EEHIC Maximum Subsidy for Retrofits- Expected EEHIC Proportional Subsidy Rate for Retrofits* Expected Fixed Cost)/( U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]* Expected EEHIC Proportional Subsidy Rate for Retrofits* Expected Reference Marginal Cost* Average Area[ Cohort,Open to Retrofitting]))-(1/(- Sensitivity of Marginal Cost to U Value+1))*(( U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]/ Reference U Value)^(- Sensitivity of Marginal Cost to U Value+1)))^(1/(- Sensitivity of Marginal Cost to U Value+1))),0)
                                                                                                                                                                                                                                                                                                                                                                                            Description: This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                            • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                                            • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #329
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            U Value by Grouping (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                            U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                                            Housing[ Cohort, Heating and Cooling System, Retrofitting Status]>1e-12, Total U Value[ Cohort, Heating and Cooling System, Retrofitting Status]/ Housing[ Cohort, Heating and Cooling System, Retrofitting Status],0)
                                                                                                                                                                                                                                                                                                                                                                                            Description: The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 8 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                                            • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                            • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                            • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                                                            • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                                                                                                                                                                                                            • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                                                                                            • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                                                                                                                                                                                                            • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                                                                                                                            • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                            • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                            • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                                                                                                                                                                                                            • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                                                                                                            • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                                                                                                            • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 4 (23.5%) (+) 2  [3,3] (-) 2  [3,3]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #330
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            U Value Increase from Source Switching (kBTU*House/(Year*Year*sf*F))
                                                                                                                                                                                                                                                                                                                                                                                            U Value Increase from Source Switching[Heating and Cooling System] = SUM(
                                                                                                                                                                                                                                                                                                                                                                                            U Value Shift from Source Switching[ Cohort!, Heating and Cooling System!, Heating and Cooling System, Retrofitting Status!])
                                                                                                                                                                                                                                                                                                                                                                                            Description: The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #331
                                                                                                                                                                                                                                                                                                                                                                                            F,A
                                                                                                                                                                                                                                                                                                                                                                                            U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                            U Value Loss from Demolition[Cohort,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                            U Value by Grouping[ Cohort, Heating and Cooling System, Retrofitting Status]* Demolitions[ Cohort, Heating and Cooling System, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                                                            Description: Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                            • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 0  [0,0] (-) 1  [3,3]
                                                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v18 #332
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            U Value of Housing Starts (kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                                                                                                            U Value of Housing Starts[Cohort,Heating and Cooling System] = IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                                            Additional Cost of Building to U Value[ Cohort, Heating and Cooling System]<0:AND: Optimal U for New Homes[ Cohort, Heating and Cooling System]< Code U, Optimal U for New Homes[ Cohort, Heating and Cooling System], Code U)
                                                                                                                                                                                                                                                                                                                                                                                            Description: Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 2 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #333
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            U Value of Retrofitting Homes (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                            U Value of Retrofitting Homes[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                            U Value by Grouping[ Cohort, Heating and Cooling System,Open to Retrofitting]
                                                                                                                                                                                                                                                                                                                                                                                            Description: The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                            • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                                                                                            • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #335
                                                                                                                                                                                                                                                                                                                                                                                            F,A
                                                                                                                                                                                                                                                                                                                                                                                            U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                            U Value Shift from Source Switching[Cohort,Heat Pump Heating and Cooling,Heating and Cooling System,Retrofitting Status] =
                                                                                                                                                                                                                                                                                                                                                                                            Houses Switching Sources[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Heat Pump Heating and Cooling, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                                                            U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] = Houses Switching Sources[ Cohort, Fossil Fuel Heating, Retrofitting Status, Heating and Cooling System]* U Value by Grouping[ Cohort, Fossil Fuel Heating, Retrofitting Status]
                                                                                                                                                                                                                                                                                                                                                                                            Description: The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 2 Views: Used By
                                                                                                                                                                                                                                                                                                                                                                                            • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                                                                                            • U Value Increase from Source Switching The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 1 (5.9%) (+) 1  [3,3] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #337
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            Unsubsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                            =
                                                                                                                                                                                                                                                                                                                                                                                            Unsubsidized Cost of Heat Pump Over Time TABLE( Time)
                                                                                                                                                                                                                                                                                                                                                                                            Description: The unsubsidized cost of heat pumps, instantiated at each time.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 3 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v8 #339
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            Unsubsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                            Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] =
                                                                                                                                                                                                                                                                                                                                                                                            Unsubsidized Retrofit Cost Intensity[ Cohort, Heating and Cooling System]* Average Area[ Cohort,Open to Retrofitting]
                                                                                                                                                                                                                                                                                                                                                                                            Description: Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v5 testing #338
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            Unsubsidized Retrofit Cost Intensity (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                            Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] = MAX(IF THEN ELSE(
                                                                                                                                                                                                                                                                                                                                                                                            U Value of Retrofitting Homes[ Cohort, Heating and Cooling System]>1e-06,( Expected Reference Marginal Cost* Reference U Value/(- Sensitivity of Marginal Cost to U Value+1))*((( Reference U Value/ U Value of Retrofitting Homes[ Cohort, Heating and Cooling System])^ Sensitivity of Marginal Cost to U Value-1)-(( Reference U Value/ Optimal U Value for Existing Homes[ Cohort, Heating and Cooling System])^( Sensitivity of Marginal Cost to U Value-1)))+ Fixed Cost per Unit Area[ Cohort],0),0)
                                                                                                                                                                                                                                                                                                                                                                                            Description: Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 4 Views: Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v8 #343
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            White Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                            =
                                                                                                                                                                                                                                                                                                                                                                                            Noise Standard Deviation*((24* Noise Correlation Time/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                                                                                                                                                                                                                                                                                                                            Description: White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                            • Change in AC Noise Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            .housingagingchain v8 #341
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            White Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                            =
                                                                                                                                                                                                                                                                                                                                                                                            Noise Standard Deviation 0*((24* Noise Correlation Time 0/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                                                                                                                                                                                                                                                                                                                            Description: White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                            • Change in AC Noise 0 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #342
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            White Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                            =
                                                                                                                                                                                                                                                                                                                                                                                            Noise Standard Deviation 1*((24* Noise Correlation Time 1/ TIME STEP)^0.5*(RANDOM 0 1()-0.5))
                                                                                                                                                                                                                                                                                                                                                                                            Description: White noise input to the pink noise process.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 1 View: Used By
                                                                                                                                                                                                                                                                                                                                                                                            • Change in AC Noise 1 Change in the pink noise value; Pink noise is a first order exponential smoothing delay of the whitenoise input.
                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                            .Control #289
                                                                                                                                                                                                                                                                                                                                                                                            A
                                                                                                                                                                                                                                                                                                                                                                                            SAVEPER (Year )
                                                                                                                                                                                                                                                                                                                                                                                            =
                                                                                                                                                                                                                                                                                                                                                                                            TIME STEP
                                                                                                                                                                                                                                                                                                                                                                                            Description: The frequency with which output is stored.
                                                                                                                                                                                                                                                                                                                                                                                            Present In 0 Views:
                                                                                                                                                                                                                                                                                                                                                                                              Used By
                                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                Top (Type) Subscripts (19 Variables)
                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                Variable Name And Description
                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #-1
                                                                                                                                                                                                                                                                                                                                                                                                Sub
                                                                                                                                                                                                                                                                                                                                                                                                Backup Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                Backup Heating:Heat Pump and Gas, Heat Pump and Oil
                                                                                                                                                                                                                                                                                                                                                                                                Present In 0 Views:
                                                                                                                                                                                                                                                                                                                                                                                                  Used By
                                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #-2
                                                                                                                                                                                                                                                                                                                                                                                                    Sub
                                                                                                                                                                                                                                                                                                                                                                                                    Central AC Cooling ()
                                                                                                                                                                                                                                                                                                                                                                                                    Central AC Cooling:Gas and Central AC, Oil and Central AC
                                                                                                                                                                                                                                                                                                                                                                                                    Present In 4 Views:
                                                                                                                                                                                                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Lifetime of Cooling Technology The average lifetime of each cooling system.Central AC data from: https://www.energy.gov/energysaver/central-air-conditioningWindow AC data from: https://www.consumerreports.org/air-conditioner/is-it-time-to-get-a-new-window-air-conditioner-a1532530762/
                                                                                                                                                                                                                                                                                                                                                                                                    • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                                                                                                                                                                    • Cost of Cooling System Replacement The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                    . #-3
                                                                                                                                                                                                                                                                                                                                                                                                    Sub
                                                                                                                                                                                                                                                                                                                                                                                                    Cohort ()
                                                                                                                                                                                                                                                                                                                                                                                                    Cohort:Before 1950, From 1950 to 1959, From 1960 to 1969, From 1970 to 1979, From 1980 to 1989, From 1990 to 1999, From 2000 to 2009, From 2010 to 2020, From 2021 to 2030, From 2031 to 2040, From 2041 to 2050
                                                                                                                                                                                                                                                                                                                                                                                                    Present In 13 Views:
                                                                                                                                                                                                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                                                                                                                                                                                                    • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                                                                                                                                                                                                                                    • Actual EEHIC Subsidy for Retrofits The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value.
                                                                                                                                                                                                                                                                                                                                                                                                    • Actual HOMES Subsidy for Retrofits The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                                                                                                                                                                                                                                                                                                                                                                    • Actual MassSave Subsidy for Retrofits The actual subsidy offered for retrofits by MassSave, not the expected value.
                                                                                                                                                                                                                                                                                                                                                                                                    • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                                                                                                                    • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                                                                                                                    • Affinity of Not Retrofitting The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
                                                                                                                                                                                                                                                                                                                                                                                                    • Affinity of Retrofitting Affinity of retrofitting, where utility value is equal to its NPV.
                                                                                                                                                                                                                                                                                                                                                                                                    • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                                                                                                    • Aging Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
                                                                                                                                                                                                                                                                                                                                                                                                    • Amoritized Subsidized Retrofit Cost The incurred total retrofit cost amoritized over the specified amoritization period.
                                                                                                                                                                                                                                                                                                                                                                                                    • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                                                                                                    • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                                                                                                    • Area of New Homes The total Area added by the construction of new homes, by cohort.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Emissions from Cooling by Grouping The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Emissions from Heating by Grouping Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Energy Cost The average cost of both heating and cooling a home, by grouping.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Energy Costs for Retrofitting Home Heating costs for each home open to retrofitting, annually, if no further retrofit measures are undertaken.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Energy Costs if Retrofitted Energy costs per year for each retrofitting house if homes retrofit to the optimal U value.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Energy Use Average energy use to both heat and cool a home.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                                                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                                                                    • Demolitions Homes that are destroyed every year.
                                                                                                                                                                                                                                                                                                                                                                                                    • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                                                                                                                                                    • Emissions by Grouping The total emissions for the most disaggregated grouping in the model.
                                                                                                                                                                                                                                                                                                                                                                                                    • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                                                                                                                                                                                                                    • Energy Use by Grouping The total amount of energy used for heating and cooling in each group.
                                                                                                                                                                                                                                                                                                                                                                                                    • Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                                                                                                                                                                                                                                                                                                                                                                    • Fixed Cost per Unit Area The fixed cost (which is constant) per square foot for an average house that is open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                                    • Fraction Retrofitting by Cohort Fraction that are retrofitting, only by cohort.
                                                                                                                                                                                                                                                                                                                                                                                                    • Fraction Retrofitting by System and Cohort The fraction of houses that are retrofitting, by heating/cooling system and cohort.
                                                                                                                                                                                                                                                                                                                                                                                                    • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                                                                                                    • Houses Considering Switching System The number of houses per year considering switching their heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                    • Houses Retrofitting Total amount of houses retrofitting in each cohort and heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                    • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                                                                                                                                                                                                                    • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                                                                                                                                    • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                                                                                                                    • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                                                                                                                                                    • Housing Starts In Each Cohort Housing starts across heating and cooling systems.
                                                                                                                                                                                                                                                                                                                                                                                                    • Housing by Cohort Number of houses per cohort
                                                                                                                                                                                                                                                                                                                                                                                                    • Housing by Cohort and Heating and Cooling System Housing by heating and cooling system and cohort, irrespective of retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                    • Housing by Cohort and Retrofitting Status Amount of housing by retrofit status and cohort.
                                                                                                                                                                                                                                                                                                                                                                                                    • Increase in U Value from Housing Starts New U value from new homes being built.
                                                                                                                                                                                                                                                                                                                                                                                                    • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                                                                                                                                                                                                                    • Indicated Homes Retrofitting Number of homes that, once delays are taken into account, will be open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                                    • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                                                                                                                                                                                                                    • Initial Area Total initial area across all houses, by cohort (assuming that average area is the same across systems).
                                                                                                                                                                                                                                                                                                                                                                                                    • Initial Average U Value The initial average U, equal to the average U value of MA SFH in 2022, from EIA RECS.
                                                                                                                                                                                                                                                                                                                                                                                                    • Initial Homes Not Retrofitting Initial homes not open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                                    • Initial Homes Retrofitting Homes that are open to retrofitting initially.
                                                                                                                                                                                                                                                                                                                                                                                                    • Initial Housing The total number of houses that begin in each cohort and heating and cooling source. Taken from CIN file.
                                                                                                                                                                                                                                                                                                                                                                                                    • Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                                                                                                                                                                                                                                    • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                                                                                                                                                                                                                    • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                                                                                                                                                                    • Marginal Cost Reductions from Retrofitting Total cost reductions from retrofitting away one unit of U value for existing homes, including reductions in both heating and cooling costs.
                                                                                                                                                                                                                                                                                                                                                                                                    • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                                                    • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                                                                                                                                                                                                                    • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                                                                                                                                                                                                                    • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                    • Net Age Shift from Retrofitting Status Shifting Shift in age within each cohort due to houses becoming open or closed to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                                    • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                                                                                                                                                                                                                    • Net Area Shift due to Retrofit Status Switching Shift in area between energy sources due to houses switching sources.
                                                                                                                                                                                                                                                                                                                                                                                                    • Net Change in Homes Retrofitting Homes that are in the process of deciding to retrofit.
                                                                                                                                                                                                                                                                                                                                                                                                    • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal Energy Cost Total energy cost if optimal U value is achieved.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal Energy Use Average energy use to heat and cool per house if U is optimal.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                                                                                                                    • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                                                                                                                    • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                    • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                    • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                                                                                                                    • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                                                                                                                                                                                                                    • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                                                                                                                                                                                                                    • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                                                                                                                                                                                                                    • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                                                                                                                    • Total Cost of Ownership of Average Home Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                                                                                                                                                                                                                                    • Total Cost of Ownership of Retrofitted Homes The total cost of ownership of owning a home that has been retrofitted to the optimal U.
                                                                                                                                                                                                                                                                                                                                                                                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                                                                                                                    • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                                                                                                    • Total U Value by Cohort Total U Value within each cohort.
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                                                                                                                                                                                                                    • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
                                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
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                                                                                                                                                                                                                                                                                                                                                                                                    Fossil Fuel Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                    Fossil Fuel Heating:Gas and Central AC, Gas and Window AC, Gas and No AC, Oil and Central AC, Oil and Window AC, Oil and No AC
                                                                                                                                                                                                                                                                                                                                                                                                    Present In 10 Views:
                                                                                                                                                                                                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                                                                                                                                                                                                    • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                                                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                                                                    • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                                                                                                    • Houses Considering Switching System The number of houses per year considering switching their heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                    • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                                                                                                                                    • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                                                                                                                                                                                                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #-5
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                                                                                                                                                                                                                                                                                                                                                                                                    Gas and Window or No AC ()
                                                                                                                                                                                                                                                                                                                                                                                                    Gas and Window or No AC:Gas and Window AC, Gas and No AC
                                                                                                                                                                                                                                                                                                                                                                                                    Present In 1 View:
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                                                                                                                                                                                                                                                                                                                                                                                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                                                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
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                                                                                                                                                                                                                                                                                                                                                                                                    Gas Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                    Gas Heating:Gas and Central AC, Gas and Window AC, Gas and No AC
                                                                                                                                                                                                                                                                                                                                                                                                    Present In 6 Views:
                                                                                                                                                                                                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                                                                                                                                                                                                    • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Lifetime of Heating Technology The average lifetime of each heating system.Heat pump data from: https://glascohvac.com/heating/heat-pumps/long-heat-pump-last/Gas data from: https://www.carrier.com/residential/en/us/products/furnaces/how-long-does-a-furnaces-last/Oil data from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                                                                    • Cost of Heating System Replacement The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                                                                    • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                                                                                                                                                                                                    • Heating Emissions Factors The pounds of CO2 emitted per kBTU of heating energy provided, for each heating fuel.Data for heat pumps (electricity) is: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/downloadRest is from: https://www.eia.gov/environment/emissions/co2_vol_mass.phpIn line with that source, I assume that each heat pump will add to the grid and is not part of base demand, and so the marginal emissions from producing electricity from heat pumps will be constant at the value as it will come from natural gas generators (explanation of which is from here: https://willbrownsberger.com/how-green-will-the-power-be/
                                                                                                                                                                                                                                                                                                                                                                                                    • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                                                                                                                                                    • Initial Heating Energy Price Price of energy used in each technology: heat pump, central AC, window AC, no AC, gas, and oil. For heat pumps and air conditioners, this is electricity.Data from (using annual 2020 data for MA):electricity: https://www.eia.gov/electricity/data/browser/#/topic/7?agg=1,0&geo=vvvvvvvvvvvvo&endsec=8&freq=M&start=200101&ctype=linechart&ltype=pin&rtype=s&pin=&rse=0&maptype=0,natural gas:https://www.eia.gov/dnav/ng/ng_pri_sum_a_EPG0_PRS_DMcf_a.htmheating oil: https://www.eia.gov/petroleum/heatingoilpropane/
                                                                                                                                                                                                                                                                                                                                                                                                    Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                    HeatPumpModel_v31 #-7
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                                                                                                                                                                                                                                                                                                                                                                                                    Heat Pump Heating and Cooling ()
                                                                                                                                                                                                                                                                                                                                                                                                    Heat Pump Heating and Cooling:Heat Pump Only, Heat Pump and Gas, Heat Pump and Oil
                                                                                                                                                                                                                                                                                                                                                                                                    Description: Houses that use heat pumps as their primary source for both heating and cooling.
                                                                                                                                                                                                                                                                                                                                                                                                    Present In 12 Views:
                                                                                                                                                                                                                                                                                                                                                                                                    Used By
                                                                                                                                                                                                                                                                                                                                                                                                    • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Lifetime of Cooling Technology The average lifetime of each cooling system.Central AC data from: https://www.energy.gov/energysaver/central-air-conditioningWindow AC data from: https://www.consumerreports.org/air-conditioner/is-it-time-to-get-a-new-window-air-conditioner-a1532530762/
                                                                                                                                                                                                                                                                                                                                                                                                    • Average Lifetime of Heating Technology The average lifetime of each heating system.Heat pump data from: https://glascohvac.com/heating/heat-pumps/long-heat-pump-last/Gas data from: https://www.carrier.com/residential/en/us/products/furnaces/how-long-does-a-furnaces-last/Oil data from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                                                                    • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                                                                    • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                                                                                                                                                                    • Cost of Cooling System Replacement The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                                                                                                                                                                                                                    • Cost of Heating System Replacement The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                                                                    • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                                                                    • Energy Use by Grouping The total amount of energy used for heating and cooling in each group.
                                                                                                                                                                                                                                                                                                                                                                                                    • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                                                                                                                                                                                                    • Heating Emissions Factors The pounds of CO2 emitted per kBTU of heating energy provided, for each heating fuel.Data for heat pumps (electricity) is: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/downloadRest is from: https://www.eia.gov/environment/emissions/co2_vol_mass.phpIn line with that source, I assume that each heat pump will add to the grid and is not part of base demand, and so the marginal emissions from producing electricity from heat pumps will be constant at the value as it will come from natural gas generators (explanation of which is from here: https://willbrownsberger.com/how-green-will-the-power-be/
                                                                                                                                                                                                                                                                                                                                                                                                    • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                                                                                                    • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                                                                                                                                                    • Houses Considering Switching System The number of houses per year considering switching their heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                    • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                                                                                                                                    • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                                                                                                                    • Initial Heating Energy Price Price of energy used in each technology: heat pump, central AC, window AC, no AC, gas, and oil. For heat pumps and air conditioners, this is electricity.Data from (using annual 2020 data for MA):electricity: https://www.eia.gov/electricity/data/browser/#/topic/7?agg=1,0&geo=vvvvvvvvvvvvo&endsec=8&freq=M&start=200101&ctype=linechart&ltype=pin&rtype=s&pin=&rse=0&maptype=0,natural gas:https://www.eia.gov/dnav/ng/ng_pri_sum_a_EPG0_PRS_DMcf_a.htmheating oil: https://www.eia.gov/petroleum/heatingoilpropane/
                                                                                                                                                                                                                                                                                                                                                                                                    • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                    • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                                                                                                                                                                                                                    • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                                                                                                                    • U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc.
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                                                                                                                                                                                                                                                                                                                                                                                                    Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                    Heating:Heat Pump, Gas, Oil
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                                                                                                                                                                                                                                                                                                                                                                                                        Heating and Cooling System ()
                                                                                                                                                                                                                                                                                                                                                                                                        Heating and Cooling System:Heat Pump Only, Heat Pump and Gas, Heat Pump and Oil, Gas and Central AC, Gas and Window AC, Gas and No AC, Oil and Central AC, Oil and Window AC, Oil and No AC
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                                                                                                                                                                                                                                                                                                                                                                                                        • Actual EEHIC Subsidy for Retrofits The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value.
                                                                                                                                                                                                                                                                                                                                                                                                        • Actual HOMES Subsidy for Retrofits The lump sum subsidy offered by the Home Owner Managing Energy Savings rebate (from the IRA), as opposed to the expected value.
                                                                                                                                                                                                                                                                                                                                                                                                        • Actual MassSave Subsidy for Retrofits The actual subsidy offered for retrofits by MassSave, not the expected value.
                                                                                                                                                                                                                                                                                                                                                                                                        • Additional Cost of Building to U Value Assuming optimal U is lower than code U, additional cost of building to optimal U instead of code u. If this cost is negative and optimal U < code U, then building to optimal U is cheaper than building to code. Lump sum subsidies are assumed to only apply to houses that are built to be more energy efficient than code. Calculated using the same method as unsubsidized retrofit costs.
                                                                                                                                                                                                                                                                                                                                                                                                        • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                                                                                                                        • Affinity of Not Retrofitting The affinity of not retrofitting; the utility or NPV of not retrofitting is just retrofit costs - energy costs saved.
                                                                                                                                                                                                                                                                                                                                                                                                        • Affinity of Retrofitting Affinity of retrofitting, where utility value is equal to its NPV.
                                                                                                                                                                                                                                                                                                                                                                                                        • Amoritized Subsidized Retrofit Cost The incurred total retrofit cost amoritized over the specified amoritization period.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Emissions by Heating and Cooling System The average CO2 emissions for each house, by heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Emissions from Cooling by Grouping The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Emissions from Heating by Grouping Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Energy Cost The average cost of both heating and cooling a home, by grouping.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Energy Costs for Retrofitting Home Heating costs for each home open to retrofitting, annually, if no further retrofit measures are undertaken.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Energy Costs if Retrofitted Energy costs per year for each retrofitting house if homes retrofit to the optimal U value.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Energy Use Average energy use to both heat and cool a home.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Energy Use by Heating and Cooling System The average energy use for each home by heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Lifetime of Cooling Technology The average lifetime of each cooling system.Central AC data from: https://www.energy.gov/energysaver/central-air-conditioningWindow AC data from: https://www.consumerreports.org/air-conditioner/is-it-time-to-get-a-new-window-air-conditioner-a1532530762/
                                                                                                                                                                                                                                                                                                                                                                                                        • Average Lifetime of Heating Technology The average lifetime of each heating system.Heat pump data from: https://glascohvac.com/heating/heat-pumps/long-heat-pump-last/Gas data from: https://www.carrier.com/residential/en/us/products/furnaces/how-long-does-a-furnaces-last/Oil data from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                                                                        • Average U Value by Heating and Cooling System The U value of the average house using each heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                        • Average U Value of Houses Switching Into Sources The average U value of houses switching into each source, for each source.
                                                                                                                                                                                                                                                                                                                                                                                                        • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                                                                        • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                                                                                                                                                                        • Cost of Bad Air Conditioning Willingness of Window AC users and those without AC to pay for central AC or heat pumps due to those technologies' inability to heat homes and their noisiness.Chosen to be sufficiently high that very few or no houses choose to keep window AC or no AC.
                                                                                                                                                                                                                                                                                                                                                                                                        • Cost of Cooling System Replacement The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                                                                                                                                                                                                                        • Cost of Heating System Replacement The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                                                                        • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                                                                        • Demolitions Homes that are destroyed every year.
                                                                                                                                                                                                                                                                                                                                                                                                        • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                                                                                                                                                        • Emissions by Grouping The total emissions for the most disaggregated grouping in the model.
                                                                                                                                                                                                                                                                                                                                                                                                        • Emissions by Heating and Cooling System The total amount of emissions for houses by Heating and Cooling System.
                                                                                                                                                                                                                                                                                                                                                                                                        • Energy Savings The amount of energy savings that not refitting houses would achieve if they were to retrofit. Because we assume area, HDD, and efficiency stay the same before and after retrofitting, this saving is solely from changing the U value.
                                                                                                                                                                                                                                                                                                                                                                                                        • Energy Use by Grouping The total amount of energy used for heating and cooling in each group.
                                                                                                                                                                                                                                                                                                                                                                                                        • Expected Heating Energy Price Energy price for one kBTU of heating used to calculate optimal U value. Third order exponential smoothing of heating energy price.
                                                                                                                                                                                                                                                                                                                                                                                                        • Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                                                                                                                                                                                                                                                                                                                                                                        • Fraction Retrofitting by System and Cohort The fraction of houses that are retrofitting, by heating/cooling system and cohort.
                                                                                                                                                                                                                                                                                                                                                                                                        • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                                                                                                                                                                                                        • Fraction of Houses in Each Heating and Cooling System The fraction of houses using each heating and cooling system
                                                                                                                                                                                                                                                                                                                                                                                                        • Fraction of Housing by Heating and Cooling System The fraction of the total housing stock using each heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                        • Heating Emissions Factors The pounds of CO2 emitted per kBTU of heating energy provided, for each heating fuel.Data for heat pumps (electricity) is: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/downloadRest is from: https://www.eia.gov/environment/emissions/co2_vol_mass.phpIn line with that source, I assume that each heat pump will add to the grid and is not part of base demand, and so the marginal emissions from producing electricity from heat pumps will be constant at the value as it will come from natural gas generators (explanation of which is from here: https://willbrownsberger.com/how-green-will-the-power-be/
                                                                                                                                                                                                                                                                                                                                                                                                        • Heating Energy Price The price to heat a home (which in this model we assume can only have one size) 1 kBTU, multiplied by the test input.
                                                                                                                                                                                                                                                                                                                                                                                                        • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                                                                                                        • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                                                                                                                                                        • Houses Considering Switching System The number of houses per year considering switching their heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                        • Houses Retrofitting Total amount of houses retrofitting in each cohort and heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                        • Houses Retrofitting per Year The number of homes retrofitting per year. This is an approximation because the number of homes actively retrofitting is equal to the number of homes open to retrofitting only if their average U value is less than optimal U. Assumes that if, say, the retrofitting delay is 5 years, then on average 20% of homes are retrofitting every year.
                                                                                                                                                                                                                                                                                                                                                                                                        • Houses Switching Into Sources The number of houses switching into each Heating and Cooling System, cohort, and retrofitting group due to system switching.
                                                                                                                                                                                                                                                                                                                                                                                                        • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                                                                                                                                        • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                                                                                                                        • Housing Starts Homes being built. Assumed to be equal to the total number of homes times a constant fractional growth rate and only homes that are not open to retrofits will be built.
                                                                                                                                                                                                                                                                                                                                                                                                        • Housing by Cohort and Heating and Cooling System Housing by heating and cooling system and cohort, irrespective of retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                        • Housing by Heating and Cooling System Number of houses by energy source across all cohorts.
                                                                                                                                                                                                                                                                                                                                                                                                        • Increase in U Value from Housing Starts New U value from new homes being built.
                                                                                                                                                                                                                                                                                                                                                                                                        • Indicated Fraction of Homes Retrofitting Proportion of households which are open to retrofitting to the optimum U. This is not necessarily all households, because the optimal U does not take into account fixed costs in retrofit costs, and so for a portion (or all) of them, retrofit costs > energy savings, and so not all (or any) households will retrofit. This also does not indicate households which are actively retrofitting, because if average U is already equal to optimum U then houses which are open to retrofitting have already retrofitted.
                                                                                                                                                                                                                                                                                                                                                                                                        • Indicated Homes Retrofitting Number of homes that, once delays are taken into account, will be open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                                        • Initial Heating Energy Price Price of energy used in each technology: heat pump, central AC, window AC, no AC, gas, and oil. For heat pumps and air conditioners, this is electricity.Data from (using annual 2020 data for MA):electricity: https://www.eia.gov/electricity/data/browser/#/topic/7?agg=1,0&geo=vvvvvvvvvvvvo&endsec=8&freq=M&start=200101&ctype=linechart&ltype=pin&rtype=s&pin=&rse=0&maptype=0,natural gas:https://www.eia.gov/dnav/ng/ng_pri_sum_a_EPG0_PRS_DMcf_a.htmheating oil: https://www.eia.gov/petroleum/heatingoilpropane/
                                                                                                                                                                                                                                                                                                                                                                                                        • Initial Homes Not Retrofitting Initial homes not open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                                        • Initial Homes Retrofitting Homes that are open to retrofitting initially.
                                                                                                                                                                                                                                                                                                                                                                                                        • Initial Housing The total number of houses that begin in each cohort and heating and cooling source. Taken from CIN file.
                                                                                                                                                                                                                                                                                                                                                                                                        • Initial Housing Starts Initial value of housing starts, initialized at 10 total houses.
                                                                                                                                                                                                                                                                                                                                                                                                        • Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                                                                                                                                                                                                                                        • Lifetime Marginal Cost Reductions from Retrofitting The amount of marginal emissions reductions over the model's lifetime. Assumes constant continuous discounting at the discount rate and infinite time horizon -- homeowners are so concerned about emissions that they consider emissions that occur after they move out.
                                                                                                                                                                                                                                                                                                                                                                                                        • Marginal Cooling Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U. Calculated as the derivative of total cooling energy costs with respect to U, where total cooling energy costs are Cooling Energy Price * Cooling Energy Use Per Square Foot, and the latter is U value * Area * Cooling Temperature Differential (CDD) / Area.
                                                                                                                                                                                                                                                                                                                                                                                                        • Marginal Cost Reductions from Retrofitting Total cost reductions from retrofitting away one unit of U value for existing homes, including reductions in both heating and cooling costs.
                                                                                                                                                                                                                                                                                                                                                                                                        • Marginal Cost at Binding U Value without EEHIC This is the marginal cost of retrofitting when the cap from the EEHIC is binding. That is, this is the value the marginal cost curve jumps to at the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                                                        • Marginal Heating Cost Reduction from Retrofitting The marginal reduction in heating costs per square foot from retrofitting away one unit of U, for existing housing. Calculated as the derivative of total heating energy costs with respect to U, where total heating energy costs are Heating Energy Price * Heating Energy Use Per Square Foot, and the latter is U value * Area * Heating Temperature Differential (HDD) / efficiency / Area.
                                                                                                                                                                                                                                                                                                                                                                                                        • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                                                                                                                                                                                                                        • Net Age Shift by System The shift in age from switching retrofit system, by cohort and by heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                        • Net Area Shift by System The shift in area from switching retrofit status, by heating and cooling system in addition to cohort.
                                                                                                                                                                                                                                                                                                                                                                                                        • Net Change in Homes Retrofitting Homes that are in the process of deciding to retrofit.
                                                                                                                                                                                                                                                                                                                                                                                                        • Net U Value Change from Retrofitting Home Shifts Net change in U value due to homes becoming open or not to retrofitting. If net change is positive, then homes are going from not being open to retrofitting to being open, meaning non-retrofitting homes' U value is flowing into the retrofitting homes' U value. If net change is negative, then houses becoming less likely to retrofit.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal Energy Cost Total energy cost if optimal U value is achieved.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal Energy Use Average energy use to heat and cool per house if U is optimal.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal U Value for Existing Homes This is the optimal value at which homes will retrofit to. This is the value at which the marginal costs of retrofitting equal the marginal benefits.This strange formulation comes from the fact that there is a discontinuity in the marginal cost curve. The intuition can be seen in this graph: https://www.desmos.com/calculator/4esbngkovt. In the graph, X is the U value to which to retrofit and y is the marginal benefit or cost, and the curved line is the marginal cost curve and the horizontal is the marginal benefit. Y, the marginal benefit, can be adjusted. I set reference marginal cost and reference U to 1 for clarity in this graph.Because the Energy Efficiency Home Improvement Credit takes of 30% of the retrofit cost up to $1200, there is a U value (x_cap in the graph) at which, below it, marginal costs benefit from the EEHIC's 30% subsidy (the red line in the graph). After that, there is no such 30% subsidy, and the marginal cost curve is shifted up (blue line in the graph). What then is the optimal U? The first if then else statement captures the fact that if the marginal cost curve with the 30% subsidy intersects the marginal benefit line, then homes just retrofit to that point. The EEHIC cap is not binding. If the cap is binding, then the second if then else statement captures the fact that if the marginal benefit is still greater than the marginal costs after the cap in EEHIC -- that is, it's still worth to retrofit even without a 30% subsidy-- then homes retrofit to the point where the higher MC curve intersects the marginal benefit. If this is not true -- if the marginal cost at the discontinuity jumps above the marginal benefit-- then retrofitting beyond the discontinuity means marginal costs are greater than marginal benefits, and so they'll retrofit to the discontinuity.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value to retrofit to should achieve if fixed costs are not taken into consideration (e.g., if fixed costs have already been paid) for existing houses). This takes into account the proportional subsidy but not the lump sum. Effect of proportional subsidies are multiplied instead of added, i.e., (1 - subsidy1)(1-subsidy2) instead of (1 - subsidy1 - subsidy2), because costs from state programs are subtracted when calculating federal subsidy in MA (https://www.masssave.com/inflation-reduction-act, "How do Mass Save rebates factor into the calculation of tax credits?")Expression is derived from the marginal energy savings from retrofitting being Energy Price and marginal cost of retrofitting being Reference MC * (1/(U/ Reference U))^Sensitivity and then solving for optimal retrofit when marginal savings equal marginal cost.This is the optimal U value if there were no cap on the Energy Efficiency Home Improvement Credit, i.e., no discontinuity the marginal cost curve.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal U Value with No EEHIC Proportional Subsidy Optimal U value if there is no proportional subsidy from the EEHIC at all.
                                                                                                                                                                                                                                                                                                                                                                                                        • Optimal U for New Homes The optimal U for houses being built, taking into account energy savings and construction costs. Calculated in a similar manner to the optimal U for existing homes.
                                                                                                                                                                                                                                                                                                                                                                                                        • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                        • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                        • Perceived Cost of Not Retrofitting Homeowners' perceived cost (or negation of the utility) for not retrofitting their home further, taking into homeowners weighupfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                                                                                                                        • Perceived Cost of Retrofitting Homeowners' perceived costs (or negation of their utility) for retrofitting their home, taking into account higher costs have less utilty and homeowners weigh upfront retrofit costs higher.
                                                                                                                                                                                                                                                                                                                                                                                                        • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                                                                                                                                                                        • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                        • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                        • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                                                                                                                                                                                                                        • Retrofitting Energy use retrofitted away. If positive, this means that energy use is being retrofitted away.
                                                                                                                                                                                                                                                                                                                                                                                                        • Subsidized Retrofit Cost The total retrofit cost, net of any subsidies for existing homes. Hassle costs are added here because subsidies cannot subsidize those directly.
                                                                                                                                                                                                                                                                                                                                                                                                        • Total Cost of Ownership of Average Home Total cost of ownership of a house without any further retrofit costs, i.e., at current energy use. Equivalent to energy costs because no retrofit costs are incurred.
                                                                                                                                                                                                                                                                                                                                                                                                        • Total Cost of Ownership of Retrofitted Homes The total cost of ownership of owning a home that has been retrofitted to the optimal U.
                                                                                                                                                                                                                                                                                                                                                                                                        • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                                                                                                                        • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                                                                                                        • Total U Value by Heating and Cooling System The total U value by heating and cooling system
                                                                                                                                                                                                                                                                                                                                                                                                        • U Value Increase from Source Switching The increase in total U value for each Heating and Cooling System from houses switching their heating and cooling systems.
                                                                                                                                                                                                                                                                                                                                                                                                        • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                                                                                                                        • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                                                                                                                        • U Value at Which EEHIC Cap Binds This the U value at which the maximum subsidy from the Energy Efficiency Home Improvement Credit (from the IRA_ will occur. Because the EEHIC pays for 30% of a retrofit's costs up to $1200, once a home will retrofit beyond this point, IT will no longer receive an additional subsidy. Thus, this is the U value at which a discontinuity in the marginal cost curve will occur-- before it, a 30% subsidy on the marginal cost will cocur, and then afterwards were will be no proportional subsidy.Formulation is derived by setting 30% of the retrofit cost from current U value to this U value equal to the maximum subsidy, and then solving for this U value. The retrofit cost from the current U to this U is equal to the definite integral from the current U to this U of the marginal cost, which is equal to Reference MC * (Reference U / U) ^sensitivity
                                                                                                                                                                                                                                                                                                                                                                                                        • U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                                                                                                                                                                                                                        • U Value of Housing Starts Equal to optimal U Value if it is lower than code U value and it is cheaper to build to lower U value. Otherwise, developers just build to code.
                                                                                                                                                                                                                                                                                                                                                                                                        • U Value of Retrofitting Homes The Average U Value of each home that is open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                                        • Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies.
                                                                                                                                                                                                                                                                                                                                                                                                        • Unsubsidized Retrofit Cost Intensity Total cost of retrofit per square foot when the marginally optimal amount of U value is retrofitted away.Calculated as definite integral of marginal cost of retrofitting, which, at a given U, is Reference MC * (Ref. U / U Value) ^ Sensitivity. The total retrofit function is then found by taking the finite integral of the marginal cost function from the indicated optimal U value to the original U value and adding the fixed cost. This cost can be theoretically negative, but if so no retrofitting will take place as the retrofitting outflow is nonnegative.The "if" statement ensures there are no retrofit costs when there are no houses in a cohort. U value must be greater than 1e-6 as this is the threshold for ZIDZ used in calculating average U.
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                                                                                                                                                                                                                                                                                                                                                                                                        New Cohorts ()
                                                                                                                                                                                                                                                                                                                                                                                                        New Cohorts:From 2021 to 2030, From 2031 to 2040, From 2041 to 2050
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                                                                                                                                                                                                                                                                                                                                                                                                            No AC Cooling ()
                                                                                                                                                                                                                                                                                                                                                                                                            No AC Cooling:Gas and No AC, Oil and No AC
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                                                                                                                                                                                                                                                                                                                                                                                                            • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Lifetime of Cooling Technology The average lifetime of each cooling system.Central AC data from: https://www.energy.gov/energysaver/central-air-conditioningWindow AC data from: https://www.consumerreports.org/air-conditioner/is-it-time-to-get-a-new-window-air-conditioner-a1532530762/
                                                                                                                                                                                                                                                                                                                                                                                                            • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                                                                            • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                                                                                                                                                                            • Cost of Bad Air Conditioning Willingness of Window AC users and those without AC to pay for central AC or heat pumps due to those technologies' inability to heat homes and their noisiness.Chosen to be sufficiently high that very few or no houses choose to keep window AC or no AC.
                                                                                                                                                                                                                                                                                                                                                                                                            • Cost of Cooling System Replacement The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                                                                                                                                                                                                                            • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                            • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                            • Present Value Replacement Cost Present value of replacement costs of both Heating and Cooling System given continuous discounting and where systems have a constant hazard rate of failure. On average, 1/L of the systems will break every year, because we assume failure rate is constant and where L is the lifetime of the system. Therefore, the average home will incur an average cost of R/L (R is replacement or upfront cost) every year. We assume that the household ignores the fact that after a finite time they'll leave the house or sell the system, because we assume they'll be able to sell the system at a price equal to the NPV at that time. Thus, selling the system or moving house does not change the NPV of the system when making the decision to switch.For houses that primarily use heat pumps, this formulation assures no double counting.
                                                                                                                                                                                                                                                                                                                                                                                                            • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
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                                                                                                                                                                                                                                                                                                                                                                                                            Oil and Window or No AC ()
                                                                                                                                                                                                                                                                                                                                                                                                            Oil and Window or No AC:Oil and Window AC, Oil and No AC
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                                                                                                                                                                                                                                                                                                                                                                                                            • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                                                                            • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
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                                                                                                                                                                                                                                                                                                                                                                                                            Oil Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                            Oil Heating:Oil and Central AC, Oil and Window AC, Oil and No AC
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                                                                                                                                                                                                                                                                                                                                                                                                            • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Lifetime of Heating Technology The average lifetime of each heating system.Heat pump data from: https://glascohvac.com/heating/heat-pumps/long-heat-pump-last/Gas data from: https://www.carrier.com/residential/en/us/products/furnaces/how-long-does-a-furnaces-last/Oil data from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                                                                            • Cost of Heating System Replacement The cost of buying and installing a heating system in each house.Took upper limits of estimates for each, since MA tends to be a more expensive state.Oil and gas cost assumed to be constant.Initial heat pump cost is from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then I assume that the cost improves in proportion to the trajectory in Mass. gov's deep decarbonization report:Gas furnace cost from: https://www.angi.com/articles/common-gas-furnace-prices.htmOil furnace cost from: https://modernize.com/hvac/heating-repair-installation/furnace/oil
                                                                                                                                                                                                                                                                                                                                                                                                            • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                                                                                                                                                                                                            • Heating Emissions Factors The pounds of CO2 emitted per kBTU of heating energy provided, for each heating fuel.Data for heat pumps (electricity) is: https://www.mass.gov/doc/2020-summary-massachusetts-ghg-emissions-reports-for-retail-sellers-of-electricity/downloadRest is from: https://www.eia.gov/environment/emissions/co2_vol_mass.phpIn line with that source, I assume that each heat pump will add to the grid and is not part of base demand, and so the marginal emissions from producing electricity from heat pumps will be constant at the value as it will come from natural gas generators (explanation of which is from here: https://willbrownsberger.com/how-green-will-the-power-be/
                                                                                                                                                                                                                                                                                                                                                                                                            • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial Heating Energy Price Price of energy used in each technology: heat pump, central AC, window AC, no AC, gas, and oil. For heat pumps and air conditioners, this is electricity.Data from (using annual 2020 data for MA):electricity: https://www.eia.gov/electricity/data/browser/#/topic/7?agg=1,0&geo=vvvvvvvvvvvvo&endsec=8&freq=M&start=200101&ctype=linechart&ltype=pin&rtype=s&pin=&rse=0&maptype=0,natural gas:https://www.eia.gov/dnav/ng/ng_pri_sum_a_EPG0_PRS_DMcf_a.htmheating oil: https://www.eia.gov/petroleum/heatingoilpropane/
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                                                                                                                                                                                                                                                                                                                                                                                                            Preexisting Cohorts ()
                                                                                                                                                                                                                                                                                                                                                                                                            Preexisting Cohorts:Before 1950, From 1950 to 1959, From 1960 to 1969, From 1970 to 1979, From 1980 to 1989, From 1990 to 1999, From 2000 to 2009, From 2010 to 2020
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                                                                                                                                                                                                                                                                                                                                                                                                            • Active Cohort Indicator The model tracks housing by age, with a cohort representing all housing built between years t0 to t0+D, where t0 is the initial time and D is the width of each cohort (Cohort Duration). If Cohort Duration is 5 years, then the first cohort C1 accumulates all new housing built from t0 to t0+D, the second cohort, C2, accumulates all new housing built from t0+D to t0+2D, and the ith cohort accumulates all new housing built from t0 + iD to t0 + (i+1)D. Note that the INTEGER function rounds (t - t0)/D down, which requires adding 1 to activate the cohort with number corresponding to the value-if-true in the IF THEN ELSE function.
                                                                                                                                                                                                                                                                                                                                                                                                            • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                                                                                                            • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                                                                                                            • Fraction Retrofitting by Cohort Fraction that are retrofitting, only by cohort.
                                                                                                                                                                                                                                                                                                                                                                                                            • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                                                                                                                            • Housing by Cohort and Retrofitting Status Amount of housing by retrofit status and cohort.
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial Area Total initial area across all houses, by cohort (assuming that average area is the same across systems).
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial Average U Value The initial average U, equal to the average U value of MA SFH in 2022, from EIA RECS.
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial Homes Not Retrofitting Initial homes not open to retrofitting.
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial Homes Retrofitting Homes that are open to retrofitting initially.
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial Housing The total number of houses that begin in each cohort and heating and cooling source. Taken from CIN file.
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                                                                                                                                                                                                                                            • Net Area Shift due to Retrofit Status Switching Shift in area between energy sources due to houses switching sources.
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                                                                                                                                                                                                                                                                                                                                                                                                            Retrofit Cost ()
                                                                                                                                                                                                                                                                                                                                                                                                            Retrofit Cost:Existing Housing, New Housing
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                                                                                                                                                                                                                                                                                                                                                                                                            Retrofitting Status ()
                                                                                                                                                                                                                                                                                                                                                                                                            Retrofitting Status:Not Open to Retrofitting, Open to Retrofitting
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                                                                                                                                                                                                                                                                                                                                                                                                            • Affinity of Heating and Cooling Systems The affinity of switching from each heating and cooling combination to each other one. If the model assumes that no one switches from one combination to another, as indicated by zero in the cost variable, then the affinity is zero.
                                                                                                                                                                                                                                                                                                                                                                                                            • Age Removal Total age lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                                                                                                            • Aging Amount of years added to the housing stocks' total age per year. Because houses age 1 year per year, this is simply 1 multplied by the number of houses per cohort.
                                                                                                                                                                                                                                                                                                                                                                                                            • Area "Total" Area for each cohort of housing . This is determined by the inflows and outflows into and out of each cohort, multiplied by the average energy use intensity in each cohort.
                                                                                                                                                                                                                                                                                                                                                                                                            • Area Removal Total area lost as houses are destroyed, scrapped, etc.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Age The age per house in each cohort and energy source. Assumes that age is constant across heating and cooling systems within each cohort and retrofitting status.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Area Average area by cohort and retrofitting status (assume it's the same across heating and cooling systems).
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Cooling Cost The average costs for keeping a home cool, by grouping.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Cooling Energy Use The average energy use for cooling. Calculated by setting efficiency times a house's cooling energy use equal to total cooling temperature differential (CDD), multiplied by U (or divided by R), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average EUI by Grouping The average energy use intensity by grouping
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Emissions by Grouping The total average emissions from heating and cooling, by cohort, retrofitting status, and Heating and Cooling System.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Emissions from Cooling by Grouping The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Emissions from Heating by Grouping Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Energy Cost The average cost of both heating and cooling a home, by grouping.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Energy Use Average energy use to both heat and cool a home.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Heating Cost The costs per year to heat one house.
                                                                                                                                                                                                                                                                                                                                                                                                            • Average Heating Energy Use The average energy use for heating annually. Calculated by setting efficiency times energy use equal to total HDD, multiplied by U (or divided by R) and divided by year (to get annual use), and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                            • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                                                                            • Cost of Switching Heating and Cooling Systems Affinities of each heating and cooling combination based on which heating and cooling combination houses have. This the numerator of a logit function. Assumes that retirement of systems is not determined by age, and so homes considering to switch heating systems do not have to replace their current one-- but they do have to purchase a system they currently do not have. The cost is determined by present cost of operating (i.e., opeating a system for infinite horizon, as it's included in sale price), in addition to current replacement costs if house does not have a system they're switching into. Any switches we assume are not possible we list as being 0.
                                                                                                                                                                                                                                                                                                                                                                                                            • Demolitions Homes that are destroyed every year.
                                                                                                                                                                                                                                                                                                                                                                                                            • EEHIC Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity, taking into account whether it has gone into effect, from the Energy Efficient Home Improvement Credit.
                                                                                                                                                                                                                                                                                                                                                                                                            • Emissions by Grouping The total emissions for the most disaggregated grouping in the model.
                                                                                                                                                                                                                                                                                                                                                                                                            • Energy Use by Grouping The total amount of energy used for heating and cooling in each group.
                                                                                                                                                                                                                                                                                                                                                                                                            • Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy.
                                                                                                                                                                                                                                                                                                                                                                                                            • Fraction of Houses Switching Fraction of houses considering switching switching from one to another. We also model "switching" from one system to the same system, as we keep track of total heat pump sales.
                                                                                                                                                                                                                                                                                                                                                                                                            • Heating Energy Use Under Alternatives The heating energy use of each group, if they were to switch into another Heating and Cooling System. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their heating energy use under alternative systems (the second "Heating and Cooling System" subscript). Houses about to retrofit use the U value that they will retrofit too; using their current U-value that they'll retrofit away from is too short cited.
                                                                                                                                                                                                                                                                                                                                                                                                            • Houses Considering Switching System The number of houses per year considering switching their heating and cooling system.
                                                                                                                                                                                                                                                                                                                                                                                                            • Houses Switching Sources The number of houses switching Heating and Cooling Systems. The first heating and cooling system subscript is the system combination they're leaving, and the h & c system subscript is the combination they're entering.
                                                                                                                                                                                                                                                                                                                                                                                                            • Housing Houses, divided into those open to retrofitting (i.e., they will retrofit if their U is not equal to optimal) and those who are not.
                                                                                                                                                                                                                                                                                                                                                                                                            • Housing by Cohort and Retrofitting Status Amount of housing by retrofit status and cohort.
                                                                                                                                                                                                                                                                                                                                                                                                            • Housing by Retrofitting Status Amount of housing by retrofitting status, across all cohorts and systems.
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial Age The initial age of each cohort. For cohorts built during the model's run, this is zero. For each pre-existing cohort, this is the length of each cohort multiplied by how many cohorts separate the pre-existing cohort from the beginning of the model. For example, if there are two pre-existing cohorts each with length 5, the first cohort at the beginning of the run is already ten years old on average.
                                                                                                                                                                                                                                                                                                                                                                                                            • Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built.
                                                                                                                                                                                                                                                                                                                                                                                                            • MassSave Expected Subsidy for Retrofits The proportional subsidy offered against the retrofit cost intensity from MassSave, taking into account whether it has gone into effect.
                                                                                                                                                                                                                                                                                                                                                                                                            • Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value.
                                                                                                                                                                                                                                                                                                                                                                                                            • Optimal Cooling Energy Use The energy used for cooling, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total cooling temperature differential(CDD), multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                            • Optimal Energy Cost Total energy cost if optimal U value is achieved.
                                                                                                                                                                                                                                                                                                                                                                                                            • Optimal Energy Use Average energy use to heat and cool per house if U is optimal.
                                                                                                                                                                                                                                                                                                                                                                                                            • Optimal Heating Cost Average heating cost if U value is optimal.
                                                                                                                                                                                                                                                                                                                                                                                                            • Optimal Heating Energy Use The energy used for heating, for the average household, if U is optimal. Calculated by setting efficiency times energy use equal to total heating temperature differential, multiplied by optimal U, and solving for energy use.
                                                                                                                                                                                                                                                                                                                                                                                                            • Peak Load from Heat Pumps on Coldest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, when heat pumps are less efficient and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                            • Peak Load from Heat Pumps on Hottest Days per Group The load that houses with heat pumps will put on the grid due to providing heating on the coldest day of the year, per year and per cohort and retrofit status.
                                                                                                                                                                                                                                                                                                                                                                                                            • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                            • Present Value of Heating Operating Costs The present value of cost to operate a heating system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and continuous discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                            • Present Value of Operating Costs Operating costs of each heating and cooling technology, in the order: heat pump only, central AC, window AC (two units), no AC, gas, oil.For window AC and no AC, this is includes the cost of the lack of comfort these technologies have. That is, it includes the amount of money that users of those technologies would pay each month to use central AC or heat pumps instead due to window ACs' noise or both technologies' inability to properly cool homes.Rough data from:Heat pump and central ac: https://carbonswitch.com/heat-pump-costs/Window AC ( 70/year): https://applianceanalysts.com/window-ac-running-costs/Gas: https://homeguide.com/costs/gas-furnace-pricesOil: https://homeguide.com/costs/oil-furnace-cost
                                                                                                                                                                                                                                                                                                                                                                                                            • Total Age "Total" age for each cohort of housing.
                                                                                                                                                                                                                                                                                                                                                                                                            • Total Present Value of Cost Total net present value of each heating and cooling combination. Assume that for systems with fossil fuel backups, the backup system is used so sparingly that its operating costs are negligible.
                                                                                                                                                                                                                                                                                                                                                                                                            • Total U Value Total U-value of homes. Note that that is not a physical quantity, as the U-value of individual homes is not additive.
                                                                                                                                                                                                                                                                                                                                                                                                            • U Value Loss from Demolition Homes' total energy use decrease from those homes being demolished.
                                                                                                                                                                                                                                                                                                                                                                                                            • U Value Shift from Source Switching The shift in total U value coming from switching sources.
                                                                                                                                                                                                                                                                                                                                                                                                            • U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                                                                                                                                                                                                                            Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                            HeatPumpModel_v31 #-17
                                                                                                                                                                                                                                                                                                                                                                                                            Sub
                                                                                                                                                                                                                                                                                                                                                                                                            Technology ()
                                                                                                                                                                                                                                                                                                                                                                                                            Technology:Heat Pump, Central AC, Window AC, No AC, Gas, Oil
                                                                                                                                                                                                                                                                                                                                                                                                            Description: The individual technologies used to heat or cool homes.
                                                                                                                                                                                                                                                                                                                                                                                                            Present In 0 Views:
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                                                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #-18
                                                                                                                                                                                                                                                                                                                                                                                                                Sub
                                                                                                                                                                                                                                                                                                                                                                                                                Traditional Cooling ()
                                                                                                                                                                                                                                                                                                                                                                                                                Traditional Cooling:Gas and Central AC, Gas and Window AC, Gas and No AC, Oil and Central AC, Oil and Window AC, Oil and No AC
                                                                                                                                                                                                                                                                                                                                                                                                                Present In 8 Views:
                                                                                                                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                                                                                                                • Cooling Energy Use Under Alternatives The cooling energy use of each group, if they were to switch into another heating and cooling source. That is, when they switch, their area and U stays the same, but the energy system's efficiency may change, meaning that each grouping (the first "Heating and Cooling System" subscript) must consider their cooling energy use under alternative systems (the second "Heating and Cooling Source" subscript).Houses that are open to retrofitting consider the optimal U that they'll retrofit to, unless that U is actually greater than their current one.
                                                                                                                                                                                                                                                                                                                                                                                                                • Present Value of Cooling Operating Costs The present value of cost to operate a cooling system, from the perspective of a house with one heating and cooling system (first H & C subscript) to another (the second). The operating cost is just the energy price times usage for cooling. Assumes constant operating costs and discount rate, with costs ending at the end of the average lifetime.
                                                                                                                                                                                                                                                                                                                                                                                                                • U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc.
                                                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #-19
                                                                                                                                                                                                                                                                                                                                                                                                                Sub
                                                                                                                                                                                                                                                                                                                                                                                                                Window AC Cooling ()
                                                                                                                                                                                                                                                                                                                                                                                                                Window AC Cooling:Gas and Window AC, Oil and Window AC
                                                                                                                                                                                                                                                                                                                                                                                                                Present In 4 Views:
                                                                                                                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                                                                                                                • Average Lifetime of Cooling Technology The average lifetime of each cooling system.Central AC data from: https://www.energy.gov/energysaver/central-air-conditioningWindow AC data from: https://www.consumerreports.org/air-conditioner/is-it-time-to-get-a-new-window-air-conditioner-a1532530762/
                                                                                                                                                                                                                                                                                                                                                                                                                • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                                                                                                                                                                                • Cost of Bad Air Conditioning Willingness of Window AC users and those without AC to pay for central AC or heat pumps due to those technologies' inability to heat homes and their noisiness.Chosen to be sufficiently high that very few or no houses choose to keep window AC or no AC.
                                                                                                                                                                                                                                                                                                                                                                                                                • Cost of Cooling System Replacement The cost of installing a cooling system in each house. Assumed to be constant, except for heat pumps.Central AC cost from: https://www.angi.com/articles/how-much-does-installing-new-ac-cost.htmWindow AC cost from: https://homeguide.com/costs/window-ac-unit-cost
                                                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                                Top (Type) Data (0 Variables)
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                                                                                                                                                                                                                                                                                                                                                                                                                Top (Type) Game (0 Variables)
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                                                                                                                                                                                                                                                                                                                                                                                                                Top (Type) Lookup (5 Variables)
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                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #136
                                                                                                                                                                                                                                                                                                                                                                                                                A,T
                                                                                                                                                                                                                                                                                                                                                                                                                Gas COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                Gas COP TABLE([(2020,0)-(2050,1)],(2020,0.9),(2030,0.925),(2040,0.95),(2050,0.95))

                                                                                                                                                                                                                                                                                                                                                                                                                Description: Efficiency of gas systems over time. Taken as the average of projected efficiency for reference gas boilers and gas furnaces, from MassDEP's Energy Pathways for Deep Decarbonization Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View:
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                                                                                                                                                                                                                                                                                                                                                                                                                • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #138
                                                                                                                                                                                                                                                                                                                                                                                                                A,T
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump Cooling COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump Cooling COP TABLE([(2020,0)-(2050,10)],(2020,4.3),(2030,4.8),(2040,5.17),(2050,5.28))

                                                                                                                                                                                                                                                                                                                                                                                                                Description: The COP of heat pumps when used for cooling. Calculated by assuming the ratio of heating and cooling COP is constant over time -- as heating COP improves the ability to cool improves proportionally-- finding cooling COP in 2020, finding the COP for cooling of heating in 2018, and then using the ratio between the two in 2020 to project future values. Data on this was difficult to find.Projected heating COP from pg. 97 of MassDEP's Energy Pathways for Deep Decarbonization: https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/downloadCooling COP in 2020 here: https://www.raleighheatingandair.com/blog/is-a-heat-pump-more-effective-at-cooling-or-heating/
                                                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View:
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                                                                                                                                                                                                                                                                                                                                                                                                                • Cooling System Efficiency The COP of different air conditioning technologies on an average day. This is not in terms of energy efficiency rating or seasonal efficiency rating, although some are calculated from those figures.For central ac: assume value of tenFor window AC (under portable AC): https://learnmetrics.com/eer-rating/All are very rough, and non-heat pump cooling systems are assumed to have constant efficiency.
                                                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #140
                                                                                                                                                                                                                                                                                                                                                                                                                A,T
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump Heating COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump Heating COP TABLE([(2020,0)-(2050,10)],(2020,2.485),(2030,2.785),(2040,2.99),(2050,3.05))

                                                                                                                                                                                                                                                                                                                                                                                                                Description: The efficiency of heat pumps for heating, over time. Taken as the average of projected COP for reference ASHP and ductless mini-splits from MassDEP's Energy Pathways Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                                                                                                                • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #245
                                                                                                                                                                                                                                                                                                                                                                                                                A,T
                                                                                                                                                                                                                                                                                                                                                                                                                Oil COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                Oil COP TABLE([(2020,0)-(2050,1)],(2020,0.835),(2030,0.84),(2050,0.84))

                                                                                                                                                                                                                                                                                                                                                                                                                Description: Efficiency of oil systems over time. Taken as the average of projected efficiency for reference distillate boilers and furnaces, from MassDEP's Energy Pathways for Deep Decarbonization Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download
                                                                                                                                                                                                                                                                                                                                                                                                                Present In 1 View:
                                                                                                                                                                                                                                                                                                                                                                                                                Used By
                                                                                                                                                                                                                                                                                                                                                                                                                • Heating System Efficiency The COP (for heat pumps) or annual fuel utilization efficiency of heating systems. Varies over time.
                                                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31 #336
                                                                                                                                                                                                                                                                                                                                                                                                                A,T
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Cost of Heat Pump Over Time TABLE([(2020,5000)-(2050,10000)],(2020,22000),(2030,20483.7 ),(2040,18967.3),(2050,17448.6))

                                                                                                                                                                                                                                                                                                                                                                                                                Description: The cost of installing and buying a heat pump over time. Initial value taken from: https://www.masssave.com/en/residential/rebates-and-incentives/heating-and-cooling/heat-pumps/air-source-heat-pumps, and then assume that ratio of future prices to initial is the same as average of reference and ductless heat pumps in MassDEP's Energy Pathways Report (pg. 97): https://www.mass.gov/doc/energy-pathways-for-deep-decarbonization-report/download. (That is, I took the ratio of the initial price to the initial price in that report, then I multiplied that ratio times all projections of future heat pump prices). I was unable to use the MassDEP report's prices directly, because they are based on national estimates from NREL, and MA is typically a more expensive state. In particular, the MassDEP projections say that heat pumps cost only $9K, but MassSave subsidy is $10K!Assumes rates of change are linear between projected points.
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                                                                                                                                                                                                                                                                                                                                                                                                                Used By Feedback Loops: 0 (0.0%) (+) 0  [0,0] (-) 0  [0,0]


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                                                                                                                                                                                                                                                                                                                                                                                                                All Variables (338 Variables + 4 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Active Cohort Indicator[Preexisting Cohorts] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar/ Home)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Additional Cost of Building to U Value[Cohort,Heating and Cooling System] (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Affinity of Not Retrofitting[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Affinity of Retrofitting[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Age Removal[Cohort,Retrofitting Status] (House * Year /Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Aging[Cohort,Retrofitting Status] (House * Year / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Aging per Year (Year / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Amoritization Period (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Annual Federal Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Annual Load from Heat Pumps (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Annual MA Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Annual Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Area[Preexisting Cohorts,Open to Retrofitting] (sf)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Area of New Homes[Cohort] (sf / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Area Removal[Cohort,Retrofitting Status] (sf /Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Autocorrelated Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Average Age[Cohort,Retrofitting Status] (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Average Age in All Housing (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Area[Cohort,Retrofitting Status] (sf / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Average Area in All Housing (sf/ House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Area of Housing Starts (sf / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Cooling Cost Across All Homes (Dollar / House/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Cooling Energy Use Across All Homes (kBTU / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Daily Load from Heat Pumps (kBTU / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions (tCO2 / House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions from Cooling by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions from Heating by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Average Energy Costs for Retrofitting Home[Cohort,Heating and Cooling System] (Dollar / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Average Energy Costs if Retrofitted[Cohort,Heating and Cooling System] (Dollar/(Year*House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Energy Use by Heating and Cooling System[Heating and Cooling System] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Energy Use in All Housing (kBTU / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average EUI in All Housing (kBTU / (sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Average Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Heating Cost Across All Homes (Dollar / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Heating Energy Use Across All Homes (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Average Income (Dollar / Hour / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Lifetime of Cooling Technology[No AC Cooling] (Years)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Average Lifetime of Heating Technology[Oil Heating] (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Subsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Average Time To Consider Switching (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average U Value by Heating and Cooling System[Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Average U Value in All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average U Value of Houses Switching Into Sources[Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C CDD on Coldest Day (F )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Change in AC Noise (1/Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Change in AC Noise 0 (1/Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Change in AC Noise 1 (1/Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18L Code U (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Cohort Duration (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cooling Degree Days (F )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cooling Emissions Factor (lb CO2 / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cooling Energy Price Step Height 1 (Dimensionless )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cooling System Efficiency[No AC Cooling] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cost of Bad Air Conditioning[No AC Cooling] (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cost of Cooling System Replacement[No AC Cooling] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cost of Heating System Replacement[Oil Heating] (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Oil] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Emissions (tCO2)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Federal Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative MA Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cumulative Subsidies (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidies for Heat Pumps (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidy for Retrofits (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Days per Year (Day / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18F,A Decrease in Code U (kBTU / (sf * Year * F) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Delay in Changing Subsidy Expectations (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Delay in Forming Expectations of Energy Price (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Delay in Forming Expectations of Retrofit Costs (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Demolition Hazard Rate (1 / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Discount Rate (1 / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C EEHIC Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C EEHIC Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Effect of Air Leakage from Window AC on Efficiency (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Emissions (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Energy Price Exponential Growth Rate (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Energy Price Exponential Growth Rate 1 (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Energy Price Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Energy Price Pulse Quantity 1 (Dimensionless*Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Energy Price Ramp Slope (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Energy Price Ramp Slope 1 (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Energy Price Step Height (Dimensionless )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Savings[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Gas Houses (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Heat Pump Houses (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Oil Houses (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected Fixed Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected Heating Energy Price[Heating and Cooling System] (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Expected Lump Sum Subsidy Intensity[Retrofit Cost] (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Expected Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Federal Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Federal Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Fixed Cost (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Fixed Cost per Unit Area[Cohort] (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction of Housing by Heating and Cooling System[Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31LI,A Fraction Retrofitting by Cohort[Cohort] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Fractional Decrease in Code U (1 / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Gas COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C HDD on Coldest Day (F )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Heat Pump Cooling COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Heat Pump COP on Coldest Days (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Heat Pump Heating COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Heating Degree Days (F )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Heating Emissions Factors[Oil Heating] (lb CO2 / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Heating Energy Price[Heating and Cooling System] (Dollar / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Heating System Efficiency[Oil Heating] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Homeowner Hours Spent Retrofitting (Hour )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C HOMES Cut Off for Savings (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A HOMES Expected Higher Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C HOMES High Subsidy Amount (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A HOMES Implemented High Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A HOMES Implemented Lower Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C HOMES Lower Subsidy Amount (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C HOMES Subsidy Final Year (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C HOMES Subsidy Implementation Year (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Considering Switching System[Cohort,Heating and Cooling System,Retrofitting Status] (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Retrofitting[Cohort,Heating and Cooling System] (Houses)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Retrofitting per Year[Cohort,Heating and Cooling System] (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Switching Into Sources[Heating and Cooling System] (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Housing[Cohort,Heating and Cooling System,Open to Retrofitting] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Cohort[Cohort] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Cohort and Heating and Cooling System[Cohort,Heating and Cooling System] (Houses)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Heating and Cooling System[Heating and Cooling System] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Retrofitting Status[Retrofitting Status] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Housing Fractional Growth Rate (1 / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Housing Starts[Cohort,Heating and Cooling System] (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing Starts Across Cohorts ()
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Housing Starts Exponential Growth Rate (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing Starts In Each Cohort[Cohort] (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Housing Starts Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Housing Starts Ramp Slope (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Housing Starts Step Height (Dimensionless )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Increase in Area per Year (sf / Year / House )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18F,A Increase in U Value from Housing Starts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Indicated Homes Retrofitting[Cohort,Heating and Cooling System] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8LI,A Initial Age[Preexisting Cohorts,Retrofitting Status] (House * Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31LI,C Initial Area[Cohort] (sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Average Area of Housing Starts (sf / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Average U Value[Cohort] (kBTU/(Year*sf*F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31LI,C Initial Code U Value (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Fraction of Homes Retrofitting (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Initial Heating Energy Price[Oil Heating] (Dollar / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingLI,A Initial Homes Not Retrofitting[Preexisting Cohorts,Heating and Cooling System] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingLI,A Initial Homes Retrofitting[Preexisting Cohorts,Heating and Cooling System] (Houses)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Housing[Cohort,Heating and Cooling System] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                .A Initial Housing Starts[Heating and Cooling System] (House/Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15LI,A Initial U Value[Preexisting Cohorts,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Input 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Actual Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C kBTU per kWH (kBTU / kWH )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Lifetime Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] (Dollar * Year * F / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Marginal Cooling Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Marginal Cost at Binding U Value without EEHIC[Cohort,Heating and Cooling System] ((Dollar / sf) / (kBTU / (sf * F * Year)))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Marginal Heating Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Massachusetts Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C MassSave Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A MassSave Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Maximum Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Monthly Total Heat Pump Sales (Houses/ Month)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Months per Year (Month / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Net Age Shift by System[Cohort,Heating and Cooling System] (Year * House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Net Age Shift from Retrofitting Status Shifting[Cohort] (House * Year / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Net Area Shift by System[Cohort,Heating and Cooling System] (sf / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Net Area Shift due to Retrofit Status Switching[Cohort] (sf / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C No Turnover Switch (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Correlation Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Correlation Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Noise Correlation Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Standard Deviation (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Standard Deviation 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Noise Standard Deviation 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Start Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Start Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Noise Start Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Oil COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Optimal Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal U Across All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18A Optimal U for New Homes[Cohort,Heating and Cooling System] (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal U Value with No EEHIC Proportional Subsidy[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Peak Cooling Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Peak Heating Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Fossil Fuel Heating,Retrofitting Status] (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Peak Load from Heat Pumps on Hottest Days per Group[Cohort,No AC Cooling,Retrofitting Status] (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Peak Load from Non Heating or Cooling Sources (kWH / Day )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Perceived Cost of Not Retrofitting[Cohort,Heating and Cooling System] (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Perceived Cost of Retrofitting[Cohort,Heating and Cooling System] (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Pounds per Ton (lb CO2 / tCO2)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Present Value of Cooling Operating Costs[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] (Dollars / (House))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Present Value of Heating Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / (House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Present Value of Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / (House) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Present Value Replacement Cost[No AC Cooling] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Proportional MassSave Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Proportional Subsidy Switch for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Pulse Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Pulse Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Pulse Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Ramp End Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Ramp End Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Ramp End Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Ramp Start Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Ramp Start Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Ramp Start Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Reference Retrofit Cost (Dollar / (House * Year) )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v9C Reference U Value (kBTU / (sf * Year * F) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Retrofit Delay (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Retrofitting[Cohort,Heating and Cooling System] (House * kBTU / (sf * F* Year) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sensitivity of Affinity to Cost (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sensitivity of Retrofits to Cost (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Amplitude (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Amplitude 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sine Amplitude 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Period (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Period 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sine Period 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Soft Costs of Retrofitting (Dollar / Home)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Step Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Step Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Step Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Subsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Subsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar /House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C System Switching SWITCH (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Time to Decide to Retrofit (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Total Age[Cohort,Open to Retrofitting] (House * Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Area (sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Cooling Cost (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Cooling Energy Use (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Cost of Ownership of Average Home[Cohort,Heating and Cooling System] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Cost of Ownership of Retrofitted Homes[Cohort,Heating and Cooling System] (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Energy Use (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Heat Pump Sales (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Heating Cost (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Heating Energy Use (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Housing Starts (House/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Total Housing Stock (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Total Initial Homes (Houses )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Total Initial Housing Starts (Houses / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Present Value of Cost[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] (House * kBTU / (Year * F * sf) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total U Value Across All Groupings (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total U Value by Cohort[Cohort] (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total U Value by Heating and Cooling System[Heating and Cooling System] (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] (kBTU / (F * sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value Increase from Source Switching[Heating and Cooling System] (kBTU*House/(Year*Year*sf*F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A U Value Loss from Demolition[Cohort,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18A U Value of Housing Starts[Cohort,Heating and Cooling System] (kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value of Retrofitting Homes[Cohort,Heating and Cooling System] (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L U Value Retrofitted Away (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Unsubsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Weight on Upfront Cost (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A White Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A White Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A White Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlC FINAL TIME (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlC INITIAL TIME (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlA SAVEPER (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlC TIME STEP (Year )



                                                                                                                                                                                                                                                                                                                                                                                                                Top

                                                                                                                                                                                                                                                                                                                                                                                                                Variable Link Detail (338 Variables + 4 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                In/Out Counts
                                                                                                                                                                                                                                                                                                                                                                                                                 In/Out Ratio 
                                                                                                                                                                                                                                                                                                                                                                                                                In Links By Polarity
                                                                                                                                                                                                                                                                                                                                                                                                                Out Links By Polarity
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing (House)  6 | 30  0.20    3| 1| 2   25| 4| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Area (sf / House)  2 | 16  0.12    2| 0| 0   16| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Input 1 (Dimensionless) 15 |  1  15.00   11| 0| 4    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Input 0 (Dimensionless) 15 |  1  15.00   11| 0| 4    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks U Value by Grouping (kBTU / (sf * F * Year))  2 | 13  0.15    1| 1| 0   12| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingInOutLinks Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))  6 |  9  0.67    3| 3| 0    7| 1| 1
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Input (Dimensionless) 15 |  0  Infinite   10| 1| 4    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingInOutLinks Total Housing Stock (House)  1 | 11  0.09    1| 0| 0    7| 4| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))  8 |  2  4.00    5| 3| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Unsubsidized Retrofit Cost Intensity (Dollar / sf)  6 |  3  2.00    1| 4| 1    3| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total U Value (House * kBTU / (Year * F * sf) )  6 |  3  2.00    2| 2| 2    3| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing Starts (Houses / Year)  4 |  5  0.80    3| 1| 0    5| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))  2 |  7  0.29    2| 0| 0    5| 2| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Delay in Changing Subsidy Expectations (Year )  0 |  9  0.00    0| 0| 0    9| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cooling System Efficiency (dmnl)  4 |  5  0.80    4| 0| 0    0| 5| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)  7 |  1  7.00    4| 3| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)  7 |  1  7.00    4| 3| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18InOutLinks Optimal U for New Homes (kBTU / (sf * Year * F))  6 |  2  3.00    4| 2| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Heating System Efficiency (dmnl)  4 |  4  1.00    4| 0| 0    0| 4| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)  3 |  5  0.60    3| 0| 0    2| 3| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Energy Use by Grouping (kBTU / Year)  2 |  6  0.33    2| 0| 0    6| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Heating Energy Use (kBTU / (Year * House))  4 |  4  1.00    3| 1| 0    4| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Cooling Energy Use (kBTU / (Year * House))  4 |  4  1.00    3| 1| 0    4| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Additional Cost of Building to U Value (Dollar / sf)  7 |  1  7.00    3| 4| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Sensitivity of Marginal Cost to U Value (dmnl )  0 |  7  0.00    0| 0| 0    4| 3| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Retrofitting (House * kBTU / (sf * F* Year) / Year)  4 |  3  1.33    2| 2| 0    2| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v9InOutLinks Reference U Value (kBTU / (sf * Year * F) )  0 |  7  0.00    0| 0| 0    4| 2| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Net Change in Homes Retrofitting (Houses / Year)  3 |  4  0.75    2| 1| 0    3| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)  5 |  2  2.50    2| 0| 3    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Houses Switching Sources (House / Year)  3 |  4  0.75    3| 0| 0    3| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Expected Subsidy for Retrofits (Dollar / House)  6 |  1  6.00    4| 0| 2    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Demolitions (House / Year)  3 |  4  0.75    2| 1| 0    3| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Area (sf)  5 |  2  2.50    4| 1| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Unsubsidized Cost of Heat Pumps (Dollar / House)  2 |  4  0.50    0| 2| 0    4| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Total Age (House * Year)  4 |  2  2.00    2| 1| 1    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Present Value Replacement Cost (Dollar / House)  5 |  1  5.00    2| 3| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))  5 |  1  5.00    3| 2| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Optimal U Value for Existing Homes (kBTU / (sf * F * Year))  5 |  1  5.00    3| 0| 2    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Optimal Heating Energy Use (kBTU / (House * Year))  4 |  2  2.00    3| 1| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Optimal Cooling Energy Use (kBTU / (Year * House))  4 |  2  2.00    3| 1| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks MassSave Expected Subsidy for Retrofits (Dollar / House)  5 |  1  5.00    5| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)  4 |  2  2.00    1| 0| 3    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)  4 |  2  2.00    1| 0| 3    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)  4 |  2  2.00    1| 0| 3    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)  4 |  2  2.00    1| 0| 3    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)  4 |  2  2.00    1| 0| 3    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)  4 |  2  2.00    1| 0| 3    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Houses Retrofitting per Year (House / Year)  4 |  2  2.00    1| 1| 2    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks HOMES Implemented Lower Subsidy (Dollar / House)  4 |  2  2.00    1| 0| 3    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks HOMES Implemented High Subsidy (Dollar / House)  4 |  2  2.00    1| 0| 3    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Heating Energy Use Under Alternatives (kBTU / (House * Year))  5 |  1  5.00    4| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Expected Heating Energy Price (Dollar / kBTU)  2 |  4  0.50    2| 0| 0    4| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)  3 |  3  1.00    3| 0| 0    2| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Expected Cooling Energy Price (Dollar / kBTU)  2 |  4  0.50    2| 0| 0    4| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks EEHIC Expected Subsidy for Retrofits (Dollar / House)  5 |  1  5.00    5| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cooling Energy Use Under Alternatives (kBTU / (House * Year))  5 |  1  5.00    4| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Area of Housing Starts (sf / House)  4 |  2  2.00    2| 2| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Active Cohort Indicator (dmnl)  5 |  1  5.00    0| 0| 5    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Unsubsidized Retrofit Cost (Dollar / House)  2 |  3  0.67    2| 0| 0    3| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Subsidized Retrofit Cost (Dollar /House)  3 |  2  1.50    2| 1| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Present Value of Heating Operating Costs (Dollar / (House))  4 |  1  4.00    3| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Present Value of Cooling Operating Costs (Dollars / (House))  4 |  1  4.00    3| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))  4 |  1  4.00    3| 1| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)  2 |  3  0.67    1| 1| 0    0| 2| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)  4 |  1  4.00    4| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing by Heating and Cooling System (House)  1 |  4  0.25    1| 0| 0    4| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing by Cohort and Retrofitting Status (House)  1 |  4  0.25    1| 0| 0    3| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Federal Annual Retrofit Subsidy (Dollar / Year)  3 |  2  1.50    3| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Discount Rate (1 / Year )  0 |  5  0.00    0| 0| 0    1| 4| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18InOutLinks Code U (kBTU / (sf * Year * F))  2 |  3  0.67    1| 1| 0    3| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Actual HOMES Subsidy for Retrofits (Dollar/ Home)  4 |  1  4.00    2| 0| 2    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks White Noise 1 (Dimensionless)  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks White Noise 0 (Dimensionless)  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks White Noise (Dimensionless)  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)  2 |  2  1.00    2| 0| 0    1| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18InOutLinks U Value of Housing Starts (kBTU / (Year * F * sf))  3 |  1  3.00    2| 0| 1    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Present Value of Cost (Dollar / House)  3 |  1  3.00    3| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Heat Pump Sales (House / Year)  1 |  3  0.33    1| 0| 0    3| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Subsidized Cost of Heat Pumps (Dollar / House)  2 |  2  1.00    1| 1| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Proportional Subsidy Switch for Retrofits (dmnl )  0 |  4  0.00    0| 0| 0    4| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Perceived Cost of Retrofitting (Dollar / (House * Year))  3 |  1  3.00    3| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Massachusetts Annual Retrofit Subsidy (Dollar / Year)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)  2 |  2  1.00    2| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks IRA Actual Subsidy for Heat Pumps (Dollar / House)  3 |  1  3.00    3| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Initial Age (House * Year)  3 |  1  3.00    0| 0| 3    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Indicated Homes Retrofitting (House)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks HOMES Expected Lower Lump Sum Subsidy (Dollar / House)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Heating Degree Days (F )  0 |  4  0.00    0| 0| 0    4| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Federal Annual Heat Pump Subsidy (Dollar / Year)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)  3 |  1  3.00    3| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Expected Fixed Cost (Dollar / House)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)  2 |  2  1.00    2| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Energy Savings (dmnl)  2 |  2  1.00    2| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Emissions by Grouping (tCO2 / Year)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Cost of Switching Heating and Cooling Systems (Dollar / House)  3 |  1  3.00    3| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cooling Degree Days (F )  0 |  4  0.00    0| 0| 0    4| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Change in AC Noise 1 (1/Year)  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Change in AC Noise 0 (1/Year)  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Change in AC Noise (1/Year)  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Average Heating Cost (Dollar / (Year * House))  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Energy Use (kBTU / (Year * House))  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Emissions from Heating by Grouping (tCO2 / (House * Year))  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Emissions from Cooling by Grouping (tCO2 / (House * Year))  3 |  1  3.00    2| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Cooling Cost (Dollar / (Year * House))  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Average Age (Year)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Annual Retrofit Subsidy (Dollar / Year)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Annual Heat Pump Subsidy (Dollar / Year)  2 |  2  1.00    2| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))  2 |  2  1.00    1| 1| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingInOutLinks Affinity of Retrofitting (dmnl)  3 |  1  3.00    1| 2| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Affinity of Not Retrofitting (dmnl)  3 |  1  3.00    1| 2| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Affinity of Heating and Cooling Systems (dmnl)  3 |  1  3.00    1| 2| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Actual MassSave Subsidy for Retrofits (Dollar / House)  3 |  1  3.00    3| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Actual EEHIC Subsidy for Retrofits (Dollar / House)  3 |  1  3.00    3| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks U Value of Retrofitting Homes (kBTU / (sf * Year * F))  1 |  2  0.50    1| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)  2 |  1  2.00    2| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Heating Energy Use (kBTU/ Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Heating Cost (Dollar / Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Cooling Energy Use (kBTU/ Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Cooling Cost (Dollar / Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Soft Costs of Retrofitting (Dollar / Home)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Present Value of Operating Costs (Dollar / (House) )  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Perceived Cost of Not Retrofitting (Dollar / (House * Year))  2 |  1  2.00    1| 1| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Optimal U Across All Housing (kBTU / (sf * F * Year))  3 |  0  Infinite    2| 1| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Optimal Heating Cost (Dollar / (Year * House))  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Optimal Energy Cost (Dollar / (Year * House))  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Optimal Cooling Cost (Dollar / (Year * House))  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Net U Value Change from Retrofitting Home Shifts (House * kBTU / (Year * F * sf) / Year)  2 |  1  2.00    2| 0| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Net Area Shift by System (sf / Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Net Age Shift by System (Year * House / Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks MassSave Subsidy for Retrofits Final Year (Year)  1 |  2  0.50    1| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Initial U Value (House * kBTU / (Year * F * sf))  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Initial Homes Retrofitting (Houses)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Initial Homes Not Retrofitting (House)  2 |  1  2.00    1| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Indicated Fraction of Homes Retrofitting (dmnl)  2 |  1  2.00    1| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18InOutLinks Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Houses Considering Switching System (Houses / Year)  2 |  1  2.00    1| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks HOMES Expected Higher Subsidy (Dollar / House)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Heating Energy Price (Dollar / (kBTU))  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Fraction of Houses in Each Heating and Cooling System (dmnl)  3 |  0  Infinite    3| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Fixed Cost per Unit Area (Dollar / sf)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Expected Subsidy for Heat Pumps (Dollar / House)  2 |  1  2.00    2| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Expected Lump Sum Subsidy Intensity (Dollar / sf)  2 |  1  2.00    1| 1| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Emissions (tCO2 / Year)  1 |  2  0.50    1| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18InOutLinks Decrease in Code U (kBTU / (sf * Year * F) / Year)  2 |  1  2.00    2| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Days per Year (Day / Year )  0 |  3  0.00    0| 0| 0    0| 3| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cost of Heating System Replacement (Dollar / House )  1 |  2  0.50    1| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cost of Cooling System Replacement (Dollar / House)  1 |  2  0.50    1| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cooling Energy Price (Dollar / kBTU)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))  3 |  0  Infinite    3| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Lifetime of Cooling Technology (Years)  1 |  2  0.50    1| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average EUI by Grouping (kBTU / (sf * Year))  3 |  0  Infinite    3| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Energy Use in All Housing (kBTU / Year / House)  2 |  1  2.00    1| 1| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Energy Cost (Dollar / (Year * House))  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Emissions by Grouping (tCO2 / (Year * House))  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Average Area in All Housing (sf/ House)  2 |  1  2.00    2| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Autocorrelated Noise 1 (Dimensionless)  1 |  2  0.50    1| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Autocorrelated Noise 0 (Dimensionless)  1 |  2  0.50    1| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Autocorrelated Noise (Dimensionless)  1 |  2  0.50    1| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Area Removal (sf /Year)  2 |  1  2.00    2| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Area of New Homes (sf / Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Annual MA Subsidies (Dollar / Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Annual Federal Subsidies (Dollar / Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Aging (House * Year / Year)  2 |  1  2.00    2| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Age Removal (House * Year /Year)  2 |  1  2.00    2| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Weight on Upfront Cost (dmnl )  0 |  2  0.00    0| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks U Value Increase from Source Switching (kBTU*House/(Year*Year*sf*F))  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total U Value by Cohort (House * kBTU / (sf * F * Year))  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total U Value Across All Groupings (House * kBTU / (sf * F * Year))  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Energy Use (kBTU / Year)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Cost of Ownership of Average Home (Dollar / (Year * House))  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Area (sf)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Sensitivity of Retrofits to Cost (dmnl )  0 |  2  0.00    0| 0| 0    0| 2| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Retrofit Delay (Year )  0 |  2  0.00    0| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Reference Retrofit Cost (Dollar / (House * Year) )  0 |  2  0.00    0| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Proportional MassSave Subsidy Implementation Year for Retrofits (Year )  0 |  2  0.00    0| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Proportional IRA Subsidy Switch for Heat Pumps (dmnl )  0 |  2  0.00    0| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )  0 |  2  0.00    0| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Pounds per Ton (lb CO2 / tCO2)  0 |  2  0.00    0| 0| 0    0| 2| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Optimal Energy Use (kBTU / (House * Year))  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Noise Correlation Time 1 (Year)  0 |  2  0.00    0| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Noise Correlation Time 0 (Year)  0 |  2  0.00    0| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Noise Correlation Time (Year)  0 |  2  0.00    0| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks No Turnover Switch (dmnl )  0 |  2  0.00    0| 0| 0    0| 2| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Net Area Shift due to Retrofit Status Switching (sf / Year)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Net Age Shift from Retrofitting Status Shifting (House * Year / Year)  1 |  1  1.00    1| 0| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Monthly Total Heat Pump Sales (Houses/ Month)  2 |  0  Infinite    1| 1| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks kBTU per kWH (kBTU / kWH )  0 |  2  0.00    0| 0| 0    0| 2| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )  0 |  2  0.00    0| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )  0 |  2  0.00    0| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Initial Housing (House)  0 |  2  0.00    0| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .InOutLinks Initial Housing Starts (House/Year)  2 |  0  Infinite    0| 0| 2    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Initial Fraction of Homes Retrofitting (dmnl )  0 |  2  0.00    0| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing Starts In Each Cohort (House / Year)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing by Retrofitting Status (House)  1 |  1  1.00    1| 0| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing by Cohort and Heating and Cooling System (Houses)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Houses Switching Into Sources (Houses / Year)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks HOMES Subsidy Implementation Year (Year )  0 |  2  0.00    0| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks HOMES Subsidy Final Year (Year)  0 |  2  0.00    0| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks HOMES Cut Off for Savings (dmnl )  0 |  2  0.00    0| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Fraction Retrofitting by Cohort (dmnl)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Fraction of Housing by Heating and Cooling System (dmnl)  2 |  0  Infinite    1| 1| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Fraction of Houses Switching (dmnl)  1 |  1  1.00    0| 0| 1    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Emissions by Heating and Cooling System (tCO2 / Year)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks EEHIC Subsidy for Retrofits Final Year (Year)  0 |  2  0.00    0| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Delay in Forming Expectations of Retrofit Costs (Year )  0 |  2  0.00    0| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Delay in Forming Expectations of Energy Price (Year )  0 |  2  0.00    0| 0| 0    2| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cumulative Subsidy for Retrofits (Dollar)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cumulative Subsidies for Heat Pumps (Dollar)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cumulative Subsidies (Dollar)  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Cohort Duration (Year )  0 |  2  0.00    0| 0| 0    0| 0| 2
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingInOutLinks Average U Value in All Housing (kBTU / (sf * F * Year))  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Subsidized Retrofit Cost (Dollar / House)  2 |  0  Infinite    1| 0| 1    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Lifetime of Heating Technology (Year)  0 |  2  0.00    0| 0| 0    1| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Indicated Fraction of Homes Retrofitting (dmnl)  2 |  0  Infinite    1| 1| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Heating Energy Use Across All Homes (kBTU / (Year * House))  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Heating Cost Across All Homes (Dollar / Year / House)  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average EUI in All Housing (kBTU / (sf * Year))  2 |  0  Infinite    1| 1| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Energy Use by Heating and Cooling System (kBTU / (House * Year))  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Average Energy Costs if Retrofitted (Dollar/(Year*House))  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Average Energy Costs for Retrofitting Home (Dollar / Year / House)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Emissions by Heating and Cooling System (tCO2 / Year / House)  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Emissions (tCO2 / House / Year)  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Daily Load from Heat Pumps (kBTU / Day)  2 |  0  Infinite    1| 1| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Cooling Energy Use Across All Homes (kBTU / Year / House)  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Cooling Cost Across All Homes (Dollar / House/ Year)  2 |  0  Infinite    1| 1| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Average Age in All Housing (Year)  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Annual Subsidies (Dollar / Year)  2 |  0  Infinite    2| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Annual Load from Heat Pumps (kBTU / Year)  1 |  1  1.00    1| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)  0 |  1  0.00    0| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks U Value Retrofitted Away (House * kBTU / (Year * F * sf))  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Initial Housing Starts (Houses / Year )  0 |  1  0.00    0| 0| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Housing Starts (House/ Year)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Time to Decide to Retrofit (Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks System Switching SWITCH (dmnl )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Step Time 1 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Step Time 0 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Step Time (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Sine Period 1 (Year)  0 |  1  0.00    0| 0| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Sine Period 0 (Year)  0 |  1  0.00    0| 0| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Sine Period (Year)  0 |  1  0.00    0| 0| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Sine Amplitude 1 (Dimensionless)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Sine Amplitude 0 (Dimensionless)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Sine Amplitude (Dimensionless)  0 |  1  0.00    0| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Sensitivity of Affinity to Cost (dmnl )  0 |  1  0.00    0| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Ramp Start Time 1 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Ramp Start Time 0 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Ramp Start Time (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Ramp End Time 1 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Ramp End Time 0 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Ramp End Time (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Pulse Time 1 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Pulse Time 0 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Pulse Time (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Peak Heating Load on Grid (kWH / Day)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Peak Cooling Load on Grid (kWH / Day)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Oil COP TABLE (dmnl)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Noise Start Time 1 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Noise Start Time 0 (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Noise Start Time (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Noise Standard Deviation 1 (Dimensionless)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Noise Standard Deviation 0 (Dimensionless)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Noise Standard Deviation (Dimensionless)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Months per Year (Month / Year )  0 |  1  0.00    0| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks MassSave Maximum Subsidy for Retrofits (Dollar / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )  0 |  1  0.00    0| 0| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)  0 |  1  0.00    0| 0| 0    0| 0| 1
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks Mass Save Proportional Subsidy Rate for Retrofits (dmnl )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks IRA Proportional Subsidy Rate for Heat Pumps (dmnl )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Initial Heating Energy Price (Dollar / (kBTU))  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Initial Cooling Energy Price (Dollar / kBTU)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Initial Code U Value (kBTU / (sf * F * Year))  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Initial Average U Value (kBTU/(Year*sf*F))  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Initial Average Area of Housing Starts (sf / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Initial Area (sf)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Increase in Area per Year (sf / Year / House )  0 |  1  0.00    0| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Housing Starts Step Height (Dimensionless )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Housing Starts Ramp Slope (1/Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Housing Starts Pulse Quantity (Dimensionless*Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Housing Starts Exponential Growth Rate (1/Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing Starts Across Cohorts ()  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing Fractional Growth Rate (1 / Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Housing by Cohort (House)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Houses Retrofitting (Houses)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15InOutLinks HOMES Lower Subsidy Amount (Dollar / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks HOMES High Subsidy Amount (Dollar / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Homeowner Hours Spent Retrofitting (Hour )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Heating Emissions Factors (lb CO2 / kBTU)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Heat Pump Heating COP TABLE (dmnl)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Heat Pump COP on Coldest Days (dmnl )  0 |  1  0.00    0| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Heat Pump Cooling COP TABLE (dmnl)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks HDD on Coldest Day (F )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Gas COP TABLE (dmnl)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Fractional Decrease in Code U (1 / Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Fraction Retrofitting by System and Cohort (dmnl)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Fraction Retrofitting (dmnl)  1 |  0  Infinite    0| 0| 1    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingInOutLinks Fixed Cost (Dollar / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Energy Use by Oil Houses (kBTU / Year)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Energy Use by Heat Pump Houses (kBTU / Year)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Energy Use by Gas Houses (kBTU/ Year)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Energy Price Step Height (Dimensionless )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Energy Price Ramp Slope 1 (1/Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Energy Price Ramp Slope (1/Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Energy Price Pulse Quantity 1 (Dimensionless*Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Energy Price Pulse Quantity (Dimensionless*Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Energy Price Exponential Growth Rate 1 (1/Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Energy Price Exponential Growth Rate (1/Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Effect of Air Leakage from Window AC on Efficiency (dmnl)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks EEHIC Proportional Subsidy Rate for Retrofits (dmnl )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks EEHIC Maximum Subsidy for Retrofits (Dollar / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Demolition Hazard Rate (1 / Year )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cumulative MA Subsidy (Dollar)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cumulative Federal Subsidy (Dollar)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cumulative Emissions (tCO2)  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cost of Bad Air Conditioning (Dollar / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cooling Energy Price Step Height 1 (Dimensionless )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Cooling Emissions Factor (lb CO2 / kBTU)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks CDD on Coldest Day (F )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Time To Consider Switching (Year )  0 |  1  0.00    0| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Average Income (Dollar / Hour / House )  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Amoritization Period (Year )  0 |  1  0.00    0| 0| 0    0| 1| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Aging per Year (Year / Year)  0 |  1  0.00    0| 0| 0    1| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Total Initial Homes (Houses ) ( 0| 0)  Infinite    0| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31InOutLinks Peak Load from Non Heating or Cooling Sources (kWH / Day ) ( 0| 0)  Infinite    0| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8InOutLinks Maximum Energy Price (Dollar / kBTU) ( 0| 0)  Infinite    0| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlInOutLinks TIME STEP (Year )  0 |  7  0.00    0| 0| 0    1| 3| 3
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlInOutLinks INITIAL TIME (Year)  0 |  5  0.00    0| 0| 0    0| 1| 4
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlInOutLinks SAVEPER (Year )  1 |  0  Infinite    1| 0| 0    0| 0| 0
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlInOutLinks FINAL TIME (Year)  0 |  1  0.00    0| 0| 0    1| 0| 0


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                                                                                                                                                                                                                                                                                                                                                                                                                Undocumented Variables (18 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Backup Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Central AC Cooling ()
                                                                                                                                                                                                                                                                                                                                                                                                                .Sub Cohort ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Fossil Fuel Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Gas and Window or No AC ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Gas Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Heating and Cooling System ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C kBTU per kWH (kBTU / kWH )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub New Cohorts ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub No AC Cooling ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Oil and Window or No AC ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Oil Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Sub Preexisting Cohorts ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Retrofit Cost ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Retrofitting Status ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Traditional Cooling ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Window AC Cooling ()



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                                                                                                                                                                                                                                                                                                                                                                                                                Supplementary Variables (0 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable



                                                                                                                                                                                                                                                                                                                                                                                                                Top

                                                                                                                                                                                                                                                                                                                                                                                                                Supplementary Variables Being Used (0 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable



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                                                                                                                                                                                                                                                                                                                                                                                                                Unused Variables (48 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Annual Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Average Age in All Housing (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Cooling Cost Across All Homes (Dollar / House/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Cooling Energy Use Across All Homes (kBTU / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Daily Load from Heat Pumps (kBTU / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions (tCO2 / House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Energy Use by Heating and Cooling System[Heating and Cooling System] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average EUI in All Housing (kBTU / (sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Heating Cost Across All Homes (Dollar / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Heating Energy Use Across All Homes (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Subsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average U Value by Heating and Cooling System[Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Average U Value in All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average U Value of Houses Switching Into Sources[Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Backup Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Emissions (tCO2)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Federal Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative MA Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cumulative Subsidies (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Gas Houses (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Heat Pump Houses (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Oil Houses (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction of Housing by Heating and Cooling System[Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Heating ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Retrofitting[Cohort,Heating and Cooling System] (Houses)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Cohort[Cohort] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing Starts Across Cohorts ()
                                                                                                                                                                                                                                                                                                                                                                                                                .A Initial Housing Starts[Heating and Cooling System] (House/Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Maximum Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Monthly Total Heat Pump Sales (Houses/ Month)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub New Cohorts ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal U Across All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Peak Cooling Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Peak Heating Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Peak Load from Non Heating or Cooling Sources (kWH / Day )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Sub Technology ()
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Housing Starts (House/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Total Initial Homes (Houses )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L U Value Retrofitted Away (House * kBTU / (Year * F * sf))



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                                                                                                                                                                                                                                                                                                                                                                                                                Stock Variables (14 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Area[Preexisting Cohorts,Open to Retrofitting] (sf)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Autocorrelated Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18L Code U (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Emissions (tCO2)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Federal Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative MA Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidies for Heat Pumps (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidy for Retrofits (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Housing[Cohort,Heating and Cooling System,Open to Retrofitting] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Total Age[Cohort,Open to Retrofitting] (House * Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] (House * kBTU / (Year * F * sf) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L U Value Retrofitted Away (House * kBTU / (Year * F * sf))



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                                                                                                                                                                                                                                                                                                                                                                                                                Equations With Embedded Data (18 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Autocorrelated Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Emissions (tCO2)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Federal Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative MA Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidies for Heat Pumps (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidy for Retrofits (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Input 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] (kBTU / (F * sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L U Value Retrofitted Away (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A White Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A White Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A White Noise 1 (Dimensionless)



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                                                                                                                                                                                                                                                                                                                                                                                                                Nonmonotonic Lookup Functions (0 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable



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                                                                                                                                                                                                                                                                                                                                                                                                                Non-Zero End Sloped Lookup Functions (5 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                Non-Zero
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Non-Zero Gas COP TABLE (dmnl)Left
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Non-Zero Heat Pump Cooling COP TABLE (dmnl)Both
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Non-Zero Heat Pump Heating COP TABLE (dmnl)Both
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Non-Zero Oil COP TABLE (dmnl)Left
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Non-Zero Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)Both


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                                                                                                                                                                                                                                                                                                                                                                                                                Cascading Lookup Functions (0 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable



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                                                                                                                                                                                                                                                                                                                                                                                                                Equations With Step Pulse Or Related Functions (3 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Input 1 (Dimensionless)



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                                                                                                                                                                                                                                                                                                                                                                                                                Equations With If Then Else Functions (21 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar/ Home)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A HOMES Implemented High Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A HOMES Implemented Lower Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Retrofitting per Year[Cohort,Heating and Cooling System] (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Net Age Shift by System[Cohort,Heating and Cooling System] (Year * House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Net Area Shift by System[Cohort,Heating and Cooling System] (sf / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] (kBTU / (F * sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18A U Value of Housing Starts[Cohort,Heating and Cooling System] (kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] (Dollar / sf)



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                                                                                                                                                                                                                                                                                                                                                                                                                Equations With Min Or Max Functions (13 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Savings[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Actual Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Retrofitting[Cohort,Heating and Cooling System] (House * kBTU / (sf * F* Year) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Subsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] (Dollar / sf)



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                                                                                                                                                                                                                                                                                                                                                                                                                Complex Variable (Richardson's Rule Threshold = 3) (39 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                Complexity
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Actual HOMES Subsidy for Retrofits (Dollar/ Home)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Affinity of Heating and Cooling Systems (dmnl)4
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Complexity Area (sf)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Average Area of Housing Starts (sf / House)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Average Heating Energy Use (kBTU / (Year * House))4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity HOMES Implemented High Subsidy (Dollar / House)4
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Complexity HOMES Implemented Lower Subsidy (Dollar / House)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Houses Retrofitting per Year (House / Year)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Housing Starts (Houses / Year)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)4
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Complexity Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)4
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Complexity Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Optimal Heating Energy Use (kBTU / (House * Year))4
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingComplexity Present Value of Heating Operating Costs (Dollar / (House))4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Retrofitting (House * kBTU / (sf * F* Year) / Year)4
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Complexity Total Age (House * Year)4
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Cooling Energy Use Under Alternatives (kBTU / (House * Year))5
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity EEHIC Expected Subsidy for Retrofits (Dollar / House)5
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Heating Energy Use Under Alternatives (kBTU / (House * Year))5
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Housing (House)5
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Complexity MassSave Expected Subsidy for Retrofits (Dollar / House)5
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)5
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Optimal U Value for Existing Homes (kBTU / (sf * F * Year))5
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))5
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Complexity Expected Subsidy for Retrofits (Dollar / House)6
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Complexity Optimal U for New Homes (kBTU / (sf * Year * F))6
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingComplexity Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))6
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Total U Value (House * kBTU / (Year * F * sf) )6
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingComplexity Unsubsidized Retrofit Cost Intensity (Dollar / sf)6
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Complexity Additional Cost of Building to U Value (Dollar / sf)7
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))8
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Complexity Input (Dimensionless)15
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Complexity Input 0 (Dimensionless)15
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Complexity Input 1 (Dimensionless)15


                                                                                                                                                                                                                                                                                                                                                                                                                Top

                                                                                                                                                                                                                                                                                                                                                                                                                Complex Stock (0 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable



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                                                                                                                                                                                                                                                                                                                                                                                                                State Variables (27 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Area[Preexisting Cohorts,Open to Retrofitting] (sf)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Autocorrelated Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18L Code U (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Emissions (tCO2)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Federal Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative MA Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidies for Heat Pumps (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidy for Retrofits (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected Fixed Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected Heating Energy Price[Heating and Cooling System] (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A HOMES Expected Higher Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Housing[Cohort,Heating and Cooling System,Open to Retrofitting] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Total Age[Cohort,Open to Retrofitting] (House * Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] (House * kBTU / (Year * F * sf) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L U Value Retrofitted Away (House * kBTU / (Year * F * sf))



                                                                                                                                                                                                                                                                                                                                                                                                                Top

                                                                                                                                                                                                                                                                                                                                                                                                                Variables With Source Information (0 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                Sources


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                                                                                                                                                                                                                                                                                                                                                                                                                Variables With Dimensionless Units (59 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Active Cohort Indicator[Preexisting Cohorts] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Affinity of Not Retrofitting[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Affinity of Retrofitting[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Aging per Year (Year / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Autocorrelated Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cooling Energy Price Step Height 1 (Dimensionless )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cooling System Efficiency[No AC Cooling] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Effect of Air Leakage from Window AC on Efficiency (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Energy Price Step Height (Dimensionless )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Savings[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction of Housing by Heating and Cooling System[Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31LI,A Fraction Retrofitting by Cohort[Cohort] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Gas COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Heat Pump Cooling COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Heat Pump COP on Coldest Days (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Heat Pump Heating COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Heating System Efficiency[Oil Heating] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C HOMES Cut Off for Savings (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Housing Starts Step Height (Dimensionless )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Fraction of Homes Retrofitting (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Input 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C No Turnover Switch (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Standard Deviation (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Standard Deviation 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Noise Standard Deviation 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Oil COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Proportional Subsidy Switch for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sensitivity of Affinity to Cost (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sensitivity of Retrofits to Cost (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Amplitude (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Amplitude 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sine Amplitude 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C System Switching SWITCH (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Weight on Upfront Cost (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A White Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A White Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A White Noise 1 (Dimensionless)



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                                                                                                                                                                                                                                                                                                                                                                                                                Variables without Predefined Min or Max Values (338 Variables + 4 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Active Cohort Indicator[Preexisting Cohorts] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar/ Home)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Additional Cost of Building to U Value[Cohort,Heating and Cooling System] (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Affinity of Not Retrofitting[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Affinity of Retrofitting[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Age Removal[Cohort,Retrofitting Status] (House * Year /Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Aging[Cohort,Retrofitting Status] (House * Year / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Aging per Year (Year / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Amoritization Period (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Annual Federal Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Annual Load from Heat Pumps (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Annual MA Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Annual Subsidies (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Area[Preexisting Cohorts,Open to Retrofitting] (sf)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Area of New Homes[Cohort] (sf / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Area Removal[Cohort,Retrofitting Status] (sf /Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Autocorrelated Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Autocorrelated Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Average Age[Cohort,Retrofitting Status] (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Average Age in All Housing (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Area[Cohort,Retrofitting Status] (sf / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Average Area in All Housing (sf/ House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Area of Housing Starts (sf / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Cooling Cost Across All Homes (Dollar / House/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Cooling Energy Use Across All Homes (kBTU / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Daily Load from Heat Pumps (kBTU / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions (tCO2 / House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions from Cooling by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Emissions from Heating by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Average Energy Costs for Retrofitting Home[Cohort,Heating and Cooling System] (Dollar / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Average Energy Costs if Retrofitted[Cohort,Heating and Cooling System] (Dollar/(Year*House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Energy Use by Heating and Cooling System[Heating and Cooling System] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Energy Use in All Housing (kBTU / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average EUI in All Housing (kBTU / (sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Average Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Heating Cost Across All Homes (Dollar / Year / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Heating Energy Use Across All Homes (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Average Income (Dollar / Hour / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Indicated Fraction of Homes Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Lifetime of Cooling Technology[No AC Cooling] (Years)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Average Lifetime of Heating Technology[Oil Heating] (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average Subsidized Retrofit Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Average Time To Consider Switching (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average U Value by Heating and Cooling System[Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Average U Value in All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Average U Value of Houses Switching Into Sources[Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C CDD on Coldest Day (F )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Change in AC Noise (1/Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8F,A Change in AC Noise 0 (1/Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Change in AC Noise 1 (1/Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18L Code U (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Cohort Duration (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cooling Degree Days (F )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cooling Emissions Factor (lb CO2 / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cooling Energy Price Step Height 1 (Dimensionless )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cooling System Efficiency[No AC Cooling] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cost of Bad Air Conditioning[No AC Cooling] (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cost of Cooling System Replacement[No AC Cooling] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Cost of Heating System Replacement[Oil Heating] (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Oil] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Emissions (tCO2)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Federal Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative MA Subsidy (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Cumulative Subsidies (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidies for Heat Pumps (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Cumulative Subsidy for Retrofits (Dollar)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Days per Year (Day / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18F,A Decrease in Code U (kBTU / (sf * Year * F) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Delay in Changing Subsidy Expectations (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Delay in Forming Expectations of Energy Price (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Delay in Forming Expectations of Retrofit Costs (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Demolition Hazard Rate (1 / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Discount Rate (1 / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C EEHIC Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C EEHIC Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Effect of Air Leakage from Window AC on Efficiency (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Emissions (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Energy Price Exponential Growth Rate (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Energy Price Exponential Growth Rate 1 (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Energy Price Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Energy Price Pulse Quantity 1 (Dimensionless*Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Energy Price Ramp Slope (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Energy Price Ramp Slope 1 (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Energy Price Step Height (Dimensionless )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Savings[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Gas Houses (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Heat Pump Houses (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Energy Use by Oil Houses (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected Fixed Cost (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected Heating Energy Price[Heating and Cooling System] (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Expected Lump Sum Subsidy Intensity[Retrofit Cost] (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Expected Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Federal Annual Heat Pump Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Federal Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Fixed Cost (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Fixed Cost per Unit Area[Cohort] (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction of Housing by Heating and Cooling System[Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction Retrofitting (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31LI,A Fraction Retrofitting by Cohort[Cohort] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Fractional Decrease in Code U (1 / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Gas COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C HDD on Coldest Day (F )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Heat Pump Cooling COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Heat Pump COP on Coldest Days (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Heat Pump Heating COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Heating Degree Days (F )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Heating Emissions Factors[Oil Heating] (lb CO2 / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Heating Energy Price[Heating and Cooling System] (Dollar / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Heating System Efficiency[Oil Heating] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Homeowner Hours Spent Retrofitting (Hour )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C HOMES Cut Off for Savings (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A HOMES Expected Higher Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15SM,A HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C HOMES High Subsidy Amount (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A HOMES Implemented High Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A HOMES Implemented Lower Subsidy (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C HOMES Lower Subsidy Amount (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C HOMES Subsidy Final Year (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C HOMES Subsidy Implementation Year (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Considering Switching System[Cohort,Heating and Cooling System,Retrofitting Status] (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Retrofitting[Cohort,Heating and Cooling System] (Houses)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Retrofitting per Year[Cohort,Heating and Cooling System] (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Houses Switching Into Sources[Heating and Cooling System] (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Housing[Cohort,Heating and Cooling System,Open to Retrofitting] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Cohort[Cohort] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Cohort and Heating and Cooling System[Cohort,Heating and Cooling System] (Houses)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Heating and Cooling System[Heating and Cooling System] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing by Retrofitting Status[Retrofitting Status] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Housing Fractional Growth Rate (1 / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Housing Starts[Cohort,Heating and Cooling System] (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing Starts Across Cohorts ()
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Housing Starts Exponential Growth Rate (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Housing Starts In Each Cohort[Cohort] (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Housing Starts Pulse Quantity (Dimensionless*Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Housing Starts Ramp Slope (1/Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Housing Starts Step Height (Dimensionless )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Increase in Area per Year (sf / Year / House )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18F,A Increase in U Value from Housing Starts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Indicated Homes Retrofitting[Cohort,Heating and Cooling System] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8LI,A Initial Age[Preexisting Cohorts,Retrofitting Status] (House * Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31LI,C Initial Area[Cohort] (sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Average Area of Housing Starts (sf / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Average U Value[Cohort] (kBTU/(Year*sf*F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31LI,C Initial Code U Value (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Cooling Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Fraction of Homes Retrofitting (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Initial Heating Energy Price[Oil Heating] (Dollar / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingLI,A Initial Homes Not Retrofitting[Preexisting Cohorts,Heating and Cooling System] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingLI,A Initial Homes Retrofitting[Preexisting Cohorts,Heating and Cooling System] (Houses)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Initial Housing[Cohort,Heating and Cooling System] (House)
                                                                                                                                                                                                                                                                                                                                                                                                                .A Initial Housing Starts[Heating and Cooling System] (House/Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15LI,A Initial U Value[Preexisting Cohorts,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Input 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Input 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Actual Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C kBTU per kWH (kBTU / kWH )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Lifetime Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] (Dollar * Year * F / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Marginal Cooling Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Marginal Cost at Binding U Value without EEHIC[Cohort,Heating and Cooling System] ((Dollar / sf) / (kBTU / (sf * F * Year)))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Marginal Heating Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / (kBTU))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Massachusetts Annual Retrofit Subsidy (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31SM,A MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C MassSave Maximum Subsidy for Retrofits (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A MassSave Subsidy for Retrofits Final Year (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Maximum Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Monthly Total Heat Pump Sales (Houses/ Month)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Months per Year (Month / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Net Age Shift by System[Cohort,Heating and Cooling System] (Year * House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Net Age Shift from Retrofitting Status Shifting[Cohort] (House * Year / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Net Area Shift by System[Cohort,Heating and Cooling System] (sf / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Net Area Shift due to Retrofit Status Switching[Cohort] (sf / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] (Houses / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C No Turnover Switch (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Correlation Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Correlation Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Noise Correlation Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Standard Deviation (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Standard Deviation 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Noise Standard Deviation 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Start Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Noise Start Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Noise Start Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Oil COP TABLE (dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Optimal Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] (kBTU / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal U Across All Housing (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18A Optimal U for New Homes[Cohort,Heating and Cooling System] (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Optimal U Value with No EEHIC Proportional Subsidy[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Peak Cooling Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Peak Heating Load on Grid (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Fossil Fuel Heating,Retrofitting Status] (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Peak Load from Heat Pumps on Hottest Days per Group[Cohort,No AC Cooling,Retrofitting Status] (kWH / Day)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Peak Load from Non Heating or Cooling Sources (kWH / Day )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Perceived Cost of Not Retrofitting[Cohort,Heating and Cooling System] (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Perceived Cost of Retrofitting[Cohort,Heating and Cooling System] (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Pounds per Ton (lb CO2 / tCO2)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Present Value of Cooling Operating Costs[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] (Dollars / (House))
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Present Value of Heating Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / (House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Present Value of Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / (House) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Present Value Replacement Cost[No AC Cooling] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Proportional MassSave Subsidy Implementation Year for Retrofits (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15C Proportional Subsidy Switch for Retrofits (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Pulse Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Pulse Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Pulse Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Ramp End Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Ramp End Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Ramp End Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Ramp Start Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Ramp Start Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Ramp Start Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Reference Retrofit Cost (Dollar / (House * Year) )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v9C Reference U Value (kBTU / (sf * Year * F) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Retrofit Delay (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A Retrofitting[Cohort,Heating and Cooling System] (House * kBTU / (sf * F* Year) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sensitivity of Affinity to Cost (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingC Sensitivity of Marginal Cost to U Value (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sensitivity of Retrofits to Cost (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Amplitude (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Amplitude 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sine Amplitude 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Period (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Sine Period 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Sine Period 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Soft Costs of Retrofitting (Dollar / Home)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Step Time (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Step Time 0 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Step Time 1 (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Subsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15A Subsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar /House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C System Switching SWITCH (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Time to Decide to Retrofit (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8L Total Age[Cohort,Open to Retrofitting] (House * Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Area (sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Cooling Cost (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Cooling Energy Use (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Cost of Ownership of Average Home[Cohort,Heating and Cooling System] (Dollar / (Year * House))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Cost of Ownership of Retrofitted Homes[Cohort,Heating and Cooling System] (Dollar / (House * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Energy Use (kBTU / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Heat Pump Sales (House / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Heating Cost (Dollar / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Heating Energy Use (kBTU/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Housing Starts (House/ Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingA Total Housing Stock (House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Total Initial Homes (Houses )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Total Initial Housing Starts (Houses / Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total Present Value of Cost[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] (House * kBTU / (Year * F * sf) )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total U Value Across All Groupings (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total U Value by Cohort[Cohort] (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Total U Value by Heating and Cooling System[Heating and Cooling System] (House * kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] (kBTU / (F * sf * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * F * Year))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value Increase from Source Switching[Heating and Cooling System] (kBTU*House/(Year*Year*sf*F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A U Value Loss from Demolition[Cohort,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18A U Value of Housing Starts[Cohort,Heating and Cooling System] (kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A U Value of Retrofitting Homes[Cohort,Heating and Cooling System] (kBTU / (sf * Year * F))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31L U Value Retrofitted Away (House * kBTU / (Year * F * sf))
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31F,A U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf) / Year)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A,T Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A Unsubsidized Cost of Heat Pumps (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar / House)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingA Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] (Dollar / sf)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31C Weight on Upfront Cost (dmnl )
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A White Noise (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8A White Noise 0 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31A White Noise 1 (Dimensionless)
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlC FINAL TIME (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlC INITIAL TIME (Year)
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlA SAVEPER (Year )
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlC TIME STEP (Year )



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                                                                                                                                                                                                                                                                                                                                                                                                                Function Sensitivity Parameters (0 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable



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                                                                                                                                                                                                                                                                                                                                                                                                                Data Lookup Tables (0 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable



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                                                                                                                                                                                                                                                                                                                                                                                                                Variables Using Macros (0 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable



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                                                                                                                                                                                                                                                                                                                                                                                                                Variables Not In Any View (1 Variables + 1 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8C Maximum Energy Price (Dollar / kBTU)
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlA SAVEPER (Year )



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                                                                                                                                                                                                                                                                                                                                                                                                                Equations With Unit Errors Or Warnings (4 Variables + 0 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                Units
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Units Heating System Efficiency (dmnl) Lhs Units: (Dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                Rhs Units: LOOKUP Used With Dimensioned Argument < (Year) >
                                                                                                                                                                                                                                                                                                                                                                                                                Complete Rhs Units: LOOKUP ( Dmnl , Year )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Units Housing Starts Across Cohorts () Lhs Units: None Specified
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Units Peak Load from Non Heating or Cooling Sources (kWH / Day ) Lhs Units: (kWH/Day)
                                                                                                                                                                                                                                                                                                                                                                                                                Rhs Units: (Dmnl)
                                                                                                                                                                                                                                                                                                                                                                                                                Complete Rhs Units: ( ( 18344.8 * 1000.0 ) * 0.461799 )
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Units Unsubsidized Cost of Heat Pumps (Dollar / House) Lhs Units: (Dollar/House)
                                                                                                                                                                                                                                                                                                                                                                                                                Rhs Units: LOOKUP Used With Dimensioned Argument < (Year) >
                                                                                                                                                                                                                                                                                                                                                                                                                Complete Rhs Units: LOOKUP ( Dollar/House , Year )


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                                                                                                                                                                                                                                                                                                                                                                                                                Units (9/42)

                                                                                                                                                                                                                                                                                                                                                                                                                Units
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Alternates
                                                                                                                                                                                                                                                                                                                                                                                                                1/Year Basic
                                                                                                                                                                                                                                                                                                                                                                                                                Dmnl Basic [Dimensionless, dmnl, Year/Year]
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar Basic
                                                                                                                                                                                                                                                                                                                                                                                                                F Basic
                                                                                                                                                                                                                                                                                                                                                                                                                Hour Basic
                                                                                                                                                                                                                                                                                                                                                                                                                House Basic [House * Year/Year, Houses, Year * House/Year]
                                                                                                                                                                                                                                                                                                                                                                                                                sf Basic
                                                                                                                                                                                                                                                                                                                                                                                                                tCO2 Basic
                                                                                                                                                                                                                                                                                                                                                                                                                Year Basic [Dimensionless*Year, Years]
                                                                                                                                                                                                                                                                                                                                                                                                                Day/Year Combined
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar*F*Year/kBTU Combined [(Dollar/sf)/(kBTU/(sf * F * Year))]
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar*F/kBTU Combined [Dollar * F/(kBTU), Dollar * F/kBTU]
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar*Year*F/kBTU Combined [(Dollar/sf)/(kBTU/(sf * Year * F)), Dollar * Year * F/kBTU, Dollar/sf/(kBTU/(sf * Year * F))]
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar/Hour*House Combined [Dollar/Hour/House]
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar/House Combined [Dollar/(House), Dollar/Home, Dollars/(House)]
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar/House*Year Combined [Dollar/(House * Year), Dollar/House/Year]
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar/kBTU Combined [Dollar/(kBTU)]
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar/sf Combined
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar/Year Combined
                                                                                                                                                                                                                                                                                                                                                                                                                Dollar/Year*House Combined [Dollar/(Year * House), Dollar/(Year*House), Dollar/Year/House]
                                                                                                                                                                                                                                                                                                                                                                                                                House*kBTU/sf*F*Year Combined [House * kBTU/(sf * F * Year)]
                                                                                                                                                                                                                                                                                                                                                                                                                House*kBTU/sf*F*Year*Year Combined [House * kBTU/(sf * F* Year)/Year]
                                                                                                                                                                                                                                                                                                                                                                                                                House*kBTU/Year*F*sf Combined [House * kBTU/(Year * F * sf)]
                                                                                                                                                                                                                                                                                                                                                                                                                House*kBTU/Year*Year*F*sf Combined [House * kBTU/(Year * F * sf)/Year]
                                                                                                                                                                                                                                                                                                                                                                                                                House*kBTU/Year*Year*sf*F Combined [House * kBTU/( Year * Year * sf * F)]
                                                                                                                                                                                                                                                                                                                                                                                                                House*Year Combined [House * Year]
                                                                                                                                                                                                                                                                                                                                                                                                                House/Month Combined [Houses/Month]
                                                                                                                                                                                                                                                                                                                                                                                                                House/Year Combined [Houses/Year]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU*House/Year*Year*sf*F Combined [kBTU*House/(Year*Year*sf*F)]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/Day Combined
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/F*sf*Year Combined [kBTU/(F * sf * Year)]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/House*Year Combined [kBTU/(House * Year)]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/kWH Combined
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/sf*F*Year Combined [kBTU/(sf * F * Year)]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/sf*Year Combined [kBTU/(sf * Year)]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/sf*Year*F Combined [kBTU/(sf * Year * F)]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/sf*Year*Year*F Combined [kBTU/(sf * Year * F)/Year]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/Year Combined
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/Year*F*sf Combined [kBTU/(Year * F * sf)]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/Year*House Combined [kBTU/(Year * House), kBTU/Year/House]
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU/Year*sf*F Combined [kBTU/(Year*sf*F)]
                                                                                                                                                                                                                                                                                                                                                                                                                kWH/Day Combined
                                                                                                                                                                                                                                                                                                                                                                                                                lb CO2/kBTU Combined
                                                                                                                                                                                                                                                                                                                                                                                                                lb CO2/tCO2 Combined
                                                                                                                                                                                                                                                                                                                                                                                                                Month/Year Combined
                                                                                                                                                                                                                                                                                                                                                                                                                sf/House Combined
                                                                                                                                                                                                                                                                                                                                                                                                                sf/Year Combined
                                                                                                                                                                                                                                                                                                                                                                                                                sf/Year*House Combined [sf/Year/House]
                                                                                                                                                                                                                                                                                                                                                                                                                tCO2/House*Year Combined [tCO2/(House * Year), tCO2/House/Year]
                                                                                                                                                                                                                                                                                                                                                                                                                tCO2/Year Combined
                                                                                                                                                                                                                                                                                                                                                                                                                tCO2/Year*House Combined [tCO2/(Year * House), tCO2/Year/House]



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                                                                                                                                                                                                                                                                                                                                                                                                                Feedback Loops (17|0 Loops ) Maximum Loop Length: 5 [2,4] | [0,0]

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                Loops
                                                                                                                                                                                                                                                                                                                                                                                                                 + 
                                                                                                                                                                                                                                                                                                                                                                                                                 - 
                                                                                                                                                                                                                                                                                                                                                                                                                 +/- Ratio 
                                                                                                                                                                                                                                                                                                                                                                                                                 ? 
                                                                                                                                                                                                                                                                                                                                                                                                                Loops (IVV)
                                                                                                                                                                                                                                                                                                                                                                                                                 + 
                                                                                                                                                                                                                                                                                                                                                                                                                 - 
                                                                                                                                                                                                                                                                                                                                                                                                                 +/- Ratio 
                                                                                                                                                                                                                                                                                                                                                                                                                 ? 
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing (House)  5 (29.4%)  3 [  2,  4]  2 [  2,  2]1.50  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total U Value (House * kBTU / (Year * F * sf) )  4 (23.5%)  2 [  3,  3]  2 [  3,  3]1.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... U Value by Grouping (kBTU / (sf * F * Year))  4 (23.5%)  2 [  3,  3]  2 [  3,  3]1.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Area (sf)  2 (11.8%)  1 [  4,  4]  1 [  3,  3]1.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Average Age (Year)  2 (11.8%)  1 [  4,  4]  1 [  3,  3]1.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Area (sf / House)  2 (11.8%)  1 [  4,  4]  1 [  3,  3]1.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Net Change in Homes Retrofitting (Houses / Year)  2 (11.8%)  1 [  4,  4]  1 [  2,  2]1.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Total Age (House * Year)  2 (11.8%)  1 [  4,  4]  1 [  3,  3]1.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Age Removal (House * Year /Year)  1 (5.9%)  0 [  0,  0]  1 [  3,  3]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Area Removal (sf /Year)  1 (5.9%)  0 [  0,  0]  1 [  3,  3]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Autocorrelated Noise (Dimensionless)  1 (5.9%)  0 [  0,  0]  1 [  2,  2]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Autocorrelated Noise 0 (Dimensionless)  1 (5.9%)  0 [  0,  0]  1 [  2,  2]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Autocorrelated Noise 1 (Dimensionless)  1 (5.9%)  0 [  0,  0]  1 [  2,  2]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Change in AC Noise (1/Year)  1 (5.9%)  0 [  0,  0]  1 [  2,  2]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Change in AC Noise 0 (1/Year)  1 (5.9%)  0 [  0,  0]  1 [  2,  2]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Change in AC Noise 1 (1/Year)  1 (5.9%)  0 [  0,  0]  1 [  2,  2]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Feedback... Code U (kBTU / (sf * Year * F))  1 (5.9%)  0 [  0,  0]  1 [  2,  2]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Feedback... Decrease in Code U (kBTU / (sf * Year * F) / Year)  1 (5.9%)  0 [  0,  0]  1 [  2,  2]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Demolitions (House / Year)  1 (5.9%)  0 [  0,  0]  1 [  2,  2]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Houses Considering Switching System (Houses / Year)  1 (5.9%)  1 [  3,  3]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Houses Switching Sources (House / Year)  1 (5.9%)  1 [  3,  3]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing by Cohort and Heating and Cooling System (Houses)  1 (5.9%)  1 [  4,  4]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing Starts (Houses / Year)  1 (5.9%)  1 [  2,  2]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Indicated Homes Retrofitting (House)  1 (5.9%)  1 [  4,  4]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Net Age Shift by System (Year * House / Year)  1 (5.9%)  1 [  4,  4]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Net Age Shift from Retrofitting Status Shifting (House * Year / Year)  1 (5.9%)  1 [  4,  4]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Net Area Shift by System (sf / Year)  1 (5.9%)  1 [  4,  4]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Net Area Shift due to Retrofit Status Switching (sf / Year)  1 (5.9%)  1 [  4,  4]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Net U Value Change from Retrofitting Home Shifts (House * kBTU / (Year * F * sf) / Year)  1 (5.9%)  1 [  3,  3]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Retrofitting (House * kBTU / (sf * F* Year) / Year)  1 (5.9%)  0 [  0,  0]  1 [  3,  3]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)  1 (5.9%)  0 [  0,  0]  1 [  3,  3]0.00  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)  1 (5.9%)  1 [  3,  3]  0 [  0,  0]Infinite  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Active Cohort Indicator (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Actual EEHIC Subsidy for Retrofits (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Actual HOMES Subsidy for Retrofits (Dollar/ Home)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Actual MassSave Subsidy for Retrofits (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Additional Cost of Building to U Value (Dollar / sf)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Affinity of Heating and Cooling Systems (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Affinity of Not Retrofitting (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingFeedback... Affinity of Retrofitting (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Aging per Year (Year / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Aging (House * Year / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Amoritization Period (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Annual Federal Subsidies (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Annual Heat Pump Subsidy (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Annual Load from Heat Pumps (kBTU / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Annual MA Subsidies (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Annual Retrofit Subsidy (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Annual Subsidies (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Area of New Homes (sf / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Average Age in All Housing (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Average Area in All Housing (sf/ House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Area of Housing Starts (sf / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Cooling Cost Across All Homes (Dollar / House/ Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Cooling Cost (Dollar / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Cooling Energy Use Across All Homes (kBTU / Year / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Cooling Energy Use (kBTU / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Daily Load from Heat Pumps (kBTU / Day)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Emissions (tCO2 / House / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Emissions by Grouping (tCO2 / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Emissions by Heating and Cooling System (tCO2 / Year / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Emissions from Cooling by Grouping (tCO2 / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Emissions from Heating by Grouping (tCO2 / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Energy Cost (Dollar / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Average Energy Costs for Retrofitting Home (Dollar / Year / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Average Energy Costs if Retrofitted (Dollar/(Year*House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Energy Use by Heating and Cooling System (kBTU / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Energy Use in All Housing (kBTU / Year / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Energy Use (kBTU / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average EUI by Grouping (kBTU / (sf * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average EUI in All Housing (kBTU / (sf * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Heating Cost Across All Homes (Dollar / Year / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Average Heating Cost (Dollar / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Heating Energy Use Across All Homes (kBTU / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Heating Energy Use (kBTU / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Income (Dollar / Hour / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Indicated Fraction of Homes Retrofitting (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Lifetime of Cooling Technology (Years)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Lifetime of Heating Technology (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Subsidized Retrofit Cost (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average Time To Consider Switching (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingFeedback... Average U Value in All Housing (kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... CDD on Coldest Day (F )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Cohort Duration (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cooling Degree Days (F )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cooling Emissions Factor (lb CO2 / kBTU)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cooling Energy Price (Dollar / kBTU)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cooling Energy Price Step Height 1 (Dimensionless )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cooling Energy Use Under Alternatives (kBTU / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cooling System Efficiency (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cost of Bad Air Conditioning (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cost of Cooling System Replacement (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cost of Heating System Replacement (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Cost of Switching Heating and Cooling Systems (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cumulative Emissions (tCO2)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cumulative Federal Subsidy (Dollar)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cumulative MA Subsidy (Dollar)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cumulative Subsidies (Dollar)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cumulative Subsidies for Heat Pumps (Dollar)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Cumulative Subsidy for Retrofits (Dollar)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Days per Year (Day / Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Delay in Changing Subsidy Expectations (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Delay in Forming Expectations of Energy Price (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Delay in Forming Expectations of Retrofit Costs (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Demolition Hazard Rate (1 / Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Discount Rate (1 / Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... EEHIC Expected Subsidy for Retrofits (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... EEHIC Maximum Subsidy for Retrofits (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... EEHIC Proportional Subsidy Rate for Retrofits (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... EEHIC Subsidy for Retrofits Final Year (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Effect of Air Leakage from Window AC on Efficiency (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Emissions (tCO2 / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Emissions by Grouping (tCO2 / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Emissions by Heating and Cooling System (tCO2 / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Energy Price Exponential Growth Rate (1/Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Energy Price Exponential Growth Rate 1 (1/Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Energy Price Pulse Quantity (Dimensionless*Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Energy Price Pulse Quantity 1 (Dimensionless*Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Energy Price Ramp Slope (1/Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Energy Price Ramp Slope 1 (1/Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Energy Price Step Height (Dimensionless )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Energy Savings (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Energy Use by Gas Houses (kBTU/ Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Energy Use by Grouping (kBTU / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Energy Use by Heat Pump Houses (kBTU / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Energy Use by Oil Houses (kBTU / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Expected Cooling Energy Price (Dollar / kBTU)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Expected Fixed Cost (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Expected Heating Energy Price (Dollar / kBTU)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Expected Lump Sum Subsidy Intensity (Dollar / sf)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Expected Subsidy for Heat Pumps (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Expected Subsidy for Retrofits (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Federal Annual Heat Pump Subsidy (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Federal Annual Retrofit Subsidy (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Fixed Cost (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Fixed Cost per Unit Area (Dollar / sf)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Fraction of Houses in Each Heating and Cooling System (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Fraction of Houses Switching (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Fraction of Housing by Heating and Cooling System (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Fraction Retrofitting (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Fraction Retrofitting by Cohort (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Fraction Retrofitting by System and Cohort (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Fractional Decrease in Code U (1 / Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Gas COP TABLE (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... HDD on Coldest Day (F )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Heat Pump Cooling COP TABLE (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Heat Pump COP on Coldest Days (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Heat Pump Heating COP TABLE (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Heating Degree Days (F )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Heating Emissions Factors (lb CO2 / kBTU)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Heating Energy Price (Dollar / (kBTU))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Heating Energy Use Under Alternatives (kBTU / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Heating System Efficiency (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Homeowner Hours Spent Retrofitting (Hour )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... HOMES Cut Off for Savings (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... HOMES Expected Higher Subsidy (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... HOMES Expected Lower Lump Sum Subsidy (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... HOMES High Subsidy Amount (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... HOMES Implemented High Subsidy (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... HOMES Implemented Lower Subsidy (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... HOMES Lower Subsidy Amount (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... HOMES Subsidy Final Year (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... HOMES Subsidy Implementation Year (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Houses Retrofitting per Year (House / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Houses Retrofitting (Houses)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Houses Switching Into Sources (Houses / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing by Cohort and Retrofitting Status (House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing by Cohort (House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing by Heating and Cooling System (House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing by Retrofitting Status (House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing Fractional Growth Rate (1 / Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing Starts Across Cohorts ()  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Housing Starts Exponential Growth Rate (1/Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Housing Starts In Each Cohort (House / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Housing Starts Pulse Quantity (Dimensionless*Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Housing Starts Ramp Slope (1/Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Housing Starts Step Height (Dimensionless )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Increase in Area per Year (sf / Year / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Feedback... Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Indicated Fraction of Homes Retrofitting (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Initial Age (House * Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Initial Area (sf)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Initial Average Area of Housing Starts (sf / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Initial Average U Value (kBTU/(Year*sf*F))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Initial Code U Value (kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Initial Cooling Energy Price (Dollar / kBTU)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Initial Fraction of Homes Retrofitting (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Initial Heating Energy Price (Dollar / (kBTU))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Initial Homes Not Retrofitting (House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Initial Homes Retrofitting (Houses)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .Feedback... Initial Housing Starts (House/Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Initial Housing (House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Initial U Value (House * kBTU / (Year * F * sf))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Input (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Input 0 (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Input 1 (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... IRA Actual Subsidy for Heat Pumps (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... IRA Proportional Subsidy Rate for Heat Pumps (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... kBTU per kWH (kBTU / kWH )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Mass Save Proportional Subsidy Rate for Retrofits (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Massachusetts Annual Retrofit Subsidy (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... MassSave Expected Subsidy for Retrofits (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... MassSave Maximum Subsidy for Retrofits (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... MassSave Subsidy for Retrofits Final Year (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Maximum Energy Price (Dollar / kBTU)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Monthly Total Heat Pump Sales (Houses/ Month)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Months per Year (Month / Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... No Turnover Switch (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Noise Correlation Time (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Noise Correlation Time 0 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Noise Correlation Time 1 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Noise Standard Deviation (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Noise Standard Deviation 0 (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Noise Standard Deviation 1 (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Noise Start Time (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Noise Start Time 0 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Noise Start Time 1 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Oil COP TABLE (dmnl)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Optimal Cooling Cost (Dollar / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Optimal Cooling Energy Use (kBTU / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Optimal Energy Cost (Dollar / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Optimal Energy Use (kBTU / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Optimal Heating Cost (Dollar / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Optimal Heating Energy Use (kBTU / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Optimal U Across All Housing (kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Feedback... Optimal U for New Homes (kBTU / (sf * Year * F))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingFeedback... Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Optimal U Value for Existing Homes (kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Peak Cooling Load on Grid (kWH / Day)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Peak Heating Load on Grid (kWH / Day)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Peak Load from Non Heating or Cooling Sources (kWH / Day )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Perceived Cost of Not Retrofitting (Dollar / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Perceived Cost of Retrofitting (Dollar / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Pounds per Ton (lb CO2 / tCO2)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Present Value of Cooling Operating Costs (Dollars / (House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Present Value of Heating Operating Costs (Dollar / (House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Present Value of Operating Costs (Dollar / (House) )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Present Value Replacement Cost (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Proportional IRA Subsidy Switch for Heat Pumps (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Proportional MassSave Subsidy Implementation Year for Retrofits (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Proportional Subsidy Switch for Retrofits (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Pulse Time (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Pulse Time 0 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Pulse Time 1 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Ramp End Time (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Ramp End Time 0 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Ramp End Time 1 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Ramp Start Time (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Ramp Start Time 0 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Ramp Start Time 1 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Reference Retrofit Cost (Dollar / (House * Year) )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v9Feedback... Reference U Value (kBTU / (sf * Year * F) )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Retrofit Delay (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Sensitivity of Affinity to Cost (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Sensitivity of Marginal Cost to U Value (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Sensitivity of Retrofits to Cost (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Sine Amplitude (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Sine Amplitude 0 (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Sine Amplitude 1 (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Sine Period (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Sine Period 0 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Sine Period 1 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Soft Costs of Retrofitting (Dollar / Home)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Step Time (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Step Time 0 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Step Time 1 (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Subsidized Cost of Heat Pumps (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Feedback... Subsidized Retrofit Cost (Dollar /House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... System Switching SWITCH (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Time to Decide to Retrofit (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Area (sf)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Cooling Cost (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Cooling Energy Use (kBTU/ Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Cost of Ownership of Average Home (Dollar / (Year * House))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Energy Use (kBTU / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Heat Pump Sales (House / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Heating Cost (Dollar / Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Heating Energy Use (kBTU/ Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Housing Starts (House/ Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingFeedback... Total Housing Stock (House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Initial Homes (Houses )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Initial Housing Starts (Houses / Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total Present Value of Cost (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total U Value Across All Groupings (House * kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total U Value by Cohort (House * kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... U Value Increase from Source Switching (kBTU*House/(Year*Year*sf*F))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Feedback... U Value of Housing Starts (kBTU / (Year * F * sf))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... U Value of Retrofitting Homes (kBTU / (sf * Year * F))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... U Value Retrofitted Away (House * kBTU / (Year * F * sf))  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Unsubsidized Cost of Heat Pumps (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingFeedback... Unsubsidized Retrofit Cost Intensity (Dollar / sf)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... Unsubsidized Retrofit Cost (Dollar / House)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... Weight on Upfront Cost (dmnl )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... White Noise (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Feedback... White Noise 0 (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Feedback... White Noise 1 (Dimensionless)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlFeedback... FINAL TIME (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlFeedback... INITIAL TIME (Year)  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlFeedback... SAVEPER (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlFeedback... TIME STEP (Year )  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]  0 (  0%)  0 [  0,  0]  0 [  0,  0]NA  0 [  0,  0]


                                                                                                                                                                                                                                                                                                                                                                                                                Top

                                                                                                                                                                                                                                                                                                                                                                                                                Exogenous Variables Analysis (160 Variables + 4 Control Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                Variable Number
                                                                                                                                                                                                                                                                                                                                                                                                                Data Source
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Active Cohort Indicator (dmnl)13 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Aging per Year (Year / Year)2Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Amoritization Period (Year )3Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Average Area of Housing Starts (sf / House)44 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Average Income (Dollar / Hour / House )5Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Average Lifetime of Cooling Technology (Years)61 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Average Lifetime of Heating Technology (Year)7Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Average Time To Consider Switching (Year )8Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous CDD on Coldest Day (F )9Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Cohort Duration (Year )10Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Cooling Degree Days (F )11Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Cooling Emissions Factor (lb CO2 / kBTU)12Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Cooling Energy Price Step Height 1 (Dimensionless )13Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Cooling System Efficiency (dmnl)144 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Cost of Bad Air Conditioning (Dollar / House )15Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Cost of Cooling System Replacement (Dollar / House)161 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Cost of Heating System Replacement (Dollar / House )171 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Days per Year (Day / Year )18Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Delay in Changing Subsidy Expectations (Year )19Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Delay in Forming Expectations of Energy Price (Year )20Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Delay in Forming Expectations of Retrofit Costs (Year )21Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Demolition Hazard Rate (1 / Year )22Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Discount Rate (1 / Year )23Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous EEHIC Maximum Subsidy for Retrofits (Dollar / House )24Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous EEHIC Proportional Subsidy Rate for Retrofits (dmnl )25Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous EEHIC Subsidy for Retrofits Final Year (Year)26Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Effect of Air Leakage from Window AC on Efficiency (dmnl)27Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Energy Price Exponential Growth Rate (1/Year )28Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Energy Price Exponential Growth Rate 1 (1/Year )29Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Energy Price Pulse Quantity (Dimensionless*Year)30Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Energy Price Pulse Quantity 1 (Dimensionless*Year)31Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Energy Price Ramp Slope (1/Year )32Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Energy Price Ramp Slope 1 (1/Year )33Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Energy Price Step Height (Dimensionless )34Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)352 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)363 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Expected Fixed Cost (Dollar / House)372 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)383 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Expected Lump Sum Subsidy Intensity (Dollar / sf)392 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)402 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)413 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)422 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))432 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Expected Subsidy for Heat Pumps (Dollar / House)442 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingExogenous Fixed Cost (Dollar / House )45Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Fractional Decrease in Code U (1 / Year )46Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Gas COP TABLE (dmnl)47Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous HDD on Coldest Day (F )48Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Heat Pump Cooling COP TABLE (dmnl)49Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Heat Pump COP on Coldest Days (dmnl )50Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Heat Pump Heating COP TABLE (dmnl)51Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Heating Degree Days (F )52Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Heating Emissions Factors (lb CO2 / kBTU)53Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Heating System Efficiency (dmnl)544 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Homeowner Hours Spent Retrofitting (Hour )55Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous HOMES Cut Off for Savings (dmnl )56Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous HOMES Expected Higher Subsidy (Dollar / House)572 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous HOMES Expected Lower Lump Sum Subsidy (Dollar / House)582 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous HOMES High Subsidy Amount (Dollar / House )59Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous HOMES Implemented High Subsidy (Dollar / House)604 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous HOMES Implemented Lower Subsidy (Dollar / House)614 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous HOMES Lower Subsidy Amount (Dollar / House )62Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous HOMES Subsidy Final Year (Year)63Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous HOMES Subsidy Implementation Year (Year )64Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Housing Fractional Growth Rate (1 / Year )65Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Housing Starts Exponential Growth Rate (1/Year )66Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Housing Starts Pulse Quantity (Dimensionless*Year)67Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Housing Starts Ramp Slope (1/Year )68Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Housing Starts Step Height (Dimensionless )69Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)704 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)714 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)724 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)734 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)744 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Increase in Area per Year (sf / Year / House )75Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Initial Area (sf)76Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Initial Average Area of Housing Starts (sf / House )77Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Initial Average U Value (kBTU/(Year*sf*F))78Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Initial Code U Value (kBTU / (sf * F * Year))79Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Initial Cooling Energy Price (Dollar / kBTU)80Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Initial Fraction of Homes Retrofitting (dmnl )81Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingExogenous Initial Heating Energy Price (Dollar / (kBTU))82Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingExogenous Initial Homes Not Retrofitting (House)832 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingExogenous Initial Homes Retrofitting (Houses)842 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .Exogenous Initial Housing Starts (House/Year)851 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Initial Housing (House)86Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous IRA Actual Subsidy for Heat Pumps (Dollar / House)873 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)884 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)894 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )90Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )91Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )92Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous IRA Proportional Subsidy Rate for Heat Pumps (dmnl )93Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous kBTU per kWH (kBTU / kWH )94Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Mass Save Proportional Subsidy Rate for Retrofits (dmnl )95Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)962 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)975 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )98Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)99Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )100Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous MassSave Maximum Subsidy for Retrofits (Dollar / House )101Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous MassSave Subsidy for Retrofits Final Year (Year)1021 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Maximum Energy Price (Dollar / kBTU)103Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Months per Year (Month / Year )104Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous No Turnover Switch (dmnl )105Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Noise Correlation Time (Year)106Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Noise Correlation Time 0 (Year)107Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Noise Correlation Time 1 (Year)108Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Noise Standard Deviation (Dimensionless)109Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Noise Standard Deviation 0 (Dimensionless)110Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Noise Standard Deviation 1 (Dimensionless)111Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Noise Start Time (Year)112Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Noise Start Time 0 (Year)113Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Noise Start Time 1 (Year)114Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Oil COP TABLE (dmnl)115Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Peak Load from Non Heating or Cooling Sources (kWH / Day )116Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Pounds per Ton (lb CO2 / tCO2)117Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Present Value Replacement Cost (Dollar / House)1185 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )119Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Proportional IRA Subsidy Switch for Heat Pumps (dmnl )120Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Proportional MassSave Subsidy Implementation Year for Retrofits (Year )121Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Exogenous Proportional Subsidy Switch for Retrofits (dmnl )122Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Pulse Time (Year)123Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Pulse Time 0 (Year)124Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Pulse Time 1 (Year)125Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Ramp End Time (Year)126Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Ramp End Time 0 (Year)127Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Ramp End Time 1 (Year)128Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Ramp Start Time (Year)129Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Ramp Start Time 0 (Year)130Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Ramp Start Time 1 (Year)131Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )132Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingExogenous Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )133Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Reference Retrofit Cost (Dollar / (House * Year) )134Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v9Exogenous Reference U Value (kBTU / (sf * Year * F) )135Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Retrofit Delay (Year )136Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Sensitivity of Affinity to Cost (dmnl )137Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingExogenous Sensitivity of Marginal Cost to U Value (dmnl )138Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Sensitivity of Retrofits to Cost (dmnl )139Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Sine Amplitude (Dimensionless)140Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Sine Amplitude 0 (Dimensionless)141Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Sine Amplitude 1 (Dimensionless)142Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Sine Period (Year)143Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Sine Period 0 (Year)144Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Sine Period 1 (Year)145Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Soft Costs of Retrofitting (Dollar / Home)1462 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Step Time (Year)147Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous Step Time 0 (Year)148Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Step Time 1 (Year)149Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Subsidized Cost of Heat Pumps (Dollar / House)1502 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous System Switching SWITCH (dmnl )151Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Time to Decide to Retrofit (Year )152Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Total Initial Homes (Houses )153Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Total Initial Housing Starts (Houses / Year )154Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)155Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Unsubsidized Cost of Heat Pumps (Dollar / House)1562 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous Weight on Upfront Cost (dmnl )157Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous White Noise (Dimensionless)1583 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Exogenous White Noise 0 (Dimensionless)1593 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Exogenous White Noise 1 (Dimensionless)1603 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlExogenous FINAL TIME (Year)161Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlExogenous INITIAL TIME (Year)162Hardcoded
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlExogenous SAVEPER (Year )1631 Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                .ControlExogenous TIME STEP (Year )164Hardcoded


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                                                                                                                                                                                                                                                                                                                                                                                                                Endogenous Variables Analysis (178 Variables + 0 Control Variables) (Maximum Endogenous Path Length: 5)

                                                                                                                                                                                                                                                                                                                                                                                                                Group
                                                                                                                                                                                                                                                                                                                                                                                                                Type
                                                                                                                                                                                                                                                                                                                                                                                                                Variable
                                                                                                                                                                                                                                                                                                                                                                                                                Variable Number
                                                                                                                                                                                                                                                                                                                                                                                                                Input Links
                                                                                                                                                                                                                                                                                                                                                                                                                Direct Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                Percent Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                Indirect Exogenous
                                                                                                                                                                                                                                                                                                                                                                                                                Indirect Minimum
                                                                                                                                                                                                                                                                                                                                                                                                                Indirect Mean
                                                                                                                                                                                                                                                                                                                                                                                                                Indirect Median
                                                                                                                                                                                                                                                                                                                                                                                                                Indirect Maximum
                                                                                                                                                                                                                                                                                                                                                                                                                Exogenous Unconnected
                                                                                                                                                                                                                                                                                                                                                                                                                Exogenous Connected
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Input (Dimensionless)1151493.3233.503.50415016
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Input 0 (Dimensionless)2151493.3233.503.50415016
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Input 1 (Dimensionless)3151493.3233.503.50415016
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Endogenous Optimal U for New Homes (kBTU / (sf * Year * F))46583.31723.414.00514422
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingEndogenous Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))56583.31923.533.00514224
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))65480.01623.624.00514620
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Actual HOMES Subsidy for Retrofits (Dollar/ Home)74375.02524.165.00513828
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Housing Starts (Houses / Year)84375.01023.303.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))94375.01023.303.50415313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))108675.02223.865.00513828
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous Additional Cost of Building to U Value (Dollar / sf)117571.42423.503.50513729
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Actual EEHIC Subsidy for Retrofits (Dollar / House)123266.71123.273.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Actual MassSave Subsidy for Retrofits (Dollar / House)133266.71123.363.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Affinity of Heating and Cooling Systems (dmnl)143266.7434.004.0051606
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Affinity of Not Retrofitting (dmnl)153266.7122.002.0021633
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingEndogenous Affinity of Retrofitting (dmnl)163266.7524.005.0051597
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Emissions from Cooling by Grouping (tCO2 / (House * Year))173266.71324.385.00515115
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Emissions from Heating by Grouping (tCO2 / (House * Year))183266.71424.295.00515016
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Change in AC Noise (1/Year)193266.7222.002.0021624
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Change in AC Noise 0 (1/Year)203266.7222.002.0021624
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Change in AC Noise 1 (1/Year)213266.7222.002.0021624
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous Cost of Switching Heating and Cooling Systems (Dollar / House)223266.7924.115.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Demolitions (House / Year)233266.71033.703.50515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))243266.71723.594.00414719
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingEndogenous Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))253266.71823.504.00414620
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Present Value of Cost (Dollar / House)263266.71524.405.00514917
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous EEHIC Expected Subsidy for Retrofits (Dollar / House)275360.02223.864.00514125
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous MassSave Expected Subsidy for Retrofits (Dollar / House)285360.02223.914.00514125
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)297457.11933.894.00514323
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)307457.12123.714.00514125
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Aging (House * Year / Year)312150.01233.583.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))322150.01434.294.50515115
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Area of New Homes (sf / Year)332150.01223.173.50515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Cooling Energy Use (kBTU / (Year * House))344250.01924.114.00514521
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Daily Load from Heat Pumps (kBTU / Day)352150.0955.005.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Heating Energy Use (kBTU / (Year * House))364250.02024.004.00514422
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Endogenous Code U (kBTU / (sf * Year * F))372150.0122.002.0021642
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Cooling Energy Price (Dollar / kBTU)382150.01522.332.00515016
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Endogenous Decrease in Code U (kBTU / (sf * Year * F) / Year)392150.0122.002.0021642
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Expected Cooling Energy Price (Dollar / kBTU)402150.01523.073.00515016
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous Expected Heating Energy Price (Dollar / kBTU)412150.01523.073.00515016
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous Expected Subsidy for Retrofits (Dollar / House)426350.03024.034.00513333
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Federal Annual Heat Pump Subsidy (Dollar / Year)432150.0933.563.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingEndogenous Fixed Cost per Unit Area (Dollar / sf)442150.01324.385.00515214
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingEndogenous Heating Energy Price (Dollar / (kBTU))452150.01522.332.00515016
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Houses Considering Switching System (Houses / Year)462150.01133.553.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Initial Age (House * Year)472150.0944.224.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous Initial U Value (House * kBTU / (Year * F * sf))482150.01233.583.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)492150.01034.004.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)502150.0823.253.0051579
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Monthly Total Heat Pump Sales (Houses/ Month)512150.0434.254.5051615
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Optimal Cooling Energy Use (kBTU / (Year * House))524250.02723.934.00513729
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Optimal Heating Energy Use (kBTU / (House * Year))534250.02823.864.00513630
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Perceived Cost of Not Retrofitting (Dollar / (House * Year))542150.00NANANANA1651
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingEndogenous Present Value of Cooling Operating Costs (Dollars / (House))554250.03924.134.00512541
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingEndogenous Present Value of Heating Operating Costs (Dollar / (House))564250.04024.104.00512442
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingEndogenous Unsubsidized Retrofit Cost Intensity (Dollar / sf)576350.02424.465.00513927
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Cooling Energy Use Under Alternatives (kBTU / (House * Year))585240.03123.774.00513333
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Heating Energy Use Under Alternatives (kBTU / (House * Year))595240.03223.724.00513234
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average EUI by Grouping (kBTU / (sf * Year))603133.31834.395.00514719
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))613133.3434.254.5051615
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Fraction of Houses in Each Heating and Cooling System (dmnl)623133.31044.304.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Houses Switching Sources (House / Year)633133.31223.924.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Housing (House)646233.31422.932.50515016
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Net Change in Homes Retrofitting (Houses / Year)653133.31433.794.00515115
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Perceived Cost of Retrofitting (Dollar / (House * Year))663133.3824.254.5051579
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous Subsidized Retrofit Cost (Dollar /House)673133.32323.964.00514224
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Houses Retrofitting per Year (House / Year)684125.02823.613.50513729
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Retrofitting (House * kBTU / (sf * F* Year) / Year)694125.02823.613.50513729
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Area (sf)705120.01233.583.50515313
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Age Removal (House * Year /Year)71200.01123.824.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Annual Federal Subsidies (Dollar / Year)72200.03034.334.00513630
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Annual Heat Pump Subsidy (Dollar / Year)73200.01033.804.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Annual Load from Heat Pumps (kBTU / Year)74100.01744.474.00514917
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Annual MA Subsidies (Dollar / Year)75200.02434.385.00514224
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Annual Retrofit Subsidy (Dollar / Year)76200.02834.394.00513828
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Annual Subsidies (Dollar / Year)77200.02444.795.00514224
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Area Removal (sf /Year)78200.01324.004.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Autocorrelated Noise (Dimensionless)79100.0322.673.0031633
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Autocorrelated Noise 0 (Dimensionless)80100.0322.673.0031633
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Autocorrelated Noise 1 (Dimensionless)81100.0322.673.0031633
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Average Age in All Housing (Year)82200.01134.004.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Average Age (Year)83200.01134.004.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Average Area in All Housing (sf/ House)84200.01334.314.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Area (sf / House)85200.01324.004.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Cooling Cost Across All Homes (Dollar / House/ Year)86200.01733.884.00514917
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Cooling Cost (Dollar / (Year * House))87200.02824.074.00513828
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Cooling Energy Use Across All Homes (kBTU / Year / House)88200.01434.214.00515214
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Emissions (tCO2 / House / Year)89200.01344.464.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Emissions by Grouping (tCO2 / (Year * House))90200.01123.364.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Emissions by Heating and Cooling System (tCO2 / Year / House)91200.01344.464.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Energy Cost (Dollar / (Year * House))92200.03534.635.00513135
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous Average Energy Costs for Retrofitting Home (Dollar / Year / House)93100.01044.705.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Average Energy Costs if Retrofitted (Dollar/(Year*House))94100.01244.755.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Energy Use by Heating and Cooling System (kBTU / (House * Year))95200.01934.004.00514719
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Energy Use in All Housing (kBTU / Year / House)96200.01244.424.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Energy Use (kBTU / (Year * House))97200.01724.005.00514917
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average EUI in All Housing (kBTU / (sf * Year))98200.0844.885.0051588
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Heating Cost Across All Homes (Dollar / Year / House)99200.01833.944.00514818
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingEndogenous Average Heating Cost (Dollar / (Year * House))100200.02924.034.00513729
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Heating Energy Use Across All Homes (kBTU / (Year * House))101200.01534.204.00515115
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Indicated Fraction of Homes Retrofitting (dmnl)102200.01344.314.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average Subsidized Retrofit Cost (Dollar / House)103200.02633.964.00514026
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))104200.01444.364.00515214
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingEndogenous Average U Value in All Housing (kBTU / (sf * F * Year))105200.01244.424.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Cumulative Emissions (tCO2)106100.01055.005.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Cumulative Federal Subsidy (Dollar)107100.01844.895.00514818
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Cumulative MA Subsidy (Dollar)108100.01144.645.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Cumulative Subsidies (Dollar)109200.0555.005.0051615
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Cumulative Subsidies for Heat Pumps (Dollar)110100.0944.675.0051579
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Cumulative Subsidy for Retrofits (Dollar)111100.01544.875.00515115
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Emissions (tCO2 / Year)112100.01544.334.00515115
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Emissions by Grouping (tCO2 / Year)113200.02233.864.00514422
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Emissions by Heating and Cooling System (tCO2 / Year)114100.01544.334.00515115
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Energy Savings (dmnl)115200.02723.894.00513927
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Energy Use by Gas Houses (kBTU/ Year)116100.01744.474.00514917
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Energy Use by Grouping (kBTU / Year)117200.02033.704.00514620
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Energy Use by Heat Pump Houses (kBTU / Year)118100.01744.474.00514917
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Energy Use by Oil Houses (kBTU / Year)119100.01744.474.00514917
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Federal Annual Retrofit Subsidy (Dollar / Year)120300.03123.774.00513531
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v5 testingEndogenous Fraction of Houses Switching (dmnl)121100.0523.604.0051615
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Fraction of Housing by Heating and Cooling System (dmnl)122200.01044.304.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Fraction Retrofitting (dmnl)123100.0755.005.0051597
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Fraction Retrofitting by Cohort (dmnl)124100.01233.583.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Fraction Retrofitting by System and Cohort (dmnl)125100.01233.583.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Houses Retrofitting (Houses)126100.01233.583.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Houses Switching Into Sources (Houses / Year)127100.01024.305.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Housing by Cohort and Heating and Cooling System (Houses)128100.01233.583.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Housing by Cohort and Retrofitting Status (House)129100.01233.583.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Housing by Cohort (House)130100.01233.583.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Housing by Heating and Cooling System (House)131100.01233.583.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Housing by Retrofitting Status (House)132100.01044.304.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Housing Starts Across Cohorts ()133100.0934.335.0051579
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Housing Starts In Each Cohort (House / Year)134100.01023.504.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Endogenous Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)135200.02523.884.00514125
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Indicated Fraction of Homes Retrofitting (dmnl)136200.0422.752.5041624
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Indicated Homes Retrofitting (House)137200.01434.144.00515214
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v15Endogenous Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)138200.03424.415.00513234
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Massachusetts Annual Retrofit Subsidy (Dollar / Year)139200.02724.044.00513927
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Net Age Shift by System (Year * House / Year)140200.01324.154.00515313
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Net Age Shift from Retrofitting Status Shifting (House * Year / Year)141100.0934.785.0051579
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Net Area Shift by System (sf / Year)142200.01524.274.00515115
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Net Area Shift due to Retrofit Status Switching (sf / Year)143100.0834.625.0051588
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Net U Value Change from Retrofitting Home Shifts (House * kBTU / (Year * F * sf) / Year)144200.01624.314.00515016
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Optimal Cooling Cost (Dollar / (Year * House))145200.03123.874.00513531
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Optimal Energy Cost (Dollar / (Year * House))146200.04234.645.00512442
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Optimal Energy Use (kBTU / (House * Year))147200.02023.704.00514620
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Optimal Heating Cost (Dollar / (Year * House))148200.03223.844.00513432
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Optimal U Across All Housing (kBTU / (sf * F * Year))149300.02723.593.00513927
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Optimal U Value for Existing Homes (kBTU / (sf * F * Year))150500.02423.834.00514224
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Peak Cooling Load on Grid (kWH / Day)151100.01823.834.00514818
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Peak Heating Load on Grid (kWH / Day)152100.01723.824.00514917
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Present Value of Operating Costs (Dollar / (House) )153200.04324.515.00512343
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))154100.02424.214.00514224
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Total Age (House * Year)155400.01123.644.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Area (sf)156100.01224.254.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Cooling Cost (Dollar / Year)157200.03034.204.50513630
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Cooling Energy Use (kBTU/ Year)158200.01823.613.00514818
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Cost of Ownership of Average Home (Dollar / (Year * House))159100.0355.005.0051633
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))160200.01124.455.00515511
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Energy Use (kBTU / Year)161100.01744.474.00514917
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Heat Pump Sales (House / Year)162100.01024.305.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Heating Cost (Dollar / Year)163200.03134.194.00513531
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Heating Energy Use (kBTU/ Year)164200.01923.583.00514719
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total Housing Starts (House/ Year)165100.01023.504.00515610
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v4 testingEndogenous Total Housing Stock (House)166100.01233.583.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total U Value Across All Groupings (House * kBTU / (sf * F * Year))167100.0944.785.0051579
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total U Value by Cohort (House * kBTU / (sf * F * Year))168100.02034.455.00514620
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))169100.02034.455.00514620
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous Total U Value (House * kBTU / (Year * F * sf) )170600.02823.894.00513828
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous U Value by Grouping (kBTU / (sf * F * Year))171200.02233.954.00514422
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous U Value Increase from Source Switching (kBTU*House/(Year*Year*sf*F))172100.01234.755.00515412
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)173200.01424.074.00515214
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v18Endogenous U Value of Housing Starts (kBTU / (Year * F * sf))174300.02623.884.00514026
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous U Value of Retrofitting Homes (kBTU / (sf * Year * F))175100.01444.364.00515214
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous U Value Retrofitted Away (House * kBTU / (Year * F * sf))176100.02424.214.00514224
                                                                                                                                                                                                                                                                                                                                                                                                                HeatPumpModel_v31Endogenous U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)177200.01624.064.00515016
                                                                                                                                                                                                                                                                                                                                                                                                                .housingagingchain v8Endogenous Unsubsidized Retrofit Cost (Dollar / House)178200.01924.265.00514719


                                                                                                                                                                                                                                                                                                                                                                                                                Top

                                                                                                                                                                                                                                                                                                                                                                                                                Macros (0 Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Name
                                                                                                                                                                                                                                                                                                                                                                                                                Macro Definition
                                                                                                                                                                                                                                                                                                                                                                                                                Expanded Macro Definition



                                                                                                                                                                                                                                                                                                                                                                                                                Top

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                                                                                                                                                                                                                                                                                                                                                                                                                Positive Polarity Causal Links (432 Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Cause
                                                                                                                                                                                                                                                                                                                                                                                                                Effect
                                                                                                                                                                                                                                                                                                                                                                                                                Polarity
                                                                                                                                                                                                                                                                                                                                                                                                                Active Cohort Indicator Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                Actual EEHIC Subsidy for Retrofits Federal Annual Retrofit Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Actual HOMES Subsidy for Retrofits Federal Annual Retrofit Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Actual MassSave Subsidy for Retrofits Massachusetts Annual Retrofit Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Affinity of Retrofitting Indicated Fraction of Homes Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Aging Total Age+
                                                                                                                                                                                                                                                                                                                                                                                                                Aging per Year Aging+
                                                                                                                                                                                                                                                                                                                                                                                                                Amoritized Subsidized Retrofit Cost Perceived Cost of Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Amoritized Subsidized Retrofit Cost Total Cost of Ownership of Retrofitted Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Federal Subsidies Cumulative Federal Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Heat Pump Subsidy Annual Subsidies+
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Heat Pump Subsidy Cumulative Subsidies for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Load from Heat Pumps Average Daily Load from Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Annual MA Subsidies Cumulative MA Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Retrofit Subsidy Annual Subsidies+
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Retrofit Subsidy Cumulative Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Area Average Area+
                                                                                                                                                                                                                                                                                                                                                                                                                Area Total Area+
                                                                                                                                                                                                                                                                                                                                                                                                                Area of New Homes Area+
                                                                                                                                                                                                                                                                                                                                                                                                                Autocorrelated Noise Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Autocorrelated Noise 0 Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Autocorrelated Noise 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Age Age Removal+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Age Net Age Shift by System+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Area Removal+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Average Cooling Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Average EUI by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Average Heating Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Cooling Energy Use Under Alternatives+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area EEHIC Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Fixed Cost per Unit Area+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Heating Energy Use Under Alternatives+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area MassSave Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Net Area Shift by System+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Optimal Cooling Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Optimal Heating Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Peak Load from Heat Pumps on Coldest Days per Group+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Peak Load from Heat Pumps on Hottest Days per Group+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area U Value at Which EEHIC Cap Binds+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area Unsubsidized Retrofit Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area of Housing Starts Area of New Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Cost Average Energy Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Cost Total Cooling Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Energy Use Average Cooling Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Energy Use Average Emissions from Cooling by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Energy Use Average Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Energy Use Total Cooling Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Emissions by Grouping Emissions by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Emissions from Cooling by Grouping Average Emissions by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Emissions from Heating by Grouping Average Emissions by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Cost Average Energy Costs for Retrofitting Home+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Costs for Retrofitting Home Total Cost of Ownership of Average Home+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Costs if Retrofitted Total Cost of Ownership of Retrofitted Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Use Average EUI by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Use Energy Use by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Use in All Housing Average EUI in All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Cost Average Energy Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Cost Total Heating Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Energy Use Average Emissions from Heating by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Energy Use Average Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Energy Use Average Heating Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Energy Use Total Heating Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Income Soft Costs of Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Lifetime of Cooling Technology Present Value of Cooling Operating Costs+
                                                                                                                                                                                                                                                                                                                                                                                                                Average Lifetime of Heating Technology Present Value of Heating Operating Costs+
                                                                                                                                                                                                                                                                                                                                                                                                                CDD on Coldest Day Peak Load from Heat Pumps on Hottest Days per Group+
                                                                                                                                                                                                                                                                                                                                                                                                                Change in AC Noise Autocorrelated Noise+
                                                                                                                                                                                                                                                                                                                                                                                                                Change in AC Noise 0 Autocorrelated Noise 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Change in AC Noise 1 Autocorrelated Noise 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Code U Additional Cost of Building to U Value+
                                                                                                                                                                                                                                                                                                                                                                                                                Code U Decrease in Code U+
                                                                                                                                                                                                                                                                                                                                                                                                                Code U U Value of Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Degree Days Average Cooling Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Degree Days Cooling Energy Use Under Alternatives+
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Degree Days Marginal Cooling Cost Reduction from Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Degree Days Optimal Cooling Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Emissions Factor Average Emissions from Cooling by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Energy Price Expected Cooling Energy Price+
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Energy Price Step Height 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Energy Use Under Alternatives Present Value of Cooling Operating Costs+
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Bad Air Conditioning Total Present Value of Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Cooling System Replacement Cost of Switching Heating and Cooling Systems+
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Cooling System Replacement Present Value Replacement Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Heating System Replacement Cost of Switching Heating and Cooling Systems+
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Heating System Replacement Present Value Replacement Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Subsidies for Heat Pumps Cumulative Subsidies+
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Subsidy for Retrofits Cumulative Subsidies+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations Expected EEHIC Maximum Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations Expected EEHIC Proportional Subsidy Rate for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations Expected IRA Proportional Subsidy Rate for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations Expected MassSave Maximum Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations Expected MassSave Proportional Subsidy Rate for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations Expected Maximum IRA Proportional Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations HOMES Expected Higher Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations HOMES Expected Lower Lump Sum Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations MassSave Expected Lump Sum Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Forming Expectations of Energy Price Expected Cooling Energy Price+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Forming Expectations of Energy Price Expected Heating Energy Price+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Forming Expectations of Retrofit Costs Expected Fixed Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Forming Expectations of Retrofit Costs Expected Reference Marginal Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Demolition Hazard Rate Demolitions+
                                                                                                                                                                                                                                                                                                                                                                                                                Demolitions Age Removal+
                                                                                                                                                                                                                                                                                                                                                                                                                Demolitions Area Removal+
                                                                                                                                                                                                                                                                                                                                                                                                                Demolitions U Value Loss from Demolition+
                                                                                                                                                                                                                                                                                                                                                                                                                Discount Rate Optimal U for New Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                EEHIC Expected Subsidy for Retrofits Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                EEHIC Maximum Subsidy for Retrofits Implemented EEHIC Maximum Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                EEHIC Proportional Subsidy Rate for Retrofits Implemented EEHIC Subsidy Proportional Rate for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Effect of Air Leakage from Window AC on Efficiency Cooling System Efficiency+
                                                                                                                                                                                                                                                                                                                                                                                                                Emissions Average Emissions+
                                                                                                                                                                                                                                                                                                                                                                                                                Emissions Cumulative Emissions+
                                                                                                                                                                                                                                                                                                                                                                                                                Emissions by Grouping Emissions+
                                                                                                                                                                                                                                                                                                                                                                                                                Emissions by Grouping Emissions by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Emissions by Heating and Cooling System Average Emissions by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Exponential Growth Rate Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Exponential Growth Rate 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Pulse Quantity Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Pulse Quantity 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Ramp Slope Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Ramp Slope 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Step Height Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Grouping Annual Load from Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Grouping Average Energy Use by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Grouping Energy Use by Gas Houses+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Grouping Energy Use by Heat Pump Houses+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Grouping Energy Use by Oil Houses+
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Grouping Total Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Cooling Energy Price Average Cooling Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Cooling Energy Price Marginal Cooling Cost Reduction from Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Cooling Energy Price Optimal Cooling Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Cooling Energy Price Present Value of Cooling Operating Costs+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected EEHIC Maximum Subsidy for Retrofits EEHIC Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected EEHIC Proportional Subsidy Rate for Retrofits EEHIC Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected EEHIC Proportional Subsidy Rate for Retrofits U Value at Which EEHIC Cap Binds+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Fixed Cost Fixed Cost per Unit Area+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Fixed Cost U Value at Which EEHIC Cap Binds+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Heating Energy Price Average Heating Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Heating Energy Price Marginal Heating Cost Reduction from Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Heating Energy Price Optimal Heating Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Heating Energy Price Present Value of Heating Operating Costs+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected IRA Proportional Subsidy Rate for Heat Pumps IRA Expected Proportional Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected MassSave Maximum Subsidy for Retrofits MassSave Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected MassSave Proportional Subsidy Rate for Retrofits Additional Cost of Building to U Value+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected MassSave Proportional Subsidy Rate for Retrofits MassSave Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Maximum IRA Proportional Subsidy for Heat Pumps IRA Expected Proportional Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Reference Marginal Cost Marginal Cost at Binding U Value without EEHIC+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Reference Marginal Cost Optimal U for New Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Reference Marginal Cost Optimal U Value for Existing Homes if no EEHIC Cap+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Reference Marginal Cost Optimal U Value with No EEHIC Proportional Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Reference Marginal Cost U Value at Which EEHIC Cap Binds+
                                                                                                                                                                                                                                                                                                                                                                                                                Federal Annual Heat Pump Subsidy Annual Federal Subsidies+
                                                                                                                                                                                                                                                                                                                                                                                                                Federal Annual Heat Pump Subsidy Annual Heat Pump Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Federal Annual Retrofit Subsidy Annual Federal Subsidies+
                                                                                                                                                                                                                                                                                                                                                                                                                Federal Annual Retrofit Subsidy Annual Retrofit Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                FINAL TIME MassSave Subsidy for Retrofits Final Year+
                                                                                                                                                                                                                                                                                                                                                                                                                Fixed Cost Expected Fixed Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Fixed Cost per Unit Area Unsubsidized Retrofit Cost Intensity+
                                                                                                                                                                                                                                                                                                                                                                                                                Fraction of Houses Switching Houses Switching Sources+
                                                                                                                                                                                                                                                                                                                                                                                                                Fraction Retrofitting by Cohort Area+
                                                                                                                                                                                                                                                                                                                                                                                                                Fractional Decrease in Code U Decrease in Code U+
                                                                                                                                                                                                                                                                                                                                                                                                                Gas COP TABLE Heating System Efficiency+
                                                                                                                                                                                                                                                                                                                                                                                                                HDD on Coldest Day Peak Load from Heat Pumps on Coldest Days per Group+
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump Cooling COP TABLE Cooling System Efficiency+
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump Heating COP TABLE Heating System Efficiency+
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Degree Days Average Heating Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Degree Days Heating Energy Use Under Alternatives+
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Degree Days Marginal Heating Cost Reduction from Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Degree Days Optimal Heating Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Emissions Factors Average Emissions from Heating by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Energy Price Expected Heating Energy Price+
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Energy Use Under Alternatives Present Value of Heating Operating Costs+
                                                                                                                                                                                                                                                                                                                                                                                                                Homeowner Hours Spent Retrofitting Soft Costs of Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Expected Higher Subsidy Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Expected Lower Lump Sum Subsidy Expected Lump Sum Subsidy Intensity+
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Expected Lower Lump Sum Subsidy Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES High Subsidy Amount HOMES Implemented High Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Implemented High Subsidy Actual HOMES Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Implemented High Subsidy HOMES Expected Higher Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Implemented Lower Subsidy Actual HOMES Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Implemented Lower Subsidy HOMES Expected Lower Lump Sum Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Lower Subsidy Amount HOMES Implemented Lower Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Considering Switching System Houses Switching Sources+
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Retrofitting per Year Federal Annual Retrofit Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Retrofitting per Year Massachusetts Annual Retrofit Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Switching Into Sources Average U Value of Houses Switching Into Sources+
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Switching Sources Houses Switching Into Sources+
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Switching Sources Total Heat Pump Sales+
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Switching Sources U Value Shift from Source Switching+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Aging+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Average Energy Use by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Average Heating Cost Across All Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Demolitions+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Emissions by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Energy Use by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Fraction Retrofitting by Cohort+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Fraction Retrofitting by System and Cohort+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Houses Considering Switching System+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Houses Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Houses Retrofitting per Year+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Housing by Cohort+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Housing by Cohort and Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Housing by Cohort and Retrofitting Status+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Housing by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Initial U Value+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Optimal U Across All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Peak Load from Heat Pumps on Coldest Days per Group+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Peak Load from Heat Pumps on Hottest Days per Group+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Total Cooling Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Total Cooling Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Total Heating Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Total Heating Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Total Housing Stock+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Cohort and Heating and Cooling System Indicated Homes Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Cohort and Retrofitting Status Average Age+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Cohort and Retrofitting Status Average Area+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Cohort and Retrofitting Status Housing by Retrofitting Status+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Heating and Cooling System Average Emissions by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Heating and Cooling System Average U Value by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Heating and Cooling System Fraction of Houses in Each Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Heating and Cooling System Fraction of Housing by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Fractional Growth Rate Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Area of New Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Housing Starts In Each Cohort+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Increase in U Value from Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Total Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Exponential Growth Rate Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts In Each Cohort Housing Starts Across Cohorts+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Pulse Quantity Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Ramp Slope Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Step Height Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented EEHIC Maximum Subsidy for Retrofits Actual EEHIC Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented EEHIC Maximum Subsidy for Retrofits Expected EEHIC Maximum Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented EEHIC Subsidy Proportional Rate for Retrofits Actual EEHIC Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented EEHIC Subsidy Proportional Rate for Retrofits Expected EEHIC Proportional Subsidy Rate for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented IRA Maximum Proportional Subsidy for Heat Pumps Expected Maximum IRA Proportional Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented IRA Maximum Proportional Subsidy for Heat Pumps IRA Actual Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented MassSave Maximum Subsidy for Retrofits Actual MassSave Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented MassSave Maximum Subsidy for Retrofits Expected MassSave Maximum Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented MassSave Subsidy Proportional Rate for Retrofits Actual MassSave Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented MassSave Subsidy Proportional Rate for Retrofits Expected MassSave Proportional Subsidy Rate for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Increase in U Value from Housing Starts Total U Value+
                                                                                                                                                                                                                                                                                                                                                                                                                Indicated Fraction of Homes Retrofitting Indicated Homes Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Indicated Homes Retrofitting Average Indicated Fraction of Homes Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Indicated Homes Retrofitting Net Change in Homes Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Age Total Age+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Area Area+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Average Area of Housing Starts Average Area of Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Average U Value Initial U Value+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Code U Value Code U+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Cooling Energy Price Cooling Energy Price+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Fraction of Homes Retrofitting Initial Homes Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Heating Energy Price Heating Energy Price+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Homes Not Retrofitting Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Homes Retrofitting Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Housing Initial Homes Not Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Housing Initial Homes Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Initial U Value Total U Value+
                                                                                                                                                                                                                                                                                                                                                                                                                Input 0 Heating Energy Price+
                                                                                                                                                                                                                                                                                                                                                                                                                Input 1 Cooling Energy Price+
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Actual Subsidy for Heat Pumps Federal Annual Heat Pump Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Expected Proportional Subsidy for Heat Pumps Expected Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Implemented Subsidy Proportional Rate for Heat Pumps Expected IRA Proportional Subsidy Rate for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Implemented Subsidy Proportional Rate for Heat Pumps IRA Actual Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Maximum Proportional Subsidy for Heat Pumps Implemented IRA Maximum Proportional Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Proportional Subsidy Rate for Heat Pumps IRA Implemented Subsidy Proportional Rate for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Marginal Cooling Cost Reduction from Retrofitting Marginal Cost Reductions from Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Marginal Cost Reductions from Retrofitting Lifetime Marginal Cost Reductions from Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Marginal Heating Cost Reduction from Retrofitting Marginal Cost Reductions from Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Mass Save Proportional Subsidy Rate for Retrofits Implemented MassSave Subsidy Proportional Rate for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Massachusetts Annual Heat Pumps Subsidy Annual Heat Pump Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Massachusetts Annual Heat Pumps Subsidy Annual MA Subsidies+
                                                                                                                                                                                                                                                                                                                                                                                                                Massachusetts Annual Retrofit Subsidy Annual MA Subsidies+
                                                                                                                                                                                                                                                                                                                                                                                                                Massachusetts Annual Retrofit Subsidy Annual Retrofit Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Expected Lump Sum Subsidy for Heat Pumps Expected Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Expected Subsidy for Retrofits Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Implemented Lump Sum Subsidy for Heat Pumps Massachusetts Annual Heat Pumps Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Implemented Lump Sum Subsidy for Heat Pumps MassSave Expected Lump Sum Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Lump Sum Subsidy Amount for Heat Pumps MassSave Implemented Lump Sum Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Maximum Subsidy for Retrofits Implemented MassSave Maximum Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                NAREPLACEMENT Average EUI by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                NAREPLACEMENT Average Lifetime of Cooling Technology+
                                                                                                                                                                                                                                                                                                                                                                                                                NAREPLACEMENT Average U Value of Houses Switching Into Sources+
                                                                                                                                                                                                                                                                                                                                                                                                                NAREPLACEMENT Cooling System Efficiency+
                                                                                                                                                                                                                                                                                                                                                                                                                NAREPLACEMENT Fraction of Houses in Each Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Net Age Shift by System Net Age Shift from Retrofitting Status Shifting+
                                                                                                                                                                                                                                                                                                                                                                                                                Net Area Shift by System Net Area Shift due to Retrofit Status Switching+
                                                                                                                                                                                                                                                                                                                                                                                                                Net Area Shift due to Retrofit Status Switching Area+
                                                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting Net Age Shift by System+
                                                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting Net Area Shift by System+
                                                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting Net U Value Change from Retrofitting Home Shifts+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Correlation Time Change in AC Noise+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Correlation Time White Noise+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Correlation Time 0 Change in AC Noise 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Correlation Time 0 White Noise 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Correlation Time 1 Change in AC Noise 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Correlation Time 1 White Noise 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Standard Deviation White Noise+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Standard Deviation 0 White Noise 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Standard Deviation 1 White Noise 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Start Time Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Start Time 0 Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Start Time 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Oil COP TABLE Heating System Efficiency+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Cost Optimal Energy Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use Optimal Cooling Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use Optimal Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Energy Cost Average Energy Costs if Retrofitted+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Heating Cost Optimal Energy Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Heating Energy Use Optimal Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Heating Energy Use Optimal Heating Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U for New Homes U Value of Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap Cooling Energy Use Under Alternatives+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap Energy Savings+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap Heating Energy Use Under Alternatives+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap Optimal Cooling Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap Optimal Heating Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Across All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap Optimal U Value for Existing Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value with No EEHIC Proportional Subsidy Optimal U Value for Existing Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Peak Load from Heat Pumps on Coldest Days per Group Peak Heating Load on Grid+
                                                                                                                                                                                                                                                                                                                                                                                                                Peak Load from Heat Pumps on Hottest Days per Group Peak Cooling Load on Grid+
                                                                                                                                                                                                                                                                                                                                                                                                                Present Value of Cooling Operating Costs Present Value of Operating Costs+
                                                                                                                                                                                                                                                                                                                                                                                                                Present Value of Heating Operating Costs Present Value of Operating Costs+
                                                                                                                                                                                                                                                                                                                                                                                                                Present Value of Operating Costs Total Present Value of Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Present Value Replacement Cost Total Present Value of Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional IRA Subsidy Switch for Heat Pumps Expected IRA Proportional Subsidy Rate for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional IRA Subsidy Switch for Heat Pumps IRA Expected Proportional Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional Subsidy Switch for Retrofits EEHIC Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional Subsidy Switch for Retrofits Expected EEHIC Proportional Subsidy Rate for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional Subsidy Switch for Retrofits Expected MassSave Proportional Subsidy Rate for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional Subsidy Switch for Retrofits MassSave Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Pulse Time Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Pulse Time 0 Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Pulse Time 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp End Time Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp End Time 0 Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp End Time 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp Start Time Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp Start Time 0 Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp Start Time 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Reference Lifetime Cost of Heating and Cooling Systems Affinity of Heating and Cooling Systems+
                                                                                                                                                                                                                                                                                                                                                                                                                Reference Marginal Cost Expected Reference Marginal Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Reference Retrofit Cost Affinity of Not Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Reference Retrofit Cost Affinity of Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Reference U Value Marginal Cost at Binding U Value without EEHIC+
                                                                                                                                                                                                                                                                                                                                                                                                                Reference U Value Optimal U for New Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Reference U Value Optimal U Value for Existing Homes if no EEHIC Cap+
                                                                                                                                                                                                                                                                                                                                                                                                                Reference U Value Optimal U Value with No EEHIC Proportional Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofit Delay Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofitting Retrofitting Across Cohorts and Systems+
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofitting U Value Retrofitted Away+
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Marginal Cost to U Value Additional Cost of Building to U Value+
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Marginal Cost to U Value Optimal U for New Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Marginal Cost to U Value Optimal U Value for Existing Homes if no EEHIC Cap+
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Marginal Cost to U Value Optimal U Value with No EEHIC Proportional Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Amplitude 0 Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Amplitude 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Soft Costs of Retrofitting Subsidized Retrofit Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Step Time Input+
                                                                                                                                                                                                                                                                                                                                                                                                                Step Time 0 Input 0+
                                                                                                                                                                                                                                                                                                                                                                                                                Step Time 1 Input 1+
                                                                                                                                                                                                                                                                                                                                                                                                                Subsidized Cost of Heat Pumps Cost of Cooling System Replacement+
                                                                                                                                                                                                                                                                                                                                                                                                                Subsidized Cost of Heat Pumps Cost of Heating System Replacement+
                                                                                                                                                                                                                                                                                                                                                                                                                Subsidized Retrofit Cost Amoritized Subsidized Retrofit Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Subsidized Retrofit Cost Average Subsidized Retrofit Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                System Switching SWITCH Houses Switching Sources+
                                                                                                                                                                                                                                                                                                                                                                                                                Time Average Area of Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                Time Cooling System Efficiency+
                                                                                                                                                                                                                                                                                                                                                                                                                Time Heating System Efficiency+
                                                                                                                                                                                                                                                                                                                                                                                                                TIME STEP SAVEPER+
                                                                                                                                                                                                                                                                                                                                                                                                                Time to Decide to Retrofit Net Change in Homes Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Age Average Age+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Age Average Age in All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Area Average Area in All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Cooling Cost Average Cooling Cost Across All Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Cooling Energy Use Average Cooling Energy Use Across All Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Cost of Ownership of Average Home Perceived Cost of Not Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Cost of Ownership of Retrofitted Homes Perceived Cost of Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Energy Use Average Energy Use in All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Heat Pump Sales Federal Annual Heat Pump Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Heat Pump Sales Massachusetts Annual Heat Pumps Subsidy+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Heat Pump Sales Monthly Total Heat Pump Sales+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Heating Cost Average Heating Cost Across All Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Heating Energy Use Average Heating Energy Use Across All Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Average Age in All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Average Area in All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Average Cooling Energy Use Across All Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Average Emissions+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Average Heating Energy Use Across All Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Average U Value in All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Fraction of Houses in Each Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Total Present Value of Cost Cost of Switching Heating and Cooling Systems+
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value Total U Value by Cohort+
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value Total U Value by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value U Value by Grouping+
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value Across All Groupings Average U Value in All Housing+
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value by Cohort Total U Value Across All Groupings+
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value by Heating and Cooling System Average U Value by Heating and Cooling System+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value at Which EEHIC Cap Binds Marginal Cost at Binding U Value without EEHIC+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value at Which EEHIC Cap Binds Optimal U Value for Existing Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Average Cooling Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Average Heating Energy Use+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Cooling Energy Use Under Alternatives+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Energy Savings+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Heating Energy Use Under Alternatives+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Net U Value Change from Retrofitting Home Shifts+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Peak Load from Heat Pumps on Coldest Days per Group+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Peak Load from Heat Pumps on Hottest Days per Group+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping U Value Loss from Demolition+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping U Value of Retrofitting Homes+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping U Value Shift from Source Switching+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value Increase from Source Switching Average U Value of Houses Switching Into Sources+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value of Housing Starts Increase in U Value from Housing Starts+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value of Retrofitting Homes U Value at Which EEHIC Cap Binds+
                                                                                                                                                                                                                                                                                                                                                                                                                U Value Shift from Source Switching U Value Increase from Source Switching+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Cost of Heat Pumps IRA Actual Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Cost of Heat Pumps IRA Expected Proportional Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Cost of Heat Pumps MassSave Implemented Lump Sum Subsidy for Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Cost of Heat Pumps Subsidized Cost of Heat Pumps+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Retrofit Cost Actual EEHIC Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Retrofit Cost Actual MassSave Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Retrofit Cost Subsidized Retrofit Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Retrofit Cost Intensity EEHIC Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Retrofit Cost Intensity MassSave Expected Subsidy for Retrofits+
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Retrofit Cost Intensity Unsubsidized Retrofit Cost+
                                                                                                                                                                                                                                                                                                                                                                                                                Weight on Upfront Cost Perceived Cost of Retrofitting+
                                                                                                                                                                                                                                                                                                                                                                                                                White Noise Change in AC Noise+
                                                                                                                                                                                                                                                                                                                                                                                                                White Noise 0 Change in AC Noise 0+
                                                                                                                                                                                                                                                                                                                                                                                                                White Noise 1 Change in AC Noise 1+



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                                                                                                                                                                                                                                                                                                                                                                                                                Negative Polarity Causal Links (87 Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Cause
                                                                                                                                                                                                                                                                                                                                                                                                                Effect
                                                                                                                                                                                                                                                                                                                                                                                                                Polarity
                                                                                                                                                                                                                                                                                                                                                                                                                Affinity of Not Retrofitting Indicated Fraction of Homes Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Age Removal Total Age-
                                                                                                                                                                                                                                                                                                                                                                                                                Amoritization Period Amoritized Subsidized Retrofit Cost-
                                                                                                                                                                                                                                                                                                                                                                                                                Area Removal Area-
                                                                                                                                                                                                                                                                                                                                                                                                                Autocorrelated Noise Change in AC Noise-
                                                                                                                                                                                                                                                                                                                                                                                                                Autocorrelated Noise 0 Change in AC Noise 0-
                                                                                                                                                                                                                                                                                                                                                                                                                Autocorrelated Noise 1 Change in AC Noise 1-
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area in All Housing Average EUI in All Housing-
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area of Housing Starts Expected Lump Sum Subsidy Intensity-
                                                                                                                                                                                                                                                                                                                                                                                                                Average Lifetime of Cooling Technology Present Value Replacement Cost-
                                                                                                                                                                                                                                                                                                                                                                                                                Average Lifetime of Heating Technology Present Value Replacement Cost-
                                                                                                                                                                                                                                                                                                                                                                                                                Average Time To Consider Switching Houses Considering Switching System-
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling System Efficiency Average Cooling Energy Use-
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling System Efficiency Cooling Energy Use Under Alternatives-
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling System Efficiency Marginal Cooling Cost Reduction from Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling System Efficiency Optimal Cooling Energy Use-
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling System Efficiency Peak Load from Heat Pumps on Hottest Days per Group-
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Switching Heating and Cooling Systems Affinity of Heating and Cooling Systems-
                                                                                                                                                                                                                                                                                                                                                                                                                Days per Year Average Daily Load from Heat Pumps-
                                                                                                                                                                                                                                                                                                                                                                                                                Days per Year Peak Load from Heat Pumps on Coldest Days per Group-
                                                                                                                                                                                                                                                                                                                                                                                                                Days per Year Peak Load from Heat Pumps on Hottest Days per Group-
                                                                                                                                                                                                                                                                                                                                                                                                                Decrease in Code U Code U-
                                                                                                                                                                                                                                                                                                                                                                                                                Demolitions Housing-
                                                                                                                                                                                                                                                                                                                                                                                                                Discount Rate Lifetime Marginal Cost Reductions from Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Discount Rate Present Value of Cooling Operating Costs-
                                                                                                                                                                                                                                                                                                                                                                                                                Discount Rate Present Value of Heating Operating Costs-
                                                                                                                                                                                                                                                                                                                                                                                                                Discount Rate Present Value Replacement Cost-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected EEHIC Maximum Subsidy for Retrofits U Value at Which EEHIC Cap Binds-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected EEHIC Proportional Subsidy Rate for Retrofits Optimal U Value for Existing Homes if no EEHIC Cap-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Lump Sum Subsidy Intensity Additional Cost of Building to U Value-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected MassSave Proportional Subsidy Rate for Retrofits Optimal U for New Homes-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected MassSave Proportional Subsidy Rate for Retrofits Optimal U Value for Existing Homes if no EEHIC Cap-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected MassSave Proportional Subsidy Rate for Retrofits Optimal U Value with No EEHIC Proportional Subsidy-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Reference Marginal Cost Additional Cost of Building to U Value-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Reference Marginal Cost Unsubsidized Retrofit Cost Intensity-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Subsidy for Heat Pumps Subsidized Cost of Heat Pumps-
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Subsidy for Retrofits Subsidized Retrofit Cost-
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump COP on Coldest Days Peak Load from Heat Pumps on Coldest Days per Group-
                                                                                                                                                                                                                                                                                                                                                                                                                Heating System Efficiency Average Heating Energy Use-
                                                                                                                                                                                                                                                                                                                                                                                                                Heating System Efficiency Heating Energy Use Under Alternatives-
                                                                                                                                                                                                                                                                                                                                                                                                                Heating System Efficiency Marginal Heating Cost Reduction from Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Heating System Efficiency Optimal Heating Energy Use-
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Average Cooling Cost Across All Homes-
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Net Change in Homes Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Housing U Value by Grouping-
                                                                                                                                                                                                                                                                                                                                                                                                                Increase in Area per Year Average Area of Housing Starts-
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Fraction of Homes Retrofitting Initial Homes Not Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                INITIAL TIME Average Area of Housing Starts-
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU per kWH Peak Load from Heat Pumps on Coldest Days per Group-
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU per kWH Peak Load from Heat Pumps on Hottest Days per Group-
                                                                                                                                                                                                                                                                                                                                                                                                                Lifetime Marginal Cost Reductions from Retrofitting Optimal U Value for Existing Homes if no EEHIC Cap-
                                                                                                                                                                                                                                                                                                                                                                                                                Lifetime Marginal Cost Reductions from Retrofitting Optimal U Value with No EEHIC Proportional Subsidy-
                                                                                                                                                                                                                                                                                                                                                                                                                Marginal Cost Reductions from Retrofitting Optimal U for New Homes-
                                                                                                                                                                                                                                                                                                                                                                                                                Months per Year Monthly Total Heat Pump Sales-
                                                                                                                                                                                                                                                                                                                                                                                                                No Turnover Switch Demolitions-
                                                                                                                                                                                                                                                                                                                                                                                                                No Turnover Switch Housing Starts-
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U for New Homes Additional Cost of Building to U Value-
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes Unsubsidized Retrofit Cost Intensity-
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Perceived Cost of Not Retrofitting Affinity of Not Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Perceived Cost of Retrofitting Affinity of Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Pounds per Ton Average Emissions from Cooling by Grouping-
                                                                                                                                                                                                                                                                                                                                                                                                                Pounds per Ton Average Emissions from Heating by Grouping-
                                                                                                                                                                                                                                                                                                                                                                                                                Reference U Value Additional Cost of Building to U Value-
                                                                                                                                                                                                                                                                                                                                                                                                                Reference U Value U Value at Which EEHIC Cap Binds-
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofit Delay Houses Retrofitting per Year-
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofitting Total U Value-
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Affinity to Cost Affinity of Heating and Cooling Systems-
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Marginal Cost to U Value Marginal Cost at Binding U Value without EEHIC-
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Marginal Cost to U Value U Value at Which EEHIC Cap Binds-
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Marginal Cost to U Value Unsubsidized Retrofit Cost Intensity-
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Retrofits to Cost Affinity of Not Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Retrofits to Cost Affinity of Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Amplitude Input-
                                                                                                                                                                                                                                                                                                                                                                                                                Time Unsubsidized Cost of Heat Pumps-
                                                                                                                                                                                                                                                                                                                                                                                                                TIME STEP White Noise-
                                                                                                                                                                                                                                                                                                                                                                                                                TIME STEP White Noise 0-
                                                                                                                                                                                                                                                                                                                                                                                                                TIME STEP White Noise 1-
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Average Energy Use in All Housing-
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Average Indicated Fraction of Homes Retrofitting-
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Fraction of Housing by Heating and Cooling System-
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock Optimal U Across All Housing-
                                                                                                                                                                                                                                                                                                                                                                                                                U Value Loss from Demolition Total U Value-
                                                                                                                                                                                                                                                                                                                                                                                                                U Value of Retrofitting Homes Unsubsidized Retrofit Cost Intensity-
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Cost of Heat Pump Over Time TABLE Unsubsidized Cost of Heat Pumps-
                                                                                                                                                                                                                                                                                                                                                                                                                Weight on Upfront Cost Perceived Cost of Not Retrofitting-



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                                                                                                                                                                                                                                                                                                                                                                                                                Function-based Polarity Causal Links (67 Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Cause
                                                                                                                                                                                                                                                                                                                                                                                                                Effect
                                                                                                                                                                                                                                                                                                                                                                                                                Polarity
                                                                                                                                                                                                                                                                                                                                                                                                                Additional Cost of Building to U Value U Value of Housing StartsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Affinity of Heating and Cooling Systems Fraction of Houses SwitchingInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Cohort Active Cohort IndicatorFunction[IFTHENELSE,INTEGER,ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                Cohort Duration Active Cohort IndicatorFunction[IFTHENELSE,INTEGER,ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                Cohort Duration Initial AgeFunction[ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                EEHIC Subsidy for Retrofits Final Year Implemented EEHIC Maximum Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                EEHIC Subsidy for Retrofits Final Year Implemented EEHIC Subsidy Proportional Rate for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Savings Actual HOMES Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Savings Expected Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Heating and Cooling System Initial Housing StartsFunction[ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Cut Off for Savings Actual HOMES Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Cut Off for Savings Expected Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Subsidy Final Year HOMES Implemented High SubsidyIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Subsidy Final Year HOMES Implemented Lower SubsidyIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Subsidy Implementation Year HOMES Implemented High SubsidyIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Subsidy Implementation Year HOMES Implemented Lower SubsidyIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Switching Sources HousingInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Average Subsidized Retrofit CostInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Cohort and Retrofitting Status Initial AgeFunction[ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Retrofitting Status Fraction RetrofittingInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                INITIAL TIME Active Cohort IndicatorFunction[IFTHENELSE,INTEGER,ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                INITIAL TIME InputInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                INITIAL TIME Input 0Inconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                INITIAL TIME Input 1Inconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Lump Sum Subsidy for Heat Pumps Final Year Implemented IRA Maximum Proportional Subsidy for Heat PumpsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Lump Sum Subsidy for Heat Pumps Final Year IRA Implemented Subsidy Proportional Rate for Heat PumpsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Proportional Subsidy Implementation Year for Heat Pumps Implemented IRA Maximum Proportional Subsidy for Heat PumpsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Proportional Subsidy Implementation Year for Heat Pumps IRA Implemented Subsidy Proportional Rate for Heat PumpsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Lifetime Marginal Cost Reductions from Retrofitting Optimal U Value for Existing HomesIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Marginal Cost at Binding U Value without EEHIC Optimal U Value for Existing HomesIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Lump Sum Subsidy for Heat Pumps Final Year MassSave Implemented Lump Sum Subsidy for Heat PumpsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Lump Sum Subsidy Implementation Year for Heat Pumps MassSave Implemented Lump Sum Subsidy for Heat PumpsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Subsidy for Retrofits Final Year Implemented MassSave Maximum Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Subsidy for Retrofits Final Year Implemented MassSave Subsidy Proportional Rate for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Net Age Shift from Retrofitting Status Shifting Total AgeInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting HousingInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Net U Value Change from Retrofitting Home Shifts Total U ValueInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap Houses Retrofitting per YearIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Preexisting Cohorts Active Cohort IndicatorFunction[IFTHENELSE,INTEGER,ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                Preexisting Cohorts Initial AgeFunction[ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional EEHIC Subsidy Implementation Year for Retrofits Implemented EEHIC Maximum Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional EEHIC Subsidy Implementation Year for Retrofits Implemented EEHIC Subsidy Proportional Rate for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional MassSave Subsidy Implementation Year for Retrofits Implemented MassSave Maximum Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional MassSave Subsidy Implementation Year for Retrofits Implemented MassSave Subsidy Proportional Rate for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Reference U Value Unsubsidized Retrofit Cost IntensityInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Period InputInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Period 0 Input 0Inconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Period 1 Input 1Inconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Time Active Cohort IndicatorFunction[IFTHENELSE,INTEGER,ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                Time HOMES Implemented High SubsidyIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Time HOMES Implemented Lower SubsidyIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Time Implemented EEHIC Maximum Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Time Implemented EEHIC Subsidy Proportional Rate for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Time Implemented IRA Maximum Proportional Subsidy for Heat PumpsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Time Implemented MassSave Maximum Subsidy for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Time Implemented MassSave Subsidy Proportional Rate for RetrofitsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Time InputInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Time Input 0Inconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Time Input 1Inconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Time IRA Implemented Subsidy Proportional Rate for Heat PumpsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                Time MassSave Implemented Lump Sum Subsidy for Heat PumpsIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                TIME STEP InputInconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                TIME STEP Input 0Inconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                TIME STEP Input 1Inconsistent
                                                                                                                                                                                                                                                                                                                                                                                                                Total Initial Housing Starts Initial Housing StartsFunction[ELMCOUNT]
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping Houses Retrofitting per YearIf Then Else Switch
                                                                                                                                                                                                                                                                                                                                                                                                                U Value Shift from Source Switching Total U ValueInconsistent



                                                                                                                                                                                                                                                                                                                                                                                                                Top

                                                                                                                                                                                                                                                                                                                                                                                                                Rate-to-rate Links (7 Variables)

                                                                                                                                                                                                                                                                                                                                                                                                                Cause
                                                                                                                                                                                                                                                                                                                                                                                                                Effect
                                                                                                                                                                                                                                                                                                                                                                                                                Demolitions Age Removal
                                                                                                                                                                                                                                                                                                                                                                                                                Demolitions Area Removal
                                                                                                                                                                                                                                                                                                                                                                                                                Demolitions U Value Loss from Demolition
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Switching Sources U Value Shift from Source Switching
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Area of New Homes
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Increase in U Value from Housing Starts
                                                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting Net U Value Change from Retrofitting Home Shifts



                                                                                                                                                                                                                                                                                                                                                                                                                Top

                                                                                                                                                                                                                                                                                                                                                                                                                View-Variable Profile

                                                                                                                                                                                                                                                                                                                                                                                                                View
                                                                                                                                                                                                                                                                                                                                                                                                                View-Variable Profile
                                                                                                                                                                                                                                                                                                                                                                                                                Not in View   2Variables (0.6%)
                                                                                                                                                                                                                                                                                                                                                                                                                Age         14Variables (3.9%)
                                                                                                                                                                                                                                                                                                                                                                                                                Area           18Variables (5%)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Attributes                                     64Variables (17.6%)
                                                                                                                                                                                                                                                                                                                                                                                                                Average and Peak Load           17Variables (4.7%)
                                                                                                                                                                                                                                                                                                                                                                                                                Carbon Emissions         13Variables (3.6%)
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Subsidies                       39Variables (10.7%)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use                 28Variables (7.7%)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Aging Chain & U Coflows                                       68Variables (18.7%)
                                                                                                                                                                                                                                                                                                                                                                                                                Input Test                                   59Variables (16.3%)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U & Retrofit Costs                         42Variables (11.6%)
                                                                                                                                                                                                                                                                                                                                                                                                                Perceived Subsidies & Costs                                     64Variables (17.6%)
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofitting Decision Making               23Variables (6.3%)
                                                                                                                                                                                                                                                                                                                                                                                                                Social Influence in Retrofitting Decisions   1Variables (0.3%)
                                                                                                                                                                                                                                                                                                                                                                                                                Switching Systems                     34Variables (9.4%)
                                                                                                                                                                                                                                                                                                                                                                                                                U Value of Housing Starts           18Variables (5%)

                                                                                                                                                                                                                                                                                                                                                                                                                Top

                                                                                                                                                                                                                                                                                                                                                                                                                List Of 16 views and their 342 Variables

                                                                                                                                                                                                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                                                                                                                                                                                                Not in View
                                                                                                                                                                                                                                                                                                                                                                                                                Age
                                                                                                                                                                                                                                                                                                                                                                                                                Area
                                                                                                                                                                                                                                                                                                                                                                                                                Average Attributes
                                                                                                                                                                                                                                                                                                                                                                                                                Average and Peak Load
                                                                                                                                                                                                                                                                                                                                                                                                                Carbon Emissions
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Subsidies
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Aging Chain & U Coflows
                                                                                                                                                                                                                                                                                                                                                                                                                Input Test
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U & Retrofit Costs
                                                                                                                                                                                                                                                                                                                                                                                                                Perceived Subsidies & Costs
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofitting Decision Making
                                                                                                                                                                                                                                                                                                                                                                                                                Social Influence in Retrofitting Decisions
                                                                                                                                                                                                                                                                                                                                                                                                                Switching Systems
                                                                                                                                                                                                                                                                                                                                                                                                                U Value of Housing Starts
                                                                                                                                                                                                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                                                                                                                                                                                                Total: 2 14 18 64 17 13 39 28 68 59 42 64 23 1 34 18 Total:
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Bad Air Conditioning (In 1 View)                                   Cost of Bad Air Conditioning (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Present Value Replacement Cost (In 1 View)                                   Present Value Replacement Cost (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Energy Use Under Alternatives (In 1 View)                                   Cooling Energy Use Under Alternatives (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Heat Pump Sales (In 3 Views)                                       Total Heat Pump Sales (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling System Efficiency (In 4 Views)                                         Cooling System Efficiency (In 4 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Subsidized Cost of Heat Pumps (In 1 View)                                   Subsidized Cost of Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Cooling System Replacement (In 1 View)                                   Cost of Cooling System Replacement (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Heating System Replacement (In 1 View)                                   Cost of Heating System Replacement (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Cost of Heat Pumps (In 3 Views)                                       Unsubsidized Cost of Heat Pumps (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Subsidy for Heat Pumps (In 2 Views)                                     Expected Subsidy for Heat Pumps (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Cost of Heat Pump Over Time TABLE (In 1 View)                                   Unsubsidized Cost of Heat Pump Over Time TABLE (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Heating System Efficiency (In 3 Views)                                       Heating System Efficiency (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Energy Use Under Alternatives (In 1 View)                                   Heating Energy Use Under Alternatives (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area (In 7 Views)                                               Average Area (In 7 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Lifetime of Cooling Technology (In 1 View)                                   Average Lifetime of Cooling Technology (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Degree Days (In 3 Views)                                       Cooling Degree Days (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                U Value by Grouping (In 8 Views)                                                 U Value by Grouping (In 8 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Present Value of Operating Costs (In 1 View)                                   Present Value of Operating Costs (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Degree Days (In 3 Views)                                       Heating Degree Days (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Cooling Energy Price (In 4 Views)                                         Expected Cooling Energy Price (In 4 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Present Value of Cost (In 1 View)                                   Total Present Value of Cost (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Affinity of Heating and Cooling Systems (In 1 View)                                   Affinity of Heating and Cooling Systems (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Reference Lifetime Cost of Heating and Cooling Systems (In 1 View)                                   Reference Lifetime Cost of Heating and Cooling Systems (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Discount Rate (In 4 Views)                                         Discount Rate (In 4 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Lifetime of Heating Technology (In 1 View)                                   Average Lifetime of Heating Technology (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Affinity to Cost (In 1 View)                                   Sensitivity of Affinity to Cost (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Time To Consider Switching (In 2 Views)                                     Average Time To Consider Switching (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Cost of Switching Heating and Cooling Systems (In 1 View)                                   Cost of Switching Heating and Cooling Systems (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Heating Energy Price (In 6 Views)                                             Expected Heating Energy Price (In 6 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Present Value of Cooling Operating Costs (In 1 View)                                   Present Value of Cooling Operating Costs (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Fraction of Houses Switching (In 2 Views)                                     Fraction of Houses Switching (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Present Value of Heating Operating Costs (In 1 View)                                   Present Value of Heating Operating Costs (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Energy Price (In 6 Views)                                             Heating Energy Price (In 6 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes if no EEHIC Cap (In 8 Views)                                                 Optimal U Value for Existing Homes if no EEHIC Cap (In 8 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Peak Load from Heat Pumps on Coldest Days per Group (In 1 View)                                   Peak Load from Heat Pumps on Coldest Days per Group (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Peak Load from Non Heating or Cooling Sources (In 1 View)                                   Peak Load from Non Heating or Cooling Sources (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Peak Load from Heat Pumps on Hottest Days per Group (In 1 View)                                   Peak Load from Heat Pumps on Hottest Days per Group (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                kBTU per kWH (In 1 View)                                   kBTU per kWH (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump COP on Coldest Days (In 1 View)                                   Heat Pump COP on Coldest Days (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Peak Cooling Load on Grid (In 1 View)                                   Peak Cooling Load on Grid (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                CDD on Coldest Day (In 1 View)                                   CDD on Coldest Day (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Peak Heating Load on Grid (In 1 View)                                   Peak Heating Load on Grid (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Daily Load from Heat Pumps (In 1 View)                                   Average Daily Load from Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                HDD on Coldest Day (In 1 View)                                   HDD on Coldest Day (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Days per Year (In 1 View)                                   Days per Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Load from Heat Pumps (In 1 View)                                   Annual Load from Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Grouping (In 2 Views)                                     Energy Use by Grouping (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing (In 7 Views)                                               Housing (In 7 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Across Cohorts (In 1 View)                                   Housing Starts Across Cohorts (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts In Each Cohort (In 1 View)                                   Housing Starts In Each Cohort (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Fraction of Homes Retrofitting (In 1 View)                                   Initial Fraction of Homes Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Monthly Total Heat Pump Sales (In 1 View)                                   Monthly Total Heat Pump Sales (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Months per Year (In 1 View)                                   Months per Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Fractional Growth Rate (In 1 View)                                   Housing Fractional Growth Rate (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts (In 3 Views)                                       Housing Starts (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Housing (In 1 View)                                   Initial Housing (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Average U Value (In 1 View)                                   Initial Average U Value (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                System Switching SWITCH (In 1 View)                                   System Switching SWITCH (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Switching Sources (In 3 Views)                                       Houses Switching Sources (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofitting (In 1 View)                                   Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                U Value Shift from Source Switching (In 2 Views)                                     U Value Shift from Source Switching (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Net U Value Change from Retrofitting Home Shifts (In 1 View)                                   Net U Value Change from Retrofitting Home Shifts (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                U Value Loss from Demolition (In 1 View)                                   U Value Loss from Demolition (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Demolitions (In 3 Views)                                       Demolitions (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                No Turnover Switch (In 1 View)                                   No Turnover Switch (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                U Value Retrofitted Away (In 1 View)                                   U Value Retrofitted Away (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofitting Across Cohorts and Systems (In 1 View)                                   Retrofitting Across Cohorts and Systems (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Retrofitting (In 1 View)                                   Houses Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Indicated Homes Retrofitting (In 2 Views)                                     Indicated Homes Retrofitting (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Cohort and Heating and Cooling System (In 2 Views)                                     Housing by Cohort and Heating and Cooling System (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value (In 2 Views)                                     Total U Value (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Indicated Fraction of Homes Retrofitting (In 2 Views)                                     Indicated Fraction of Homes Retrofitting (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Considering Switching System (In 1 View)                                   Houses Considering Switching System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Net Change in Homes Retrofitting (In 3 Views)                                       Net Change in Homes Retrofitting (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Time to Decide to Retrofit (In 1 View)                                   Time to Decide to Retrofit (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Demolition Hazard Rate (In 1 View)                                   Demolition Hazard Rate (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofit Delay (In 2 Views)                                     Retrofit Delay (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Initial Homes (In 1 View)                                   Total Initial Homes (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Weight on Upfront Cost (In 2 Views)                                     Weight on Upfront Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Cost of Ownership of Average Home (In 2 Views)                                     Total Cost of Ownership of Average Home (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Perceived Cost of Retrofitting (In 2 Views)                                     Perceived Cost of Retrofitting (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Reference Retrofit Cost (In 2 Views)                                     Reference Retrofit Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Retrofits to Cost (In 2 Views)                                     Sensitivity of Retrofits to Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Code U (In 2 Views)                                     Code U (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U for New Homes (In 2 Views)                                     Optimal U for New Homes (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                U Value of Housing Starts (In 2 Views)                                     U Value of Housing Starts (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Increase in U Value from Housing Starts (In 1 View)                                   Increase in U Value from Housing Starts (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial U Value (In 1 View)                                   Initial U Value (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Amoritized Subsidized Retrofit Cost (In 3 Views)                                       Amoritized Subsidized Retrofit Cost (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected MassSave Proportional Subsidy Rate for Retrofits (In 4 Views)                                         Expected MassSave Proportional Subsidy Rate for Retrofits (In 4 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Expected Lower Lump Sum Subsidy (In 3 Views)                                       HOMES Expected Lower Lump Sum Subsidy (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Expected Subsidy for Retrofits (In 2 Views)                                     MassSave Expected Subsidy for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Subsidy for Retrofits (In 4 Views)                                         Expected Subsidy for Retrofits (In 4 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Costs for Retrofitting Home (In 2 Views)                                     Average Energy Costs for Retrofitting Home (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Mass Save Proportional Subsidy Rate for Retrofits (In 2 Views)                                     Mass Save Proportional Subsidy Rate for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional MassSave Subsidy Implementation Year for Retrofits (In 2 Views)                                     Proportional MassSave Subsidy Implementation Year for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Active Cohort Indicator (In 1 View)                                   Active Cohort Indicator (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Costs if Retrofitted (In 2 Views)                                     Average Energy Costs if Retrofitted (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Retrofit Cost (In 4 Views)                                         Unsubsidized Retrofit Cost (In 4 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Cohort Duration (In 2 Views)                                     Cohort Duration (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Homes Retrofitting (In 1 View)                                   Initial Homes Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Unsubsidized Retrofit Cost Intensity (In 4 Views)                                         Unsubsidized Retrofit Cost Intensity (In 4 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Homes Not Retrofitting (In 1 View)                                   Initial Homes Not Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Fixed Cost per Unit Area (In 2 Views)                                     Fixed Cost per Unit Area (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Fixed Cost (In 2 Views)                                     Fixed Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Sensitivity of Marginal Cost to U Value (In 4 Views)                                         Sensitivity of Marginal Cost to U Value (In 4 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Reference Marginal Cost (In 2 Views)                                     Reference Marginal Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                INITIAL TIME (In 3 Views)                                       INITIAL TIME (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Pounds per Ton (In 1 View)                                   Pounds per Ton (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Emissions from Cooling by Grouping (In 1 View)                                   Average Emissions from Cooling by Grouping (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Emissions by Grouping (In 2 Views)                                     Emissions by Grouping (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Emissions from Heating by Grouping (In 1 View)                                   Average Emissions from Heating by Grouping (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Energy Use (In 3 Views)                                       Average Cooling Energy Use (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Energy Use (In 3 Views)                                       Average Heating Energy Use (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Emissions (In 1 View)                                   Cumulative Emissions (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Emissions by Heating and Cooling System (In 2 Views)                                     Average Emissions by Heating and Cooling System (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Emissions (In 2 Views)                                     Emissions (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Emissions by Grouping (In 2 Views)                                     Average Emissions by Grouping (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Emissions Factor (In 1 View)                                   Cooling Emissions Factor (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Heating Emissions Factors (In 1 View)                                   Heating Emissions Factors (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Gas Houses (In 1 View)                                   Energy Use by Gas Houses (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Heat Pump Houses (In 1 View)                                   Energy Use by Heat Pump Houses (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use by Oil Houses (In 1 View)                                   Energy Use by Oil Houses (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Indicated Fraction of Homes Retrofitting (In 2 Views)                                     Average Indicated Fraction of Homes Retrofitting (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Fraction of Housing by Heating and Cooling System (In 1 View)                                   Fraction of Housing by Heating and Cooling System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Energy Use Across All Homes (In 1 View)                                   Average Cooling Energy Use Across All Homes (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Cost Across All Homes (In 1 View)                                   Average Heating Cost Across All Homes (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Heating Cost (In 1 View)                                   Total Heating Cost (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Area (In 1 View)                                   Total Area (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Cooling Energy Use (In 1 View)                                   Total Cooling Energy Use (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Cost Across All Homes (In 1 View)                                   Average Cooling Cost Across All Homes (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Energy Use Across All Homes (In 1 View)                                   Average Heating Energy Use Across All Homes (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Cooling Cost (In 1 View)                                   Total Cooling Cost (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Starts (In 1 View)                                   Total Housing Starts (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Heating Energy Use (In 1 View)                                   Total Heating Energy Use (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Emissions by Heating and Cooling System (In 1 View)                                   Emissions by Heating and Cooling System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Fraction of Houses in Each Heating and Cooling System (In 1 View)                                   Fraction of Houses in Each Heating and Cooling System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Emissions (In 1 View)                                   Average Emissions (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average U Value of Houses Switching Into Sources (In 1 View)                                   Average U Value of Houses Switching Into Sources (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average U Value by Heating and Cooling System (In 1 View)                                   Average U Value by Heating and Cooling System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Switching Into Sources (In 1 View)                                   Houses Switching Into Sources (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Heating and Cooling System (In 1 View)                                   Housing by Heating and Cooling System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                U Value Increase from Source Switching (In 1 View)                                   U Value Increase from Source Switching (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value by Heating and Cooling System (In 1 View)                                   Total U Value by Heating and Cooling System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Use by Heating and Cooling System (In 1 View)                                   Average Energy Use by Heating and Cooling System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average EUI in All Housing (In 1 View)                                   Average EUI in All Housing (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Use in All Housing (In 1 View)                                   Average Energy Use in All Housing (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average EUI by Grouping (In 1 View)                                   Average EUI by Grouping (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Energy Use (In 1 View)                                   Total Energy Use (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Cooling Cost (In 2 Views)                                     Average Cooling Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Use (In 2 Views)                                     Average Energy Use (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Retrofitting Status (In 1 View)                                   Housing by Retrofitting Status (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Fraction Retrofitting (In 1 View)                                   Fraction Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value by Cohort (In 1 View)                                   Total U Value by Cohort (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total U Value Across All Groupings (In 1 View)                                   Total U Value Across All Groupings (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Fraction Retrofitting by System and Cohort (In 1 View)                                   Fraction Retrofitting by System and Cohort (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Across All Housing (In 1 View)                                   Optimal U Across All Housing (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Fraction Retrofitting by Cohort (In 2 Views)                                     Fraction Retrofitting by Cohort (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Cohort and Retrofitting Status (In 3 Views)                                       Housing by Cohort and Retrofitting Status (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing by Cohort (In 1 View)                                   Housing by Cohort (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Area (In 2 Views)                                     Area (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area in All Housing (In 2 Views)                                     Average Area in All Housing (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Age (In 2 Views)                                     Total Age (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Age in All Housing (In 2 Views)                                     Average Age in All Housing (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Heating Cost (In 2 Views)                                     Average Heating Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average U Value in All Housing (In 1 View)                                   Average U Value in All Housing (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Housing Stock (In 2 Views)                                     Total Housing Stock (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Affinity of Retrofitting (In 2 Views)                                     Affinity of Retrofitting (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value with No EEHIC Proportional Subsidy (In 1 View)                                   Optimal U Value with No EEHIC Proportional Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                U Value at Which EEHIC Cap Binds (In 1 View)                                   U Value at Which EEHIC Cap Binds (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U Value for Existing Homes (In 1 View)                                   Optimal U Value for Existing Homes (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Marginal Cost at Binding U Value without EEHIC (In 1 View)                                   Marginal Cost at Binding U Value without EEHIC (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Subsidized Retrofit Cost (In 1 View)                                   Average Subsidized Retrofit Cost (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Lifetime Marginal Cost Reductions from Retrofitting (In 1 View)                                   Lifetime Marginal Cost Reductions from Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional EEHIC Subsidy Implementation Year for Retrofits (In 2 Views)                                     Proportional EEHIC Subsidy Implementation Year for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected EEHIC Maximum Subsidy for Retrofits (In 2 Views)                                     Expected EEHIC Maximum Subsidy for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected EEHIC Proportional Subsidy Rate for Retrofits (In 2 Views)                                     Expected EEHIC Proportional Subsidy Rate for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Income (In 1 View)                                   Average Income (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                EEHIC Subsidy for Retrofits Final Year (In 2 Views)                                     EEHIC Subsidy for Retrofits Final Year (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Homeowner Hours Spent Retrofitting (In 1 View)                                   Homeowner Hours Spent Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Soft Costs of Retrofitting (In 1 View)                                   Soft Costs of Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Marginal Cooling Cost Reduction from Retrofitting (In 2 Views)                                     Marginal Cooling Cost Reduction from Retrofitting (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                U Value of Retrofitting Homes (In 1 View)                                   U Value of Retrofitting Homes (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Amoritization Period (In 1 View)                                   Amoritization Period (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Subsidized Retrofit Cost (In 1 View)                                   Subsidized Retrofit Cost (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Marginal Cost Reductions from Retrofitting (In 2 Views)                                     Marginal Cost Reductions from Retrofitting (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Fixed Cost (In 2 Views)                                     Expected Fixed Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Reference Marginal Cost (In 4 Views)                                         Expected Reference Marginal Cost (In 4 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Reference U Value (In 3 Views)                                       Reference U Value (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Marginal Heating Cost Reduction from Retrofitting (In 1 View)                                   Marginal Heating Cost Reduction from Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Energy Use (In 1 View)                                   Optimal Cooling Energy Use (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Effect of Air Leakage from Window AC on Efficiency (In 1 View)                                   Effect of Air Leakage from Window AC on Efficiency (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Gas COP TABLE (In 1 View)                                   Gas COP TABLE (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump Cooling COP TABLE (In 1 View)                                   Heat Pump Cooling COP TABLE (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Oil COP TABLE (In 1 View)                                   Oil COP TABLE (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Heat Pump Heating COP TABLE (In 1 View)                                   Heat Pump Heating COP TABLE (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Energy Cost (In 2 Views)                                     Optimal Energy Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Energy Cost (In 2 Views)                                     Average Energy Cost (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Energy Price (In 3 Views)                                       Cooling Energy Price (In 3 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Heating Cost (In 1 View)                                   Optimal Heating Cost (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Energy Use (In 1 View)                                   Optimal Energy Use (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Heating Energy Use (In 1 View)                                   Optimal Heating Energy Use (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal Cooling Cost (In 1 View)                                   Optimal Cooling Cost (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Area of Housing Starts (In 2 Views)                                     Average Area of Housing Starts (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Code U Value (In 1 View)                                   Initial Code U Value (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Fractional Decrease in Code U (In 1 View)                                   Fractional Decrease in Code U (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Decrease in Code U (In 1 View)                                   Decrease in Code U (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Additional Cost of Building to U Value (In 1 View)                                   Additional Cost of Building to U Value (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Lump Sum Subsidy Intensity (In 1 View)                                   Expected Lump Sum Subsidy Intensity (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Increase in Area per Year (In 1 View)                                   Increase in Area per Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Average Area of Housing Starts (In 1 View)                                   Initial Average Area of Housing Starts (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Net Area Shift due to Retrofit Status Switching (In 1 View)                                   Net Area Shift due to Retrofit Status Switching (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Area (In 1 View)                                   Initial Area (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Area of New Homes (In 1 View)                                   Area of New Homes (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Area Removal (In 1 View)                                   Area Removal (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Net Area Shift by System (In 1 View)                                   Net Area Shift by System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Actual EEHIC Subsidy for Retrofits (In 1 View)                                   Actual EEHIC Subsidy for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Actual HOMES Subsidy for Retrofits (In 1 View)                                   Actual HOMES Subsidy for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Actual MassSave Subsidy for Retrofits (In 1 View)                                   Actual MassSave Subsidy for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Federal Subsidies (In 1 View)                                   Annual Federal Subsidies (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Heat Pump Subsidy (In 1 View)                                   Annual Heat Pump Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Annual MA Subsidies (In 1 View)                                   Annual MA Subsidies (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Retrofit Subsidy (In 1 View)                                   Annual Retrofit Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Annual Subsidies (In 1 View)                                   Annual Subsidies (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Subsidies for Heat Pumps (In 1 View)                                   Cumulative Subsidies for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Savings (In 2 Views)                                     Energy Savings (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Federal Annual Heat Pump Subsidy (In 1 View)                                   Federal Annual Heat Pump Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Actual Subsidy for Heat Pumps (In 1 View)                                   IRA Actual Subsidy for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Massachusetts Annual Retrofit Subsidy (In 1 View)                                   Massachusetts Annual Retrofit Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Federal Annual Retrofit Subsidy (In 1 View)                                   Federal Annual Retrofit Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Federal Subsidy (In 1 View)                                   Cumulative Federal Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative MA Subsidy (In 1 View)                                   Cumulative MA Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Subsidies (In 1 View)                                   Cumulative Subsidies (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Massachusetts Annual Heat Pumps Subsidy (In 1 View)                                   Massachusetts Annual Heat Pumps Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Implemented Lump Sum Subsidy for Heat Pumps (In 2 Views)                                     MassSave Implemented Lump Sum Subsidy for Heat Pumps (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Cut Off for Savings (In 2 Views)                                     HOMES Cut Off for Savings (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Subsidy for Retrofits (In 1 View)                                   Cumulative Subsidy for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Houses Retrofitting per Year (In 1 View)                                   Houses Retrofitting per Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented EEHIC Maximum Subsidy for Retrofits (In 2 Views)                                     Implemented EEHIC Maximum Subsidy for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Implemented High Subsidy (In 2 Views)                                     HOMES Implemented High Subsidy (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented EEHIC Subsidy Proportional Rate for Retrofits (In 2 Views)                                     Implemented EEHIC Subsidy Proportional Rate for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional IRA Subsidy Switch for Heat Pumps (In 2 Views)                                     Proportional IRA Subsidy Switch for Heat Pumps (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented IRA Maximum Proportional Subsidy for Heat Pumps (In 2 Views)                                     Implemented IRA Maximum Proportional Subsidy for Heat Pumps (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Implemented Subsidy Proportional Rate for Heat Pumps (In 2 Views)                                     IRA Implemented Subsidy Proportional Rate for Heat Pumps (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Maximum Proportional Subsidy for Heat Pumps (In 2 Views)                                     IRA Maximum Proportional Subsidy for Heat Pumps (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Implemented Lower Subsidy (In 2 Views)                                     HOMES Implemented Lower Subsidy (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented MassSave Maximum Subsidy for Retrofits (In 2 Views)                                     Implemented MassSave Maximum Subsidy for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                Implemented MassSave Subsidy Proportional Rate for Retrofits (In 2 Views)                                     Implemented MassSave Subsidy Proportional Rate for Retrofits (In 2 Views)
                                                                                                                                                                                                                                                                                                                                                                                                                EEHIC Expected Subsidy for Retrofits (In 1 View)                                   EEHIC Expected Subsidy for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                EEHIC Maximum Subsidy for Retrofits (In 1 View)                                   EEHIC Maximum Subsidy for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Subsidy Final Year (In 1 View)                                   HOMES Subsidy Final Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                EEHIC Proportional Subsidy Rate for Retrofits (In 1 View)                                   EEHIC Proportional Subsidy Rate for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES High Subsidy Amount (In 1 View)                                   HOMES High Subsidy Amount (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Expected Higher Subsidy (In 1 View)                                   HOMES Expected Higher Subsidy (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Expected Proportional Subsidy for Heat Pumps (In 1 View)                                   IRA Expected Proportional Subsidy for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Expected Lump Sum Subsidy for Heat Pumps (In 1 View)                                   MassSave Expected Lump Sum Subsidy for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Lump Sum Subsidy Amount for Heat Pumps (In 1 View)                                   MassSave Lump Sum Subsidy Amount for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Lump Sum Subsidy for Heat Pumps Final Year (In 1 View)                                   MassSave Lump Sum Subsidy for Heat Pumps Final Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (In 1 View)                                   MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Lump Sum Subsidy for Heat Pumps Final Year (In 1 View)                                   IRA Lump Sum Subsidy for Heat Pumps Final Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Subsidy for Retrofits Final Year (In 1 View)                                   MassSave Subsidy for Retrofits Final Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Proportional Subsidy Implementation Year for Heat Pumps (In 1 View)                                   IRA Proportional Subsidy Implementation Year for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                IRA Proportional Subsidy Rate for Heat Pumps (In 1 View)                                   IRA Proportional Subsidy Rate for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected IRA Proportional Subsidy Rate for Heat Pumps (In 1 View)                                   Expected IRA Proportional Subsidy Rate for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected Maximum IRA Proportional Subsidy for Heat Pumps (In 1 View)                                   Expected Maximum IRA Proportional Subsidy for Heat Pumps (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Lower Subsidy Amount (In 1 View)                                   HOMES Lower Subsidy Amount (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Proportional Subsidy Switch for Retrofits (In 1 View)                                   Proportional Subsidy Switch for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Expected MassSave Maximum Subsidy for Retrofits (In 1 View)                                   Expected MassSave Maximum Subsidy for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Forming Expectations of Energy Price (In 1 View)                                   Delay in Forming Expectations of Energy Price (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Forming Expectations of Retrofit Costs (In 1 View)                                   Delay in Forming Expectations of Retrofit Costs (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Delay in Changing Subsidy Expectations (In 1 View)                                   Delay in Changing Subsidy Expectations (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                HOMES Subsidy Implementation Year (In 1 View)                                   HOMES Subsidy Implementation Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                MassSave Maximum Subsidy for Retrofits (In 1 View)                                   MassSave Maximum Subsidy for Retrofits (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                FINAL TIME (In 1 View)                                   FINAL TIME (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Cost of Ownership of Retrofitted Homes (In 1 View)                                   Total Cost of Ownership of Retrofitted Homes (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Affinity of Not Retrofitting (In 1 View)                                   Affinity of Not Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Perceived Cost of Not Retrofitting (In 1 View)                                   Perceived Cost of Not Retrofitting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Net Age Shift by System (In 1 View)                                   Net Age Shift by System (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Net Age Shift from Retrofitting Status Shifting (In 1 View)                                   Net Age Shift from Retrofitting Status Shifting (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Age (In 1 View)                                   Initial Age (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Age Removal (In 1 View)                                   Age Removal (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Aging (In 1 View)                                   Aging (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Average Age (In 1 View)                                   Average Age (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Aging per Year (In 1 View)                                   Aging per Year (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Input 1 (In 1 View)                                   Input 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Autocorrelated Noise 1 (In 1 View)                                   Autocorrelated Noise 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Standard Deviation 1 (In 1 View)                                   Noise Standard Deviation 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Start Time 1 (In 1 View)                                   Noise Start Time 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Change in AC Noise 1 (In 1 View)                                   Change in AC Noise 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Cooling Energy Price Step Height 1 (In 1 View)                                   Cooling Energy Price Step Height 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Exponential Growth Rate 1 (In 1 View)                                   Energy Price Exponential Growth Rate 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Pulse Quantity 1 (In 1 View)                                   Energy Price Pulse Quantity 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Ramp Slope 1 (In 1 View)                                   Energy Price Ramp Slope 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Cooling Energy Price (In 1 View)                                   Initial Cooling Energy Price (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Amplitude 1 (In 1 View)                                   Sine Amplitude 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Period 1 (In 1 View)                                   Sine Period 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Step Time 1 (In 1 View)                                   Step Time 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Correlation Time 1 (In 1 View)                                   Noise Correlation Time 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Pulse Time 1 (In 1 View)                                   Pulse Time 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp Start Time 1 (In 1 View)                                   Ramp Start Time 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                White Noise 1 (In 1 View)                                   White Noise 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp End Time 1 (In 1 View)                                   Ramp End Time 1 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total Initial Housing Starts (In 1 View)                                   Total Initial Housing Starts (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Exponential Growth Rate (In 1 View)                                   Energy Price Exponential Growth Rate (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Autocorrelated Noise 0 (In 1 View)                                   Autocorrelated Noise 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Period 0 (In 1 View)                                   Sine Period 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Ramp Slope (In 1 View)                                   Energy Price Ramp Slope (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Step Height (In 1 View)                                   Energy Price Step Height (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Pulse Time 0 (In 1 View)                                   Pulse Time 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Change in AC Noise 0 (In 1 View)                                   Change in AC Noise 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Standard Deviation 0 (In 1 View)                                   Noise Standard Deviation 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Start Time 0 (In 1 View)                                   Noise Start Time 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Input 0 (In 1 View)                                   Input 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp End Time 0 (In 1 View)                                   Ramp End Time 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Step Time 0 (In 1 View)                                   Step Time 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Amplitude 0 (In 1 View)                                   Sine Amplitude 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                White Noise 0 (In 1 View)                                   White Noise 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Price Pulse Quantity (In 1 View)                                   Energy Price Pulse Quantity (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp Start Time 0 (In 1 View)                                   Ramp Start Time 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Correlation Time 0 (In 1 View)                                   Noise Correlation Time 0 (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Autocorrelated Noise (In 1 View)                                   Autocorrelated Noise (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Change in AC Noise (In 1 View)                                   Change in AC Noise (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Exponential Growth Rate (In 1 View)                                   Housing Starts Exponential Growth Rate (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp Start Time (In 1 View)                                   Ramp Start Time (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Input (In 1 View)                                   Input (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Correlation Time (In 1 View)                                   Noise Correlation Time (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Standard Deviation (In 1 View)                                   Noise Standard Deviation (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Noise Start Time (In 1 View)                                   Noise Start Time (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Pulse Quantity (In 1 View)                                   Housing Starts Pulse Quantity (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Pulse Time (In 1 View)                                   Pulse Time (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Ramp End Time (In 1 View)                                   Ramp End Time (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Step Time (In 1 View)                                   Step Time (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Ramp Slope (In 1 View)                                   Housing Starts Ramp Slope (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                White Noise (In 1 View)                                   White Noise (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Amplitude (In 1 View)                                   Sine Amplitude (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Sine Period (In 1 View)                                   Sine Period (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Starts Step Height (In 1 View)                                   Housing Starts Step Height (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Heating Energy Price (In 1 View)                                   Initial Heating Energy Price (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Initial Housing Starts (In 1 View)                                   Initial Housing Starts (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                TIME STEP (In 1 View)                                   TIME STEP (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Maximum Energy Price (In 1 View)                                   Maximum Energy Price (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                SAVEPER (In 1 View)                                   SAVEPER (In 1 View)
                                                                                                                                                                                                                                                                                                                                                                                                                Total: 2 14 18 64 17 13 39 28 68 59 42 64 23 1 34 18 Total:
                                                                                                                                                                                                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                                                                                                                                                                                                Not in View
                                                                                                                                                                                                                                                                                                                                                                                                                Age
                                                                                                                                                                                                                                                                                                                                                                                                                Area
                                                                                                                                                                                                                                                                                                                                                                                                                Average Attributes
                                                                                                                                                                                                                                                                                                                                                                                                                Average and Peak Load
                                                                                                                                                                                                                                                                                                                                                                                                                Carbon Emissions
                                                                                                                                                                                                                                                                                                                                                                                                                Cumulative Subsidies
                                                                                                                                                                                                                                                                                                                                                                                                                Energy Use
                                                                                                                                                                                                                                                                                                                                                                                                                Housing Aging Chain & U Coflows
                                                                                                                                                                                                                                                                                                                                                                                                                Input Test
                                                                                                                                                                                                                                                                                                                                                                                                                Optimal U & Retrofit Costs
                                                                                                                                                                                                                                                                                                                                                                                                                Perceived Subsidies & Costs
                                                                                                                                                                                                                                                                                                                                                                                                                Retrofitting Decision Making
                                                                                                                                                                                                                                                                                                                                                                                                                Social Influence in Retrofitting Decisions
                                                                                                                                                                                                                                                                                                                                                                                                                Switching Systems
                                                                                                                                                                                                                                                                                                                                                                                                                U Value of Housing Starts
                                                                                                                                                                                                                                                                                                                                                                                                                 

                                                                                                                                                                                                                                                                                                                                                                                                                Source File: C:\Users\cstafford\Downloads\HeatPumpModel_v31.mdl (Sat Mar 16 20:31:48 EDT 2024)
                                                                                                                                                                                                                                                                                                                                                                                                                Report Created On Sat Mar 16 20:33:42 EDT 2024
                                                                                                                                                                                                                                                                                                                                                                                                                SDM-Doc Tool Version 1.4.7
                                                                                                                                                                                                                                                                                                                                                                                                                Global Security Sciences Division
                                                                                                                                                                                                                                                                                                                                                                                                                Argonne National Laboratory