Documentation of HeatPumpModel

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:

#320
A

Average Attributes
Social Influence in Retrofitting Decisions

Used By

Average Age in All Housing Average age of houses, regardless of cohort
Average Area in All Housing The average are of all houses, regardless of what group they're in.
Average Cooling Energy Use Across All Homes The amount of energy an average home spends on cooling, regardless of cohort, retrofit status, etc.
Average Emissions The average CO2 emissions for a household, not disaggregated into any grouping.
Average Energy Use in All Housing The average energy use across all stocks.
Average Heating Energy Use Across All Homes The average heating energy use per home, regardless of cohort, system,etc.
Average Indicated Fraction of Homes Retrofitting The average fraction of homes that will retrofit retrofitting after decision delayacross all housing.
Average U Value in All Housing The average U Value over the entire housing stock, not disaggregated by any groupings.
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.
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.

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: Switching Systems 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: Area Average Attributes Average and Peak Load Energy Use Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Switching Systems 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: Switching Systems 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: Housing Aging Chain & U Coflows Switching Systems Used By Houses Considering Switching System The number of houses per year considering switching their heating and cooling system. 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: Energy Use Optimal U & Retrofit Costs Switching Systems 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: Switching Systems 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: Average and Peak Load Energy Use Optimal U & Retrofit Costs Switching Systems 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems U Value of Housing Starts 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: Energy Use Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems U Value of Housing Starts 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: Perceived Subsidies & Costs Switching Systems Used By Subsidized Cost of Heat Pumps The upfront cost of heat pump once subsidies are taken into account. 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: Housing Aging Chain & U Coflows Switching Systems 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: Energy Use Optimal U & Retrofit Costs Switching Systems 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: Energy Use Housing Aging Chain & U Coflows Input Test Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Switching Systems 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: Energy Use Optimal U & Retrofit Costs Switching Systems 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: Average Attributes Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Cumulative Subsidies Housing Aging Chain & U Coflows Switching Systems Used By Federal Annual Heat Pump Subsidy The amount of subsidies the federal government spends on heat pumps through the Inflation Reduction Act every year. Massachusetts Annual Heat Pumps Subsidy The actual subsidy provided for purchase of heat pumps by Massachusetts, as opposed to what the subsidy expected by homeowners is. Monthly Total Heat Pump Sales The number of homes buying heat pumps, every year. 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: Switching Systems 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: Average and Peak Load Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems 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: Switching Systems Used By Unsubsidized Cost of Heat Pumps The unsubsidized cost of heat pumps, instantiated at each time. 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: Cumulative Subsidies Perceived Subsidies & Costs Switching Systems Used By IRA Actual Subsidy for Heat Pumps The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value. IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. MassSave Implemented Lump Sum Subsidy for Heat Pumps Lump sum subsidy from MassSave that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year. Subsidized Cost of Heat Pumps The upfront cost of heat pump once subsidies are taken into account. 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: U Value of Housing Starts 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: Area U Value of Housing Starts Used By Area of New Homes The total Area added by the construction of new homes, by cohort. Expected Lump Sum Subsidy Intensity Lump sum subsidy for retrofits per square foot. 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: Housing Aging Chain & U Coflows U Value of Housing Starts 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: U Value of Housing Starts 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems U Value of Housing Starts 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: Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems U Value of Housing Starts 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: U Value of Housing Starts 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs U Value of Housing Starts 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making U Value of Housing Starts 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: U Value of Housing Starts Used By Decrease in Code U The change in code U from policy. 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs U Value of Housing Starts Used By Expected Lump Sum Subsidy Intensity Lump sum subsidy for retrofits per square foot. Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: U Value of Housing Starts 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: Optimal U & Retrofit Costs U Value of Housing Starts Used By 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. 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: Optimal U & Retrofit Costs U Value of Housing Starts 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: Housing Aging Chain & U Coflows U Value of Housing Starts 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: Optimal U & Retrofit Costs Retrofitting Decision Making U Value of Housing Starts 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Retrofitting Decision Making U Value of Housing Starts 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: Housing Aging Chain & U Coflows U Value of Housing Starts Used By Increase in U Value from Housing Starts New U value from new homes being built. Feedback Loops:** 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]

Top

(Group) . (1 Variables)

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:

#194
A

Input Test

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: Perceived Subsidies & Costs Used By MassSave Subsidy for Retrofits Final Year The year in which the subsidy is phased out. If final time, then has no ending data. 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: Area Housing Aging Chain & U Coflows Input Test 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: Input Test 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: U Value of Housing Starts 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Retrofitting Decision Making 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. Total Cost of Ownership of Retrofitted Homes The total cost of ownership of owning a home that has been retrofitted to the optimal U. 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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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: Switching Systems 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: Perceived Subsidies & Costs Used By Expected EEHIC Maximum Subsidy for Retrofits Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays. Expected EEHIC Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. Expected IRA Proportional Subsidy Rate for Heat Pumps Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. Expected MassSave Maximum Subsidy for Retrofits Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays. Expected MassSave Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. Expected Maximum IRA Proportional Subsidy for Heat Pumps Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays. 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 HOMES Expected Lower Lump Sum Subsidy Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. MassSave Expected Lump Sum Subsidy for Heat Pumps Expected lump sum subsidy that lowers subsidized retrofit costs from the state, taking into account information delays. 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: Perceived Subsidies & Costs 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: Perceived Subsidies & Costs 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs 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: Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems U Value of Housing Starts 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: U Value of Housing Starts 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: Perceived Subsidies & Costs Used By 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. 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs U Value of Housing Starts 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making U Value of Housing Starts 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs U Value of Housing Starts Used By Expected Lump Sum Subsidy Intensity Lump sum subsidy for retrofits per square foot. Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Cumulative Subsidies Perceived Subsidies & Costs 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 Lower Lump Sum Subsidy Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. 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: Perceived Subsidies & Costs 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: Perceived Subsidies & Costs Used By HOMES Implemented High Subsidy Implemented higher subsidy from the HOMES rebate program. 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	#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: Cumulative Subsidies Perceived Subsidies & Costs Used By Actual MassSave Subsidy for Retrofits The actual subsidy offered for retrofits by MassSave, not the expected value. Expected MassSave Maximum Subsidy for Retrofits Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Actual MassSave Subsidy for Retrofits The actual subsidy offered for retrofits by MassSave, not the expected value. Expected MassSave Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. 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: Housing Aging Chain & U Coflows 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: Optimal U & Retrofit Costs U Value of Housing Starts 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs Used By Implemented MassSave Subsidy Proportional Rate for Retrofits 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. 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs Used By Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Perceived Subsidies & Costs Used By Implemented MassSave Maximum Subsidy for Retrofits Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs Used By Implemented MassSave Maximum Subsidy for Retrofits Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. Implemented MassSave Subsidy Proportional Rate for Retrofits 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. 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: Perceived Subsidies & Costs 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. Expected EEHIC Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. Expected MassSave Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. 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. 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: Optimal U & Retrofit Costs Used By Amoritized Subsidized Retrofit Cost The incurred total retrofit cost amoritized over the specified amoritization period. Average Subsidized Retrofit Cost The average subsidized retrofit cost across all houses. 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: Housing Aging Chain & U Coflows U Value of Housing Starts 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: U Value of Housing Starts 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows U Value of Housing Starts 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: Housing Aging Chain & U Coflows U Value of Housing Starts Used By Increase in U Value from Housing Starts New U value from new homes being built. 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: Average Attributes Retrofitting Decision Making 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: Average Attributes 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: Average Attributes Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems 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: Average Attributes Social Influence in Retrofitting Decisions Used By Average Age in All Housing Average age of houses, regardless of cohort Average Area in All Housing The average are of all houses, regardless of what group they're in. Average Cooling Energy Use Across All Homes The amount of energy an average home spends on cooling, regardless of cohort, retrofit status, etc. Average Emissions The average CO2 emissions for a household, not disaggregated into any grouping. Average Energy Use in All Housing The average energy use across all stocks. Average Heating Energy Use Across All Homes The average heating energy use per home, regardless of cohort, system,etc. Average Indicated Fraction of Homes Retrofitting The average fraction of homes that will retrofit retrofitting after decision delayacross all housing. Average U Value in All Housing The average U Value over the entire housing stock, not disaggregated by any groupings. 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. 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. 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: Average Attributes Energy Use Used By Average Energy Cost The average cost of both heating and cooling a home, by grouping. Total Heating Cost The total amount of money spent on heating homes. 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs 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: Housing Aging Chain & U Coflows Switching Systems 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: Energy Use Housing Aging Chain & U Coflows Input Test Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Input Test 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Optimal U & Retrofit Costs Used By 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. 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: Switching Systems 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: Switching Systems 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:* Housing Aging Chain & U Coflows Perceived Subsidies & Costs Used By 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 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Retrofitting Decision Making U Value of Housing Starts 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making 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. 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. Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies. 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: Housing Aging Chain & U Coflows 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: Age 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 YearSUM( 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: Age 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: Age 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: Area Average Attributes 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 StartsSUM( Housing Starts[ Cohort, Heating and Cooling System!]) Description:* The total Area added by the construction of new homes, by cohort. Present In 1 View: Area 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: Area 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: Input Test 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: Input Test 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: Age 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: Area Average Attributes 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: Area Average Attributes Used By Average EUI in All Housing The average energy use intensity across all housing. Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
.housingagingchain v8	#42 A	*Average Energy Costs if Retrofitted (Dollar/(YearHouse)) 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: Housing Aging Chain & U Coflows Retrofitting Decision Making Used By Total Cost of Ownership of Retrofitted Homes The total cost of ownership of owning a home that has been retrofitted to the optimal U. 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: Input Test 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: Input Test 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: Age Housing Aging Chain & U Coflows 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: Input Test 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 (DimensionlessYear) = 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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 (DimensionlessYear) = 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: Input Test 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: Input Test 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: Input Test 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: Age 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 AmplitudeSIN(23.14159( 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: Input Test 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 0SIN(23.14159( 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: Input Test 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: Area Used By Net Area Shift due to Retrofit Status Switching Shift in area between energy sources due to houses switching sources. 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: Input Test 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: Input Test 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: Input Test 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: Input Test Used By White Noise 0 White noise input to the pink noise process. 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Age Average Attributes 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: Cumulative Subsidies Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Retrofitting Decision Making Used By Actual EEHIC Subsidy for Retrofits The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value. Actual MassSave Subsidy for Retrofits The actual subsidy offered for retrofits by MassSave, not the expected value. 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	#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: Input Test 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: Input Test 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)

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:

.housingagingchain v9

#285
C

Optimal U & Retrofit Costs
Retrofitting Decision Making
U Value of Housing Starts

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: Cumulative Subsidies Used By Federal Annual Retrofit Subsidy The amount of federal subsidies spent by the federal government, through the IRA. 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: Cumulative Subsidies Used By Federal Annual Retrofit Subsidy The amount of federal subsidies spent by the federal government, through the IRA. 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: Cumulative Subsidies Used By Massachusetts Annual Retrofit Subsidy Amount of money Massachusetts spends on MassSave subsidies for retrofits, yearly. 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: Switching Systems 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: Retrofitting Decision Making 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: Optimal U & Retrofit Costs Used By Amoritized Subsidized Retrofit Cost The incurred total retrofit cost amoritized over the specified amoritization period. 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual Subsidies The amount of subsidies spent on heat pumps and retrofits every year. Cumulative Subsidies for Heat Pumps The total amount of dollars spent on subsidizing heat pumps throughout the model's run. 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: Average and Peak Load Used By Average Daily Load from Heat Pumps The average load on the electric grid from heat pumps, per day. 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual Subsidies The amount of subsidies spent on heat pumps and retrofits every year. Cumulative Subsidy for Retrofits The total amount spent on retrofits since the beginning of the model's run. 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: Cumulative Subsidies 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: Input Test 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: Area Average Attributes Average and Peak Load Energy Use Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Area U Value of Housing Starts Used By Area of New Homes The total Area added by the construction of new homes, by cohort. Expected Lump Sum Subsidy Intensity Lump sum subsidy for retrofits per square foot. 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: Average Attributes Energy Use Used By Average Energy Cost The average cost of both heating and cooling a home, by grouping. Total Cooling Cost The total amount of money spent on cooling homes, per year. 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: Average Attributes 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: Average Attributes Carbon Emissions Energy Use Used By Average Cooling Cost The average costs for keeping a home cool, by grouping. Average Emissions from Cooling by Grouping The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status. Average Energy Use Average energy use to both heat and cool a home. Total Cooling Energy Use The total amount of energy spent on cooling homes. 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: Average Attributes 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: Average and Peak Load 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: Average Attributes 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: Average Attributes Carbon Emissions Used By Emissions by Grouping The total emissions for the most disaggregated grouping in the model. 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: Average Attributes Carbon Emissions 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: Carbon Emissions 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: Carbon Emissions 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: Energy Use Retrofitting Decision Making Used By Average Energy Costs for Retrofitting Home Heating costs for each home open to retrofitting, annually, if no further retrofit measures are undertaken. 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: Average Attributes Energy Use Used By Average EUI by Grouping The average energy use intensity by grouping Energy Use by Grouping The total amount of energy used for heating and cooling in each group. 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: Average Attributes 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: Average Attributes Used By Average EUI in All Housing The average energy use intensity across all housing. 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: Average Attributes 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: Average Attributes 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: Average Attributes 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: Average Attributes Carbon Emissions Energy Use Used By Average Emissions from Heating by Grouping Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc. Average Energy Use Average energy use to both heat and cool a home. Average Heating Cost The costs per year to heat one house. Total Heating Energy Use The total amount of energy spent on heating per year. 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: Average Attributes 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: Optimal U & Retrofit Costs 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: Average Attributes Optimal U & Retrofit Costs 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: Switching Systems 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: Switching Systems 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: Optimal U & Retrofit Costs 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: Housing Aging Chain & U Coflows Switching Systems Used By Houses Considering Switching System The number of houses per year considering switching their heating and cooling system. 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: Average Attributes 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: Average Attributes 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: Average and Peak Load Used By 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	#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: Input Test 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: Energy Use Optimal U & Retrofit Costs Switching Systems 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: Carbon Emissions Used By Average Emissions from Cooling by Grouping The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status. 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: Energy Use Input Test Perceived Subsidies & Costs 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: Input Test 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: Switching Systems 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: Average and Peak Load Energy Use Optimal U & Retrofit Costs Switching Systems 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Carbon Emissions 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: Cumulative Subsidies 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: Cumulative Subsidies 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: Cumulative Subsidies 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: Cumulative Subsidies 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: Cumulative Subsidies 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: Average and Peak Load Used By Average Daily Load from Heat Pumps The average load on the electric grid from heat pumps, per day. 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. 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: Housing Aging Chain & U Coflows Used By Demolitions Homes that are destroyed every year. 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: Age Area Housing Aging Chain & U Coflows 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems U Value of Housing Starts 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: Perceived Subsidies & Costs Used By Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Perceived Subsidies & Costs Used By Implemented EEHIC Maximum Subsidy for Retrofits Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Perceived Subsidies & Costs 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Used By Implemented EEHIC Maximum Subsidy for Retrofits Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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	#95 C	Effect of Air Leakage from Window AC on Efficiency (dmnl) = 0.910/11 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: Energy Use 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: Average Attributes Carbon Emissions 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: Average Attributes Carbon Emissions Used By Emissions The total amount of emissions across all housing groups. Emissions by Heating and Cooling System The total amount of emissions for houses by Heating and Cooling System. 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: Average Attributes Used By Average Emissions by Heating and Cooling System The average CO2 emissions for each house, by heating and cooling system. 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: Input Test 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 (DimensionlessYear) = 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: Input Test 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: Input Test 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: Cumulative Subsidies Perceived Subsidies & Costs 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. Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Average Attributes 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: Average Attributes Average and Peak Load Used By Annual Load from Heat Pumps The load on the electric grid from servicing heating and cooling demand from heat pumps, across the whole year. Average Energy Use by Heating and Cooling System The average energy use for each home by heating and cooling system. Energy Use by Gas Houses The total amount of energy for heating and cooling used by homes which primarily use gas to heat their homes. Energy Use by Heat Pump Houses The amount of energy used for heating and cooling by homes which primarily use heat pumps to heat their home. Energy Use by Oil Houses The total amount of energy for heating and cooling used by homes primarily using oil to heat their home. Total Energy Use The total energy use for all homes in the model. 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: Average Attributes 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: Average Attributes 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: Energy Use Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs 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: Perceived Subsidies & Costs Used By IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. 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: Perceived Subsidies & Costs Used By IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. 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: Perceived Subsidies & Costs Switching Systems Used By Subsidized Cost of Heat Pumps The upfront cost of heat pump once subsidies are taken into account. 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual Federal Subsidies The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year. Annual Retrofit Subsidy The subsidies for retrofits paid out every year. 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: Average Attributes 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: Average Attributes 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: Average Attributes 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: Area Average Attributes 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: Average Attributes 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: U Value of Housing Starts Used By Decrease in Code U The change in code U from policy. 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: Energy Use 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: Average and Peak Load Used By 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. 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: Energy Use 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: Average and Peak Load Used By 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. 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: Energy Use 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: Energy Use Optimal U & Retrofit Costs Switching Systems 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: Carbon Emissions Used By Average Emissions from Heating by Grouping Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc. 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: Switching Systems 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: Energy Use Optimal U & Retrofit Costs Switching Systems 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: Optimal U & Retrofit Costs 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: Cumulative Subsidies Perceived Subsidies & Costs 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. Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Perceived Subsidies & Costs Used By Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Perceived Subsidies & Costs Used By HOMES Implemented High Subsidy Implemented higher subsidy from the HOMES rebate program. 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: Cumulative Subsidies Perceived Subsidies & Costs 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: Perceived Subsidies & Costs Used By HOMES Implemented High Subsidy Implemented higher subsidy from the HOMES rebate program. 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	#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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Cumulative Subsidies Used By Federal Annual Retrofit Subsidy The amount of federal subsidies spent by the federal government, through the IRA. Massachusetts Annual Retrofit Subsidy Amount of money Massachusetts spends on MassSave subsidies for retrofits, yearly. 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: Average Attributes Used By Average U Value of Houses Switching Into Sources The average U value of houses switching into each source, for each source. 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: Age Average Attributes Housing Aging Chain & U Coflows Used By Houses Switching Into Sources The number of houses switching into each Heating and Cooling System, cohort, and retrofitting group due to system switching. 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. Total Heat Pump Sales Number of houses buying heat pumps every year. U Value Shift from Source Switching The shift in total U value coming from switching sources. 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: Age Average Attributes Average and Peak Load Carbon Emissions Cumulative Subsidies Housing Aging Chain & U Coflows Optimal U & Retrofit Costs 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. Average Cooling Cost Across All Homes The average cost to cool a home, for all cohorts and systems. Average Energy Use by Heating and Cooling System The average energy use for each home by heating and cooling system. Average Heating Cost Across All Homes The average amount a home spends on heating, regardless of cohort or heating and cooling system. Average Subsidized Retrofit Cost The average subsidized retrofit cost across all houses. Demolitions Homes that are destroyed every year. 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. 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. 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. 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 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. Housing by Heating and Cooling System Number of houses by energy source across all cohorts. Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built. Net Change in Homes Retrofitting Homes that are in the process of deciding to retrofit. 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. 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. Total Cooling Cost The total amount of money spent on cooling homes, per year. Total Cooling Energy Use The total amount of energy spent on cooling homes. Total Heating Cost The total amount of money spent on heating homes. Total Heating Energy Use The total amount of energy spent on heating per year. Total Housing Stock Total number of houses across all cohorts, heating/cooling systems, and retrofitting status. U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc. 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: Average Attributes 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: Average Attributes Housing Aging Chain & U Coflows Used By Indicated Homes Retrofitting Number of homes that, once delays are taken into account, will be open to retrofitting. 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: Age Area Average Attributes 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: Average Attributes Used By Average Emissions by Heating and Cooling System The average CO2 emissions for each house, by heating and cooling system. Average U Value by Heating and Cooling System The U value of the average house using each heating and cooling system. 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. 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: Average Attributes 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: Housing Aging Chain & U Coflows 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 RateSUM( 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: Area Average Attributes Housing Aging Chain & U Coflows Used By Area of New Homes The total Area added by the construction of new homes, 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 Starts In Each Cohort Housing starts across heating and cooling systems. Increase in U Value from Housing Starts New U value from new homes being built. Total Housing Starts The total housing starts across all cohorts and sources. 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows Used By Housing Starts Across Cohorts Housing starts across all cohorts. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Actual EEHIC Subsidy for Retrofits The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value. Expected EEHIC Maximum Subsidy for Retrofits Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Actual EEHIC Subsidy for Retrofits The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value. Expected EEHIC Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Expected Maximum IRA Proportional Subsidy for Heat Pumps Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays. IRA Actual Subsidy for Heat Pumps The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value. 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: Area Used By Average Area of Housing Starts The average area of housing starts. 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: Housing Aging Chain & U Coflows Retrofitting Decision Making Used By Indicated Homes Retrofitting Number of homes that, once delays are taken into account, will be open to retrofitting. 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: Average Attributes Housing Aging Chain & U Coflows Used By Average Indicated Fraction of Homes Retrofitting The average fraction of homes that will retrofit retrofitting after decision delayacross all housing. Net Change in Homes Retrofitting Homes that are in the process of deciding to retrofit. 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: Area 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: Area Used By Average Area of Housing Starts The average area of housing starts. Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
HeatPumpModel_v31	#187 C	*Initial Average U Value (kBTU/(YearsfF))* 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: Housing Aging Chain & U Coflows 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: U Value of Housing Starts 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: Input Test 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: Housing Aging Chain & U Coflows Used By Initial Homes Not Retrofitting Initial homes not open to retrofitting. Initial Homes Retrofitting Homes that are open to retrofitting initially. 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: Housing Aging Chain & U Coflows Used By Initial Homes Not Retrofitting Initial homes not open to retrofitting. Initial Homes Retrofitting Homes that are open to retrofitting initially. 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 1SIN(23.14159( 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: Input Test 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: Cumulative Subsidies Used By Federal Annual Heat Pump Subsidy The amount of subsidies the federal government spends on heat pumps through the Inflation Reduction Act every year. 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: Perceived Subsidies & Costs Used By Expected Subsidy for Heat Pumps Total subsidy offered against retrofit cost across both lump sum and proportional subsidies. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Expected IRA Proportional Subsidy Rate for Heat Pumps Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. IRA Actual Subsidy for Heat Pumps The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value. 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: Perceived Subsidies & Costs Used By IRA Implemented Subsidy Proportional Rate for Heat Pumps 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. Implemented IRA Maximum Proportional Subsidy for Heat Pumps Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Implemented IRA Maximum Proportional Subsidy for Heat Pumps Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Perceived Subsidies & Costs Used By IRA Implemented Subsidy Proportional Rate for Heat Pumps 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. Implemented IRA Maximum Proportional Subsidy for Heat Pumps Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Perceived Subsidies & Costs Used By IRA Implemented Subsidy Proportional Rate for Heat Pumps 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. 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: Average and Peak Load Used By 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. 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: Optimal U & Retrofit Costs 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: Optimal U & Retrofit Costs U Value of Housing Starts Used By 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. 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: Optimal U & Retrofit Costs 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual MA Subsidies The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps. Annual Retrofit Subsidy The subsidies for retrofits paid out every year. 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: Perceived Subsidies & Costs Used By Expected Subsidy for Heat Pumps Total subsidy offered against retrofit cost across both lump sum and proportional subsidies. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By MassSave Expected Lump Sum Subsidy for Heat Pumps Expected lump sum subsidy that lowers subsidized retrofit costs from the state, taking into account information delays. Massachusetts Annual Heat Pumps Subsidy The actual subsidy provided for purchase of heat pumps by Massachusetts, as opposed to what the subsidy expected by homeowners is. 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: Perceived Subsidies & Costs Used By MassSave Implemented Lump Sum Subsidy for Heat Pumps Lump sum subsidy from MassSave 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	#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: Perceived Subsidies & Costs Used By MassSave Implemented Lump Sum Subsidy for Heat Pumps Lump sum subsidy from MassSave 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	#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: Perceived Subsidies & Costs Used By MassSave Implemented Lump Sum Subsidy for Heat Pumps Lump sum subsidy from MassSave 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	#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: Perceived Subsidies & Costs Used By Implemented MassSave Maximum Subsidy for Retrofits Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. Implemented MassSave Subsidy Proportional Rate for Retrofits 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. 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows Used By Monthly Total Heat Pump Sales The number of homes buying heat pumps, every year. 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: Age Used By Net Age Shift from Retrofitting Status Shifting Shift in age within each cohort due to houses becoming open or closed to retrofitting. 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: Age 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: Area 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: Age Area Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Input Test 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: Input Test Used By White Noise 1 White noise input to the pink noise process. 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: Input Test 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: Energy Use 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: Energy Use Used By Optimal Energy Cost Total energy cost if optimal U value is achieved. 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: Energy Use Used By Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value. Optimal Energy Use Average energy use to heat and cool per house if U is optimal. 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: Energy Use Retrofitting Decision Making Used By Average Energy Costs if Retrofitted Energy costs per year for each retrofitting house if homes retrofit to the optimal U value. 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: Energy Use 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: Energy Use Used By Optimal Energy Cost Total energy cost if optimal U value is achieved. 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: Energy Use Used By 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. 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: Average Attributes 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: Optimal U & Retrofit Costs 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	#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: Optimal U & Retrofit Costs 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: Average and Peak Load 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: Average and Peak Load 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: Average and Peak Load Used By Peak Heating Load on Grid Annual load from heat pumps providing heating on the coldest days, across all groups. 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: Average and Peak Load Used By Peak Cooling Load on Grid Annual load from heat pumps providing heating on the coldest day, across all groups. 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 ) = 18344.810000.461799 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: Average and Peak Load 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: Retrofitting Decision Making 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: Housing Aging Chain & U Coflows Retrofitting Decision Making Used By Affinity of Retrofitting Affinity of retrofitting, where utility value is equal to its NPV. 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: Carbon Emissions Used By 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. 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: Switching Systems 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: Switching Systems 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Used By Implemented EEHIC Maximum Subsidy for Retrofits Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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	#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: Cumulative Subsidies Perceived Subsidies & Costs Used By Expected IRA Proportional Subsidy Rate for Heat Pumps Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. 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: Input Test 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	#277 C	Ramp End Time 1 (Year) = 1e+09 Description: End time for the ramp input. Present In 1 View: Input Test 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	#280 C	Ramp Start Time 1 (Year) = 5 Description: Start time for the ramp input. Present In 1 View: Input Test 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: Switching Systems 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	#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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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. Affinity of Retrofitting Affinity of retrofitting, where utility value is equal to its NPV. 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: Cumulative Subsidies Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows Used By Retrofitting Across Cohorts and Systems The total amount of retrofits across all cohorts and heating/cooling systems. 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 Retrofitted Away Total amount of U value that has been retrofitted away. 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: Housing Aging Chain & U Coflows 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: Switching Systems 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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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. Affinity of Retrofitting Affinity of retrofitting, where utility value is equal to its NPV. 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: Input Test 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: Input Test 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: Optimal U & Retrofit Costs 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: Input Test 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: Switching Systems 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows Used By Net Change in Homes Retrofitting Homes that are in the process of deciding to retrofit. 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: Average Attributes Used By Average Area in All Housing The average are of all houses, regardless of what group they're in. 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: Average Attributes Used By Average Cooling Cost Across All Homes The average cost to cool a home, for all cohorts and systems. 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: Average Attributes Used By Average Cooling Energy Use Across All Homes The amount of energy an average home spends on cooling, regardless of cohort, retrofit status, etc. 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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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: Retrofitting Decision Making 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: Average Attributes Used By Average Energy Use in All Housing The average energy use across all stocks. 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: Cumulative Subsidies Housing Aging Chain & U Coflows Switching Systems Used By Federal Annual Heat Pump Subsidy The amount of subsidies the federal government spends on heat pumps through the Inflation Reduction Act every year. Massachusetts Annual Heat Pumps Subsidy The actual subsidy provided for purchase of heat pumps by Massachusetts, as opposed to what the subsidy expected by homeowners is. Monthly Total Heat Pump Sales The number of homes buying heat pumps, every year. 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: Average Attributes Used By Average Heating Cost Across All Homes The average amount a home spends on heating, regardless of cohort or heating and cooling system. 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: Average Attributes Used By Average Heating Energy Use Across All Homes The average heating energy use per home, regardless of cohort, system,etc. 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: Average Attributes 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: Housing Aging Chain & U Coflows 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: Input Test Used By Initial Housing Starts Initial value of housing starts, initialized at 10 total houses. 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: Switching Systems 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 System] dt + 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: Average Attributes Housing Aging Chain & U Coflows Used By Total U Value by Cohort Total U Value within each cohort. Total U Value by Heating and Cooling System The total U value by heating and cooling system U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc. 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: Average Attributes Used By Average U Value in All Housing The average U Value over the entire housing stock, not disaggregated by any groupings. 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: Average Attributes Used By Total U Value Across All Groupings Total U value across all groupings of households. 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: Average Attributes Used By Average U Value by Heating and Cooling System The U value of the average house using each heating and cooling system. 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: Optimal U & Retrofit Costs 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: Average and Peak Load Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems 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 (kBTUHouse/(YearYearsfF))* 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: Average Attributes Used By Average U Value of Houses Switching Into Sources The average U value of houses switching into each source, for each source. 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: Housing Aging Chain & U Coflows 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: Optimal U & Retrofit Costs 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: Housing Aging Chain & U Coflows 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: Average Attributes Housing Aging Chain & U Coflows 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: Switching Systems Used By Unsubsidized Cost of Heat Pumps The unsubsidized cost of heat pumps, instantiated at each time. 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: Cumulative Subsidies Perceived Subsidies & Costs Switching Systems Used By IRA Actual Subsidy for Heat Pumps The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value. IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. MassSave Implemented Lump Sum Subsidy for Heat Pumps Lump sum subsidy from MassSave that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year. Subsidized Cost of Heat Pumps The upfront cost of heat pump once subsidies are taken into account. 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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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: Input Test 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: Area Average Attributes 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: Input Test 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: Input Test 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: Input Test 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: Housing Aging Chain & U Coflows U Value of Housing Starts 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: Carbon Emissions 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: Cumulative Subsidies 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: Cumulative Subsidies 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: Cumulative Subsidies 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: Cumulative Subsidies 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: Age Average Attributes Average and Peak Load Carbon Emissions Cumulative Subsidies Housing Aging Chain & U Coflows Optimal U & Retrofit Costs 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. Average Cooling Cost Across All Homes The average cost to cool a home, for all cohorts and systems. Average Energy Use by Heating and Cooling System The average energy use for each home by heating and cooling system. Average Heating Cost Across All Homes The average amount a home spends on heating, regardless of cohort or heating and cooling system. Average Subsidized Retrofit Cost The average subsidized retrofit cost across all houses. Demolitions Homes that are destroyed every year. 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. 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. 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. 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 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. Housing by Heating and Cooling System Number of houses by energy source across all cohorts. Initial U Value Initial U value of cohorts; must be zero for cohorts not yet built. Net Change in Homes Retrofitting Homes that are in the process of deciding to retrofit. 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. 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. Total Cooling Cost The total amount of money spent on cooling homes, per year. Total Cooling Energy Use The total amount of energy spent on cooling homes. Total Heating Cost The total amount of money spent on heating homes. Total Heating Energy Use The total amount of energy spent on heating per year. Total Housing Stock Total number of houses across all cohorts, heating/cooling systems, and retrofitting status. U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc. 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: Age Average Attributes 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 System] dt + 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: Average Attributes Housing Aging Chain & U Coflows Used By Total U Value by Cohort Total U Value within each cohort. Total U Value by Heating and Cooling System The total U value by heating and cooling system U Value by Grouping The average U value in each home by cohort, heating/cooling system, etc. 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: Housing Aging Chain & U Coflows 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: Energy Use Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs 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: Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems U Value of Housing Starts 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: Perceived Subsidies & Costs Used By IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. 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: Perceived Subsidies & Costs Used By 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. 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs U Value of Housing Starts 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: Perceived Subsidies & Costs Used By IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making U Value of Housing Starts 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: Perceived Subsidies & Costs Used By Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs U Value of Housing Starts Used By Expected Lump Sum Subsidy Intensity Lump sum subsidy for retrofits per square foot. Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Perceived Subsidies & Costs Used By Expected Subsidy for Heat Pumps Total subsidy offered against retrofit cost across both lump sum and proportional subsidies. 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: Area Average Attributes 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: Age 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: Area 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: U Value of Housing Starts 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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)

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:

#184
LI,A

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: Age 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: Optimal U & Retrofit Costs Used By Amoritized Subsidized Retrofit Cost The incurred total retrofit cost amoritized over the specified amoritization period. 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: Optimal U & Retrofit Costs 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: Switching Systems 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: Switching Systems 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: Housing Aging Chain & U Coflows Switching Systems Used By Houses Considering Switching System The number of houses per year considering switching their heating and cooling system. 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: Average and Peak Load Used By 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]
.housingagingchain v8	#66 C	Cohort Duration (Year ) = 10 Description: The width (duration) of each cohort. Present In 2 Views: Age Housing Aging Chain & U Coflows 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: Energy Use Optimal U & Retrofit Costs Switching Systems 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: Carbon Emissions Used By Average Emissions from Cooling by Grouping The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status. 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: Input Test 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: Switching Systems 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: Switching Systems 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: Average and Peak Load Used By Average Daily Load from Heat Pumps The average load on the electric grid from heat pumps, per day. 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. 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: Perceived Subsidies & Costs Used By Expected EEHIC Maximum Subsidy for Retrofits Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays. Expected EEHIC Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. Expected IRA Proportional Subsidy Rate for Heat Pumps Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. Expected MassSave Maximum Subsidy for Retrofits Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays. Expected MassSave Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. Expected Maximum IRA Proportional Subsidy for Heat Pumps Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays. 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 HOMES Expected Lower Lump Sum Subsidy Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. MassSave Expected Lump Sum Subsidy for Heat Pumps Expected lump sum subsidy that lowers subsidized retrofit costs from the state, taking into account information delays. 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: Perceived Subsidies & Costs 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: Perceived Subsidies & Costs 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: Housing Aging Chain & U Coflows Used By Demolitions Homes that are destroyed every year. 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems U Value of Housing Starts 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: Perceived Subsidies & Costs Used By Implemented EEHIC Maximum Subsidy for Retrofits Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Perceived Subsidies & Costs 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Used By Implemented EEHIC Maximum Subsidy for Retrofits Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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	#95 C	Effect of Air Leakage from Window AC on Efficiency (dmnl) = 0.910/11 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: Energy Use 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]
.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: Input Test 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: Input Test 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 (DimensionlessYear) = 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: Input Test 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 (DimensionlessYear) = 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs 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 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: U Value of Housing Starts Used By Decrease in Code U The change in code U from policy. 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: Average and Peak Load Used By 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. 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: Average and Peak Load Used By 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. 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: Energy Use Optimal U & Retrofit Costs Switching Systems 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: Carbon Emissions Used By Average Emissions from Heating by Grouping Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc. 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: Optimal U & Retrofit Costs 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: Cumulative Subsidies Perceived Subsidies & Costs 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. Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Perceived Subsidies & Costs Used By HOMES Implemented High Subsidy Implemented higher subsidy from the HOMES rebate program. 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: Perceived Subsidies & Costs 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: Perceived Subsidies & Costs Used By HOMES Implemented High Subsidy Implemented higher subsidy from the HOMES rebate program. 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: Perceived Subsidies & Costs Used By HOMES Implemented High Subsidy Implemented higher subsidy from the HOMES rebate program. 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	#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: Housing Aging Chain & U Coflows 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: Input Test 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 (DimensionlessYear) = 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: Input Test 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: Input Test 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: Input Test 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: Area Used By Average Area of Housing Starts The average area of housing starts. 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: Area 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: Area Used By Average Area of Housing Starts The average area of housing starts. Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
HeatPumpModel_v31	#187 C	*Initial Average U Value (kBTU/(YearsfF))* 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: Housing Aging Chain & U Coflows 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: U Value of Housing Starts 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: Input Test 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: Housing Aging Chain & U Coflows Used By Initial Homes Not Retrofitting Initial homes not open to retrofitting. Initial Homes Retrofitting Homes that are open to retrofitting initially. 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: Input Test 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows Used By Initial Homes Not Retrofitting Initial homes not open to retrofitting. Initial Homes Retrofitting Homes that are open to retrofitting initially. 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: Housing Aging Chain & U Coflows 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: Perceived Subsidies & Costs Used By IRA Implemented Subsidy Proportional Rate for Heat Pumps 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. Implemented IRA Maximum Proportional Subsidy for Heat Pumps Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Implemented IRA Maximum Proportional Subsidy for Heat Pumps Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Perceived Subsidies & Costs Used By IRA Implemented Subsidy Proportional Rate for Heat Pumps 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. Implemented IRA Maximum Proportional Subsidy for Heat Pumps Maximum proportional subsidy for heat pumps that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Perceived Subsidies & Costs Used By IRA Implemented Subsidy Proportional Rate for Heat Pumps 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. 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: Average and Peak Load Used By 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. 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs Used By Implemented MassSave Subsidy Proportional Rate for Retrofits 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. 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: Perceived Subsidies & Costs Used By MassSave Implemented Lump Sum Subsidy for Heat Pumps Lump sum subsidy from MassSave 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	#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: Perceived Subsidies & Costs Used By MassSave Implemented Lump Sum Subsidy for Heat Pumps Lump sum subsidy from MassSave 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	#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: Perceived Subsidies & Costs Used By MassSave Implemented Lump Sum Subsidy for Heat Pumps Lump sum subsidy from MassSave 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	#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: Perceived Subsidies & Costs Used By Implemented MassSave Maximum Subsidy for Retrofits Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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: Housing Aging Chain & U Coflows Used By Monthly Total Heat Pump Sales The number of homes buying heat pumps, every year. 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: Housing Aging Chain & U Coflows 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test Used By White Noise 0 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: Input Test Used By White Noise 1 White noise input to the pink noise process. 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: Input Test 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: Input Test 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: Input Test 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 ) = 18344.810000.461799 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: Average and Peak Load 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: Carbon Emissions Used By 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. 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Used By Implemented EEHIC Maximum Subsidy for Retrofits Maximum proportional subsidy from EEHIC that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. 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	#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: Cumulative Subsidies Perceived Subsidies & Costs Used By Expected IRA Proportional Subsidy Rate for Heat Pumps Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs Used By Implemented MassSave Maximum Subsidy for Retrofits Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. Implemented MassSave Subsidy Proportional Rate for Retrofits 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. 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: Perceived Subsidies & Costs 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. Expected EEHIC Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. Expected MassSave Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. 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. 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Switching Systems 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:* Housing Aging Chain & U Coflows Perceived Subsidies & Costs Used By 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	#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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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. Affinity of Retrofitting Affinity of retrofitting, where utility value is equal to its NPV. 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: Optimal U & Retrofit Costs Retrofitting Decision Making U Value of Housing Starts 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: Cumulative Subsidies Housing Aging Chain & U Coflows 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	#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: Switching Systems 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Retrofitting Decision Making U Value of Housing Starts 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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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. Affinity of Retrofitting Affinity of retrofitting, where utility value is equal to its NPV. 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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: Input Test 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	#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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows Used By Net Change in Homes Retrofitting Homes that are in the process of deciding to retrofit. 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: Housing Aging Chain & U Coflows 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: Input Test Used By Initial Housing Starts Initial value of housing starts, initialized at 10 total houses. 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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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	#126 C	FINAL TIME (Year) = 2050 Description: The final time for the simulation. Present In 1 View: Perceived Subsidies & Costs Used By MassSave Subsidy for Retrofits Final Year The year in which the subsidy is phased out. If final time, then has no ending data. 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: Area Housing Aging Chain & U Coflows Input Test 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: Input Test 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: Age 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 YearSUM( 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: Age 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual Subsidies The amount of subsidies spent on heat pumps and retrofits every year. Cumulative Subsidies for Heat Pumps The total amount of dollars spent on subsidizing heat pumps throughout the model's run. 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual Subsidies The amount of subsidies spent on heat pumps and retrofits every year. Cumulative Subsidy for Retrofits The total amount spent on retrofits since the beginning of the model's run. 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 StartsSUM( Housing Starts[ Cohort, Heating and Cooling System!]) Description:* The total Area added by the construction of new homes, by cohort. Present In 1 View: Area 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: Area 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: Input Test 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: Input Test 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: Input Test 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: U Value of Housing Starts 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: Age Area Housing Aging Chain & U Coflows 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: Average Attributes Carbon Emissions 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: Age Average Attributes Housing Aging Chain & U Coflows Used By Houses Switching Into Sources The number of houses switching into each Heating and Cooling System, cohort, and retrofitting group due to system switching. 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. Total Heat Pump Sales Number of houses buying heat pumps every year. U Value Shift from Source Switching The shift in total U value coming from switching sources. 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 RateSUM( 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: Area Average Attributes Housing Aging Chain & U Coflows Used By Area of New Homes The total Area added by the construction of new homes, 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 Starts In Each Cohort Housing starts across heating and cooling systems. Increase in U Value from Housing Starts New U value from new homes being built. Total Housing Starts The total housing starts across all cohorts and sources. 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: Housing Aging Chain & U Coflows 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: Age 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: Area 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: Age Area Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows Used By Retrofitting Across Cohorts and Systems The total amount of retrofits across all cohorts and heating/cooling systems. 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 Retrofitted Away Total amount of U value that has been retrofitted away. 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: Housing Aging Chain & U Coflows 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: Average Attributes Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Cumulative Subsidies Used By Federal Annual Retrofit Subsidy The amount of federal subsidies spent by the federal government, through the IRA. 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: Cumulative Subsidies Used By Federal Annual Retrofit Subsidy The amount of federal subsidies spent by the federal government, through the IRA. 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: Cumulative Subsidies Used By Massachusetts Annual Retrofit Subsidy Amount of money Massachusetts spends on MassSave subsidies for retrofits, yearly. 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: U Value of Housing Starts 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: Switching Systems 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: Retrofitting Decision Making 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: Average Attributes Retrofitting Decision Making 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: Age 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 YearSUM( 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: Age 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Retrofitting Decision Making 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. Total Cost of Ownership of Retrofitted Homes The total cost of ownership of owning a home that has been retrofitted to the optimal U. 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual Subsidies The amount of subsidies spent on heat pumps and retrofits every year. Cumulative Subsidies for Heat Pumps The total amount of dollars spent on subsidizing heat pumps throughout the model's run. 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: Average and Peak Load Used By Average Daily Load from Heat Pumps The average load on the electric grid from heat pumps, per day. 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual Subsidies The amount of subsidies spent on heat pumps and retrofits every year. Cumulative Subsidy for Retrofits The total amount spent on retrofits since the beginning of the model's run. 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: Cumulative Subsidies 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 StartsSUM( Housing Starts[ Cohort, Heating and Cooling System!]) Description:* The total Area added by the construction of new homes, by cohort. Present In 1 View: Area 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: Area 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: Age 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: Area Average Attributes 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: Area Average Attributes Average and Peak Load Energy Use Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Area Average Attributes Used By Average EUI in All Housing The average energy use intensity across all housing. 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: Area U Value of Housing Starts Used By Area of New Homes The total Area added by the construction of new homes, by cohort. Expected Lump Sum Subsidy Intensity Lump sum subsidy for retrofits per square foot. 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: Average Attributes Energy Use Used By Average Energy Cost The average cost of both heating and cooling a home, by grouping. Total Cooling Cost The total amount of money spent on cooling homes, per year. 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: Average Attributes 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: Average Attributes Carbon Emissions Energy Use Used By Average Cooling Cost The average costs for keeping a home cool, by grouping. Average Emissions from Cooling by Grouping The GHG emissions from cooling the average home, by cohort, heating and cooling system, and retrofitting status. Average Energy Use Average energy use to both heat and cool a home. Total Cooling Energy Use The total amount of energy spent on cooling homes. 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: Average Attributes 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: Average and Peak Load 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: Average Attributes 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: Average Attributes Carbon Emissions Used By Emissions by Grouping The total emissions for the most disaggregated grouping in the model. 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: Average Attributes Carbon Emissions 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: Carbon Emissions 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: Carbon Emissions 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: Energy Use Retrofitting Decision Making Used By Average Energy Costs for Retrofitting Home Heating costs for each home open to retrofitting, annually, if no further retrofit measures are undertaken. 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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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/(YearHouse)) 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: Housing Aging Chain & U Coflows Retrofitting Decision Making Used By Total Cost of Ownership of Retrofitted Homes The total cost of ownership of owning a home that has been retrofitted to the optimal U. 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: Average Attributes Energy Use Used By Average EUI by Grouping The average energy use intensity by grouping Energy Use by Grouping The total amount of energy used for heating and cooling in each group. 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: Average Attributes 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: Average Attributes Used By Average EUI in All Housing The average energy use intensity across all housing. 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: Average Attributes 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: Average Attributes 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: Average Attributes Energy Use Used By Average Energy Cost The average cost of both heating and cooling a home, by grouping. Total Heating Cost The total amount of money spent on heating homes. 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: Average Attributes 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: Average Attributes Carbon Emissions Energy Use Used By Average Emissions from Heating by Grouping Disaggregated carbon dioxide emissions from heating for each house, by cohort, retrofitting status, etc. Average Energy Use Average energy use to both heat and cool a home. Average Heating Cost The costs per year to heat one house. Total Heating Energy Use The total amount of energy spent on heating per year. 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: Average Attributes 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: Average Attributes Optimal U & Retrofit Costs 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: Optimal U & Retrofit Costs 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: Average Attributes 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: Average Attributes 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: Average Attributes 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: Input Test 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: Input Test 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: Input Test 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: Energy Use Input Test Perceived Subsidies & Costs 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: Switching Systems 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: Average and Peak Load Energy Use Optimal U & Retrofit Costs Switching Systems 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: Switching Systems 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: Switching Systems 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: Cumulative Subsidies 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: U Value of Housing Starts 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: Age Area Housing Aging Chain & U Coflows 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: Perceived Subsidies & Costs Used By Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Average Attributes Carbon Emissions 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: Average Attributes Carbon Emissions Used By Emissions The total amount of emissions across all housing groups. Emissions by Heating and Cooling System The total amount of emissions for houses by Heating and Cooling System. 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: Average Attributes Used By Average Emissions by Heating and Cooling System The average CO2 emissions for each house, by heating and cooling system. 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: Cumulative Subsidies Perceived Subsidies & Costs 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. Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Average Attributes 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: Average Attributes Average and Peak Load Used By Annual Load from Heat Pumps The load on the electric grid from servicing heating and cooling demand from heat pumps, across the whole year. Average Energy Use by Heating and Cooling System The average energy use for each home by heating and cooling system. Energy Use by Gas Houses The total amount of energy for heating and cooling used by homes which primarily use gas to heat their homes. Energy Use by Heat Pump Houses The amount of energy used for heating and cooling by homes which primarily use heat pumps to heat their home. Energy Use by Oil Houses The total amount of energy for heating and cooling used by homes primarily using oil to heat their home. Total Energy Use The total energy use for all homes in the model. 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: Average Attributes 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: Average Attributes 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: Energy Use Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs 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: Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems U Value of Housing Starts 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: Perceived Subsidies & Costs Used By IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. 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: U Value of Housing Starts 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: Perceived Subsidies & Costs Used By 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. 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs U Value of Housing Starts 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: Perceived Subsidies & Costs Used By IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. 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: Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making U Value of Housing Starts 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: Perceived Subsidies & Costs Switching Systems Used By Subsidized Cost of Heat Pumps The upfront cost of heat pump once subsidies are taken into account. 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual Federal Subsidies The amount of money the federal government spends on subsidies for heat pumps and retrofits, each year. Annual Retrofit Subsidy The subsidies for retrofits paid out every year. 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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs 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: Average Attributes 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: Housing Aging Chain & U Coflows Switching Systems 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: Average Attributes 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: Average Attributes 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: Area Average Attributes 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: Average Attributes 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: Energy Use Housing Aging Chain & U Coflows Input Test Optimal U & Retrofit Costs Perceived Subsidies & Costs Switching Systems 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: Switching Systems 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: Energy Use Optimal U & Retrofit Costs Switching Systems 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: Perceived Subsidies & Costs Used By Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs U Value of Housing Starts Used By Expected Lump Sum Subsidy Intensity Lump sum subsidy for retrofits per square foot. Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Cumulative Subsidies Perceived Subsidies & Costs 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: Cumulative Subsidies Perceived Subsidies & Costs 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 Lower Lump Sum Subsidy Expected lump sum subsidy that lowers subsidized retrofit costs, taking into account information delays. 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Cumulative Subsidies Used By Federal Annual Retrofit Subsidy The amount of federal subsidies spent by the federal government, through the IRA. Massachusetts Annual Retrofit Subsidy Amount of money Massachusetts spends on MassSave subsidies for retrofits, yearly. 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: Average Attributes Used By Average U Value of Houses Switching Into Sources The average U value of houses switching into each source, for each source. 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: Age Average Attributes Housing Aging Chain & U Coflows Used By Houses Switching Into Sources The number of houses switching into each Heating and Cooling System, cohort, and retrofitting group due to system switching. 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. Total Heat Pump Sales Number of houses buying heat pumps every year. U Value Shift from Source Switching The shift in total U value coming from switching sources. 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: Average Attributes 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: Average Attributes Housing Aging Chain & U Coflows Used By Indicated Homes Retrofitting Number of homes that, once delays are taken into account, will be open to retrofitting. 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: Age Area Average Attributes 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: Average Attributes Used By Average Emissions by Heating and Cooling System The average CO2 emissions for each house, by heating and cooling system. Average U Value by Heating and Cooling System The U value of the average house using each heating and cooling system. 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. 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: Average Attributes 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 RateSUM( 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: Area Average Attributes Housing Aging Chain & U Coflows Used By Area of New Homes The total Area added by the construction of new homes, 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 Starts In Each Cohort Housing starts across heating and cooling systems. Increase in U Value from Housing Starts New U value from new homes being built. Total Housing Starts The total housing starts across all cohorts and sources. 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows Used By Housing Starts Across Cohorts Housing starts across all cohorts. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Actual EEHIC Subsidy for Retrofits The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value. Expected EEHIC Maximum Subsidy for Retrofits Expected maximum proportional subsidy that lowers subsidized retrofit costs from the Energy Efficiency Home Improvement Credit, taking into account information delays. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Actual EEHIC Subsidy for Retrofits The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value. Expected EEHIC Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Expected Maximum IRA Proportional Subsidy for Heat Pumps Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays. IRA Actual Subsidy for Heat Pumps The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Actual MassSave Subsidy for Retrofits The actual subsidy offered for retrofits by MassSave, not the expected value. Expected MassSave Maximum Subsidy for Retrofits Expected maximum proportional subsidy that lowers subsidized retrofit costs, taking into account information delays. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Actual MassSave Subsidy for Retrofits The actual subsidy offered for retrofits by MassSave, not the expected value. Expected MassSave Proportional Subsidy Rate for Retrofits Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows Retrofitting Decision Making Used By Indicated Homes Retrofitting Number of homes that, once delays are taken into account, will be open to retrofitting. 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: Average Attributes Housing Aging Chain & U Coflows Used By Average Indicated Fraction of Homes Retrofitting The average fraction of homes that will retrofit retrofitting after decision delayacross all housing. Net Change in Homes Retrofitting Homes that are in the process of deciding to retrofit. 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: Age 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: Input Test 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 AmplitudeSIN(23.14159( 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: Input Test 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 0SIN(23.14159( 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: Input Test 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 1SIN(23.14159( 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: Input Test 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: Cumulative Subsidies Used By Federal Annual Heat Pump Subsidy The amount of subsidies the federal government spends on heat pumps through the Inflation Reduction Act every year. 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: Perceived Subsidies & Costs Used By Expected Subsidy for Heat Pumps Total subsidy offered against retrofit cost across both lump sum and proportional subsidies. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By Expected IRA Proportional Subsidy Rate for Heat Pumps Expected proportional subsidy rate that lowers subsidized retrofit costs, taking into account information delays. IRA Actual Subsidy for Heat Pumps The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value. 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: Optimal U & Retrofit Costs 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: Optimal U & Retrofit Costs U Value of Housing Starts Used By 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. 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: Optimal U & Retrofit Costs 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: Optimal U & Retrofit Costs U Value of Housing Starts 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: Optimal U & Retrofit Costs Used By 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. 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: Cumulative Subsidies 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: Cumulative Subsidies Used By Annual MA Subsidies The subsidies that the Massachusetts state government gives out per year for both retrofits and heat pumps. Annual Retrofit Subsidy The subsidies for retrofits paid out every year. 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: Perceived Subsidies & Costs Used By Expected Subsidy for Heat Pumps Total subsidy offered against retrofit cost across both lump sum and proportional subsidies. 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: Housing Aging Chain & U Coflows Perceived Subsidies & Costs Used By Expected Subsidy for Retrofits Total subsidy offered against retrofit cost across both lump sum and proportional subsidy. 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: Cumulative Subsidies Perceived Subsidies & Costs Used By MassSave Expected Lump Sum Subsidy for Heat Pumps Expected lump sum subsidy that lowers subsidized retrofit costs from the state, taking into account information delays. Massachusetts Annual Heat Pumps Subsidy The actual subsidy provided for purchase of heat pumps by Massachusetts, as opposed to what the subsidy expected by homeowners is. 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: Perceived Subsidies & Costs Used By Implemented MassSave Maximum Subsidy for Retrofits Maximum proportional subsidy that is actually implemented. Equal to zero before implementation year and to maximum proportional subsidy after implementation year. Implemented MassSave Subsidy Proportional Rate for Retrofits 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. 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: Housing Aging Chain & U Coflows 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: Age Used By Net Age Shift from Retrofitting Status Shifting Shift in age within each cohort due to houses becoming open or closed to retrofitting. 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: Age 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: Area Used By Net Area Shift due to Retrofit Status Switching Shift in area between energy sources due to houses switching sources. 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: Area 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: Age Area Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows 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: Energy Use Used By Optimal Energy Cost Total energy cost if optimal U value is achieved. 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: Energy Use Used By Optimal Cooling Cost The average cost of cooling, if homes have the optimal U value. Optimal Energy Use Average energy use to heat and cool per house if U is optimal. 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: Energy Use Retrofitting Decision Making Used By Average Energy Costs if Retrofitted Energy costs per year for each retrofitting house if homes retrofit to the optimal U value. 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: Energy Use 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: Energy Use Used By Optimal Energy Cost Total energy cost if optimal U value is achieved. 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: Energy Use Used By 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. 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: Average Attributes 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: Housing Aging Chain & U Coflows U Value of Housing Starts 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: Optimal U & Retrofit Costs 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: Average Attributes Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems 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: Optimal U & Retrofit Costs 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: Average and Peak Load 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: Average and Peak Load 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: Average and Peak Load Used By Peak Heating Load on Grid Annual load from heat pumps providing heating on the coldest days, across all groups. 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: Average and Peak Load Used By Peak Cooling Load on Grid Annual load from heat pumps providing heating on the coldest day, across all groups. 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: Retrofitting Decision Making 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: Housing Aging Chain & U Coflows Retrofitting Decision Making Used By Affinity of Retrofitting Affinity of retrofitting, where utility value is equal to its NPV. 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Switching Systems 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: Housing Aging Chain & U Coflows Used By Retrofitting Across Cohorts and Systems The total amount of retrofits across all cohorts and heating/cooling systems. 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 Retrofitted Away Total amount of U value that has been retrofitted away. 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: Housing Aging Chain & U Coflows 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: Optimal U & Retrofit Costs 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: Switching Systems 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: Optimal U & Retrofit Costs Used By Amoritized Subsidized Retrofit Cost The incurred total retrofit cost amoritized over the specified amoritization period. Average Subsidized Retrofit Cost The average subsidized retrofit cost across all houses. 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: Average Attributes Used By Average Area in All Housing The average are of all houses, regardless of what group they're in. 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: Average Attributes Used By Average Cooling Cost Across All Homes The average cost to cool a home, for all cohorts and systems. 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: Average Attributes Used By Average Cooling Energy Use Across All Homes The amount of energy an average home spends on cooling, regardless of cohort, retrofit status, etc. 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: Housing Aging Chain & U Coflows Retrofitting Decision Making 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: Retrofitting Decision Making 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: Average Attributes Used By Average Energy Use in All Housing The average energy use across all stocks. 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: Cumulative Subsidies Housing Aging Chain & U Coflows Switching Systems Used By Federal Annual Heat Pump Subsidy The amount of subsidies the federal government spends on heat pumps through the Inflation Reduction Act every year. Massachusetts Annual Heat Pumps Subsidy The actual subsidy provided for purchase of heat pumps by Massachusetts, as opposed to what the subsidy expected by homeowners is. Monthly Total Heat Pump Sales The number of homes buying heat pumps, every year. 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: Average Attributes Used By Average Heating Cost Across All Homes The average amount a home spends on heating, regardless of cohort or heating and cooling system. 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: Average Attributes Used By Average Heating Energy Use Across All Homes The average heating energy use per home, regardless of cohort, system,etc. 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: Average Attributes 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: Average Attributes Social Influence in Retrofitting Decisions Used By Average Age in All Housing Average age of houses, regardless of cohort Average Area in All Housing The average are of all houses, regardless of what group they're in. Average Cooling Energy Use Across All Homes The amount of energy an average home spends on cooling, regardless of cohort, retrofit status, etc. Average Emissions The average CO2 emissions for a household, not disaggregated into any grouping. Average Energy Use in All Housing The average energy use across all stocks. Average Heating Energy Use Across All Homes The average heating energy use per home, regardless of cohort, system,etc. Average Indicated Fraction of Homes Retrofitting The average fraction of homes that will retrofit retrofitting after decision delayacross all housing. Average U Value in All Housing The average U Value over the entire housing stock, not disaggregated by any groupings. 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. 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. 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: Switching Systems 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: Average Attributes Used By Average U Value in All Housing The average U Value over the entire housing stock, not disaggregated by any groupings. 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: Average Attributes Used By Total U Value Across All Groupings Total U value across all groupings of households. 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: Average Attributes Used By Average U Value by Heating and Cooling System The U value of the average house using each heating and cooling system. 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: Optimal U & Retrofit Costs 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: Average and Peak Load Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems 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 (kBTUHouse/(YearYearsfF))* 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: Average Attributes Used By Average U Value of Houses Switching Into Sources The average U value of houses switching into each source, for each source. 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: Housing Aging Chain & U Coflows 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: Housing Aging Chain & U Coflows U Value of Housing Starts Used By Increase in U Value from Housing Starts New U value from new homes being built. 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: Optimal U & Retrofit Costs 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: Average Attributes Housing Aging Chain & U Coflows 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: Cumulative Subsidies Perceived Subsidies & Costs Switching Systems Used By IRA Actual Subsidy for Heat Pumps The actual implemented subsidy for heat pumps from the Inflation Reduction Act, as opposed to the expected subsidy value. IRA Expected Proportional Subsidy for Heat Pumps The IRA's subsidies for a heat pump's upfront costsintensity, taking into account whether it has gone into effect. MassSave Implemented Lump Sum Subsidy for Heat Pumps Lump sum subsidy from MassSave that is actually implemented. Equal to zero before implementation year and to lump sum subsidy after implementation year. Subsidized Cost of Heat Pumps The upfront cost of heat pump once subsidies are taken into account. 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: Cumulative Subsidies Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Retrofitting Decision Making Used By Actual EEHIC Subsidy for Retrofits The actual subsidy for retrofits by the Energy Efficiency Home Improvement Credit, not the expected value. Actual MassSave Subsidy for Retrofits The actual subsidy offered for retrofits by MassSave, not the expected value. 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	#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: Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making 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. 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. Unsubsidized Retrofit Cost Total retrofit cost without taking into account subsidies. 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: Input Test 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: Input Test 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: Input Test 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: Average and Peak Load Energy Use Optimal U & Retrofit Costs Switching Systems 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: Age Area Average Attributes Average and Peak Load Carbon Emissions Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems U Value of Housing Starts 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]
HeatPumpModel_v31	#-4 Sub	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: Age Average Attributes Average and Peak Load Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems 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 Sub	Gas and Window or No AC () Gas and Window or No AC:Gas and Window AC, Gas and No AC Present In 1 View: Switching Systems 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. 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	#-6 Sub	Gas Heating () Gas Heating:Gas and Central AC, Gas and Window AC, Gas and No AC Present In 6 Views: Carbon Emissions Energy Use Housing Aging Chain & U Coflows Input Test Optimal U & Retrofit Costs Switching Systems 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 Sub	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: Age 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 Switching Systems 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. Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
HeatPumpModel_v31	#-9 Sub	Heating () Heating:Heat Pump, Gas, Oil Present In 0 Views: Used By Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
HeatPumpModel_v31	#-8 Sub	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 Present In 14 Views: 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 Switching Systems U Value of Housing Starts Used By 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. Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
HeatPumpModel_v31	#-10 Sub	New Cohorts () New Cohorts:From 2021 to 2030, From 2031 to 2040, From 2041 to 2050 Present In 0 Views: Used By Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
HeatPumpModel_v31	#-11 Sub	No AC Cooling () No AC Cooling:Gas and No AC, Oil and No AC Present In 6 Views: Average Attributes Average and Peak Load Carbon Emissions Energy Use Optimal U & Retrofit Costs Switching Systems 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 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. Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
HeatPumpModel_v31	#-12 Sub	Oil and Window or No AC () Oil and Window or No AC:Oil and Window AC, Oil and No AC Present In 1 View: Switching Systems 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. 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	#-13 Sub	Oil Heating () Oil Heating:Oil and Central AC, Oil and Window AC, Oil and No AC Present In 6 Views: Carbon Emissions Energy Use Housing Aging Chain & U Coflows Input Test Optimal U & Retrofit Costs Switching Systems 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]
.housingagingchain v8	#-14 Sub	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 Present In 8 Views: Age Area Average Attributes Average and Peak Load Carbon Emissions Cumulative Subsidies Housing Aging Chain & U Coflows Optimal U & Retrofit Costs 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. 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. Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
HeatPumpModel_v31	#-15 Sub	Retrofit Cost () Retrofit Cost:Existing Housing, New Housing Present In 1 View: U Value of Housing Starts Used By Expected Lump Sum Subsidy Intensity Lump sum subsidy for retrofits per square foot. Feedback Loops: 0 (0.0%) (+) 0 [0,0] (-) 0 [0,0]
HeatPumpModel_v31	#-16 Sub	Retrofitting Status () Retrofitting Status:Not Open to Retrofitting, Open to Retrofitting Present In 12 Views: Age Area Average Attributes Average and Peak Load Carbon Emissions Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems 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. 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: Used By 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: Average and Peak Load Cumulative Subsidies Energy Use Housing Aging Chain & U Coflows Optimal U & Retrofit Costs Perceived Subsidies & Costs Retrofitting Decision Making Switching Systems 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: Average and Peak Load Energy Use Optimal U & Retrofit Costs Switching Systems 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]

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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: Energy Use 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: Energy Use 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: Energy Use 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: Energy Use 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. Present In 1 View: Switching Systems Used By Unsubsidized Cost of Heat Pumps The unsubsidized cost of heat pumps, instantiated at each time. 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 v8	C	Active Cohort Indicator[Preexisting Cohorts] (dmnl)
HeatPumpModel_v31	A	Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
HeatPumpModel_v31	A	Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar/ Home)
HeatPumpModel_v31	A	Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
.housingagingchain v15	A	Additional Cost of Building to U Value[Cohort,Heating and Cooling System] (Dollar / sf)
HeatPumpModel_v31	A	Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Affinity of Not Retrofitting[Cohort,Heating and Cooling System] (dmnl)
.housingagingchain v4 testing	A	Affinity of Retrofitting[Cohort,Heating and Cooling System] (dmnl)
.housingagingchain v8	F,A	Age Removal[Cohort,Retrofitting Status] (House * Year /Year)
.housingagingchain v8	F,A	Aging[Cohort,Retrofitting Status] (House * Year / Year)
.housingagingchain v8	C	Aging per Year (Year / Year)
HeatPumpModel_v31	C	Amoritization Period (Year )
.housingagingchain v15	A	Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar / (House * Year))
HeatPumpModel_v31	F,A	Annual Federal Subsidies (Dollar / Year)
HeatPumpModel_v31	F,A	Annual Heat Pump Subsidy (Dollar / Year)
HeatPumpModel_v31	A	Annual Load from Heat Pumps (kBTU / Year)
HeatPumpModel_v31	F,A	Annual MA Subsidies (Dollar / Year)
HeatPumpModel_v31	F,A	Annual Retrofit Subsidy (Dollar / Year)
HeatPumpModel_v31	A	Annual Subsidies (Dollar / Year)
.housingagingchain v8	L	Area[Preexisting Cohorts,Open to Retrofitting] (sf)
.housingagingchain v8	F,A	Area of New Homes[Cohort] (sf / Year)
.housingagingchain v8	F,A	Area Removal[Cohort,Retrofitting Status] (sf /Year)
.housingagingchain v8	L	Autocorrelated Noise (Dimensionless)
.housingagingchain v8	L	Autocorrelated Noise 0 (Dimensionless)
HeatPumpModel_v31	L	Autocorrelated Noise 1 (Dimensionless)
.housingagingchain v8	A	Average Age[Cohort,Retrofitting Status] (Year)
.housingagingchain v8	A	Average Age in All Housing (Year)
HeatPumpModel_v31	A	Average Area[Cohort,Retrofitting Status] (sf / House)
.housingagingchain v8	A	Average Area in All Housing (sf/ House)
HeatPumpModel_v31	A	Average Area of Housing Starts (sf / House)
HeatPumpModel_v31	A	Average Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	A	Average Cooling Cost Across All Homes (Dollar / House/ Year)
HeatPumpModel_v31	C	Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] (kBTU / (Year * House))
HeatPumpModel_v31	A	Average Cooling Energy Use Across All Homes (kBTU / Year / House)
HeatPumpModel_v31	A	Average Daily Load from Heat Pumps (kBTU / Day)
HeatPumpModel_v31	A	Average Emissions (tCO2 / House / Year)
HeatPumpModel_v31	A	Average Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (Year * House))
HeatPumpModel_v31	A	Average Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year / House)
HeatPumpModel_v31	A	Average Emissions from Cooling by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (House * Year))
HeatPumpModel_v31	A	Average Emissions from Heating by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (House * Year))
HeatPumpModel_v31	A	Average Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
.housingagingchain v15	A	Average Energy Costs for Retrofitting Home[Cohort,Heating and Cooling System] (Dollar / Year / House)
.housingagingchain v8	A	Average Energy Costs if Retrofitted[Cohort,Heating and Cooling System] (Dollar/(Year*House))
HeatPumpModel_v31	A	Average Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (Year * House))
HeatPumpModel_v31	A	Average Energy Use by Heating and Cooling System[Heating and Cooling System] (kBTU / (House * Year))
HeatPumpModel_v31	A	Average Energy Use in All Housing (kBTU / Year / House)
HeatPumpModel_v31	A	Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * Year))
HeatPumpModel_v31	A	Average EUI in All Housing (kBTU / (sf * Year))
.housingagingchain v5 testing	A	Average Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	A	Average Heating Cost Across All Homes (Dollar / Year / House)
HeatPumpModel_v31	A	Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (Year * House))
HeatPumpModel_v31	A	Average Heating Energy Use Across All Homes (kBTU / (Year * House))
HeatPumpModel_v31	C	Average Income (Dollar / Hour / House )
HeatPumpModel_v31	A	Average Indicated Fraction of Homes Retrofitting (dmnl)
HeatPumpModel_v31	A	Average Lifetime of Cooling Technology[No AC Cooling] (Years)
HeatPumpModel_v31	C	Average Lifetime of Heating Technology[Oil Heating] (Year)
HeatPumpModel_v31	A	Average Subsidized Retrofit Cost (Dollar / House)
HeatPumpModel_v31	C	Average Time To Consider Switching (Year )
HeatPumpModel_v31	A	Average U Value by Heating and Cooling System[Heating and Cooling System] (kBTU / (sf * F * Year))
.housingagingchain v4 testing	A	Average U Value in All Housing (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Average U Value of Houses Switching Into Sources[Heating and Cooling System] (kBTU / (sf * F * Year))
HeatPumpModel_v31	C	CDD on Coldest Day (F )
.housingagingchain v8	F,A	Change in AC Noise (1/Year)
.housingagingchain v8	F,A	Change in AC Noise 0 (1/Year)
HeatPumpModel_v31	F,A	Change in AC Noise 1 (1/Year)
.housingagingchain v18	L	Code U (kBTU / (sf * Year * F))
.housingagingchain v8	C	Cohort Duration (Year )
HeatPumpModel_v31	C	Cooling Degree Days (F )
HeatPumpModel_v31	C	Cooling Emissions Factor (lb CO2 / kBTU)
HeatPumpModel_v31	A	Cooling Energy Price (Dollar / kBTU)
HeatPumpModel_v31	C	Cooling Energy Price Step Height 1 (Dimensionless )
HeatPumpModel_v31	A	Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
HeatPumpModel_v31	A	Cooling System Efficiency[No AC Cooling] (dmnl)
HeatPumpModel_v31	C	Cost of Bad Air Conditioning[No AC Cooling] (Dollar / House )
HeatPumpModel_v31	C	Cost of Cooling System Replacement[No AC Cooling] (Dollar / House)
HeatPumpModel_v31	C	Cost of Heating System Replacement[Oil Heating] (Dollar / House )
.housingagingchain v15	A	Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Oil] (Dollar / House)
HeatPumpModel_v31	L	Cumulative Emissions (tCO2)
HeatPumpModel_v31	L	Cumulative Federal Subsidy (Dollar)
HeatPumpModel_v31	L	Cumulative MA Subsidy (Dollar)
HeatPumpModel_v31	A	Cumulative Subsidies (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidies for Heat Pumps (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidy for Retrofits (Dollar)
HeatPumpModel_v31	C	Days per Year (Day / Year )
.housingagingchain v18	F,A	Decrease in Code U (kBTU / (sf * Year * F) / Year)
.housingagingchain v15	C	Delay in Changing Subsidy Expectations (Year )
.housingagingchain v15	C	Delay in Forming Expectations of Energy Price (Year )
.housingagingchain v15	C	Delay in Forming Expectations of Retrofit Costs (Year )
HeatPumpModel_v31	C	Demolition Hazard Rate (1 / Year )
HeatPumpModel_v31	F,A	Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] (House / Year)
HeatPumpModel_v31	C	Discount Rate (1 / Year )
HeatPumpModel_v31	A	EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
HeatPumpModel_v31	C	EEHIC Maximum Subsidy for Retrofits (Dollar / House )
HeatPumpModel_v31	C	EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
HeatPumpModel_v31	C	EEHIC Subsidy for Retrofits Final Year (Year)
HeatPumpModel_v31	C	Effect of Air Leakage from Window AC on Efficiency (dmnl)
HeatPumpModel_v31	F,A	Emissions (tCO2 / Year)
HeatPumpModel_v31	A	Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / Year)
HeatPumpModel_v31	A	Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year)
.housingagingchain v8	C	Energy Price Exponential Growth Rate (1/Year )
HeatPumpModel_v31	C	Energy Price Exponential Growth Rate 1 (1/Year )
.housingagingchain v8	C	Energy Price Pulse Quantity (Dimensionless*Year)
HeatPumpModel_v31	C	Energy Price Pulse Quantity 1 (Dimensionless*Year)
.housingagingchain v8	C	Energy Price Ramp Slope (1/Year )
HeatPumpModel_v31	C	Energy Price Ramp Slope 1 (1/Year )
.housingagingchain v8	C	Energy Price Step Height (Dimensionless )
HeatPumpModel_v31	A	Energy Savings[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Energy Use by Gas Houses (kBTU/ Year)
HeatPumpModel_v31	A	Energy Use by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / Year)
HeatPumpModel_v31	A	Energy Use by Heat Pump Houses (kBTU / Year)
HeatPumpModel_v31	A	Energy Use by Oil Houses (kBTU / Year)
HeatPumpModel_v31	SM,A	Expected Cooling Energy Price (Dollar / kBTU)
HeatPumpModel_v31	SM,A	Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
HeatPumpModel_v31	SM,A	Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
.housingagingchain v15	SM,A	Expected Fixed Cost (Dollar / House)
.housingagingchain v15	SM,A	Expected Heating Energy Price[Heating and Cooling System] (Dollar / kBTU)
HeatPumpModel_v31	SM,A	Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
.housingagingchain v15	A	Expected Lump Sum Subsidy Intensity[Retrofit Cost] (Dollar / sf)
.housingagingchain v15	SM,A	Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
.housingagingchain v15	SM,A	Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
HeatPumpModel_v31	SM,A	Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	SM,A	Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
HeatPumpModel_v31	A	Expected Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	A	Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
HeatPumpModel_v31	A	Federal Annual Heat Pump Subsidy (Dollar / Year)
HeatPumpModel_v31	A	Federal Annual Retrofit Subsidy (Dollar / Year)
.housingagingchain v5 testing	C	Fixed Cost (Dollar / House )
.housingagingchain v5 testing	A	Fixed Cost per Unit Area[Cohort] (Dollar / sf)
HeatPumpModel_v31	A	Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] (dmnl)
.housingagingchain v5 testing	A	Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Fraction of Housing by Heating and Cooling System[Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Fraction Retrofitting (dmnl)
HeatPumpModel_v31	LI,A	Fraction Retrofitting by Cohort[Cohort] (dmnl)
HeatPumpModel_v31	A	Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	C	Fractional Decrease in Code U (1 / Year )
HeatPumpModel_v31	A,T	Gas COP TABLE (dmnl)
HeatPumpModel_v31	C	HDD on Coldest Day (F )
HeatPumpModel_v31	A,T	Heat Pump Cooling COP TABLE (dmnl)
HeatPumpModel_v31	C	Heat Pump COP on Coldest Days (dmnl )
HeatPumpModel_v31	A,T	Heat Pump Heating COP TABLE (dmnl)
HeatPumpModel_v31	C	Heating Degree Days (F )
HeatPumpModel_v31	C	Heating Emissions Factors[Oil Heating] (lb CO2 / kBTU)
.housingagingchain v5 testing	A	Heating Energy Price[Heating and Cooling System] (Dollar / (kBTU))
HeatPumpModel_v31	A	Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
HeatPumpModel_v31	A	Heating System Efficiency[Oil Heating] (dmnl)
HeatPumpModel_v31	C	Homeowner Hours Spent Retrofitting (Hour )
HeatPumpModel_v31	C	HOMES Cut Off for Savings (dmnl )
HeatPumpModel_v31	SM,A	HOMES Expected Higher Subsidy (Dollar / House)
.housingagingchain v15	SM,A	HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
HeatPumpModel_v31	C	HOMES High Subsidy Amount (Dollar / House )
HeatPumpModel_v31	A	HOMES Implemented High Subsidy (Dollar / House)
.housingagingchain v15	A	HOMES Implemented Lower Subsidy (Dollar / House)
.housingagingchain v15	C	HOMES Lower Subsidy Amount (Dollar / House )
HeatPumpModel_v31	C	HOMES Subsidy Final Year (Year)
.housingagingchain v15	C	HOMES Subsidy Implementation Year (Year )
HeatPumpModel_v31	A	Houses Considering Switching System[Cohort,Heating and Cooling System,Retrofitting Status] (Houses / Year)
HeatPumpModel_v31	A	Houses Retrofitting[Cohort,Heating and Cooling System] (Houses)
HeatPumpModel_v31	A	Houses Retrofitting per Year[Cohort,Heating and Cooling System] (House / Year)
HeatPumpModel_v31	A	Houses Switching Into Sources[Heating and Cooling System] (Houses / Year)
HeatPumpModel_v31	F,A	Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (House / Year)
HeatPumpModel_v31	L	Housing[Cohort,Heating and Cooling System,Open to Retrofitting] (House)
HeatPumpModel_v31	A	Housing by Cohort[Cohort] (House)
HeatPumpModel_v31	A	Housing by Cohort and Heating and Cooling System[Cohort,Heating and Cooling System] (Houses)
HeatPumpModel_v31	A	Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] (House)
HeatPumpModel_v31	A	Housing by Heating and Cooling System[Heating and Cooling System] (House)
HeatPumpModel_v31	A	Housing by Retrofitting Status[Retrofitting Status] (House)
HeatPumpModel_v31	C	Housing Fractional Growth Rate (1 / Year )
HeatPumpModel_v31	F,A	Housing Starts[Cohort,Heating and Cooling System] (Houses / Year)
HeatPumpModel_v31	A	Housing Starts Across Cohorts ()
.housingagingchain v8	C	Housing Starts Exponential Growth Rate (1/Year )
HeatPumpModel_v31	A	Housing Starts In Each Cohort[Cohort] (House / Year)
.housingagingchain v8	C	Housing Starts Pulse Quantity (Dimensionless*Year)
.housingagingchain v8	C	Housing Starts Ramp Slope (1/Year )
.housingagingchain v8	C	Housing Starts Step Height (Dimensionless )
HeatPumpModel_v31	A	Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
HeatPumpModel_v31	A	Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
HeatPumpModel_v31	A	Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	A	Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
.housingagingchain v15	A	Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
HeatPumpModel_v31	C	Increase in Area per Year (sf / Year / House )
.housingagingchain v18	F,A	Increase in U Value from Housing Starts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
HeatPumpModel_v31	A	Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Indicated Homes Retrofitting[Cohort,Heating and Cooling System] (House)
.housingagingchain v8	LI,A	Initial Age[Preexisting Cohorts,Retrofitting Status] (House * Year)
HeatPumpModel_v31	LI,C	Initial Area[Cohort] (sf)
HeatPumpModel_v31	C	Initial Average Area of Housing Starts (sf / House )
HeatPumpModel_v31	C	Initial Average U Value[Cohort] (kBTU/(YearsfF))
HeatPumpModel_v31	LI,C	Initial Code U Value (kBTU / (sf * F * Year))
HeatPumpModel_v31	C	Initial Cooling Energy Price (Dollar / kBTU)
HeatPumpModel_v31	C	Initial Fraction of Homes Retrofitting (dmnl )
.housingagingchain v5 testing	C	Initial Heating Energy Price[Oil Heating] (Dollar / (kBTU))
.housingagingchain v5 testing	LI,A	Initial Homes Not Retrofitting[Preexisting Cohorts,Heating and Cooling System] (House)
.housingagingchain v5 testing	LI,A	Initial Homes Retrofitting[Preexisting Cohorts,Heating and Cooling System] (Houses)
HeatPumpModel_v31	C	Initial Housing[Cohort,Heating and Cooling System] (House)
.	A	Initial Housing Starts[Heating and Cooling System] (House/Year)
.housingagingchain v15	LI,A	Initial U Value[Preexisting Cohorts,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf))
.housingagingchain v8	A	Input (Dimensionless)
.housingagingchain v8	A	Input 0 (Dimensionless)
HeatPumpModel_v31	A	Input 1 (Dimensionless)
HeatPumpModel_v31	A	IRA Actual Subsidy for Heat Pumps (Dollar / House)
HeatPumpModel_v31	A	IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
HeatPumpModel_v31	A	IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
HeatPumpModel_v31	C	IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )
HeatPumpModel_v31	C	IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )
HeatPumpModel_v31	C	IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )
HeatPumpModel_v31	C	IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
HeatPumpModel_v31	C	kBTU per kWH (kBTU / kWH )
HeatPumpModel_v31	A	Lifetime Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] (Dollar * Year * F / kBTU)
HeatPumpModel_v31	A	Marginal Cooling Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / (kBTU))
HeatPumpModel_v31	A	Marginal Cost at Binding U Value without EEHIC[Cohort,Heating and Cooling System] ((Dollar / sf) / (kBTU / (sf * F * Year)))
.housingagingchain v15	A	Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / kBTU)
.housingagingchain v5 testing	A	Marginal Heating Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / (kBTU))
.housingagingchain v15	C	Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
HeatPumpModel_v31	A	Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)
HeatPumpModel_v31	A	Massachusetts Annual Retrofit Subsidy (Dollar / Year)
HeatPumpModel_v31	SM,A	MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	A	MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
HeatPumpModel_v31	A	MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
HeatPumpModel_v31	C	MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )
HeatPumpModel_v31	C	MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)
HeatPumpModel_v31	C	MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )
.housingagingchain v15	C	MassSave Maximum Subsidy for Retrofits (Dollar / House )
HeatPumpModel_v31	A	MassSave Subsidy for Retrofits Final Year (Year)
.housingagingchain v8	C	Maximum Energy Price (Dollar / kBTU)
HeatPumpModel_v31	A	Monthly Total Heat Pump Sales (Houses/ Month)
HeatPumpModel_v31	C	Months per Year (Month / Year )
HeatPumpModel_v31	A	Net Age Shift by System[Cohort,Heating and Cooling System] (Year * House / Year)
HeatPumpModel_v31	F,A	Net Age Shift from Retrofitting Status Shifting[Cohort] (House * Year / Year)
.housingagingchain v8	A	Net Area Shift by System[Cohort,Heating and Cooling System] (sf / Year)
HeatPumpModel_v31	F,A	Net Area Shift due to Retrofit Status Switching[Cohort] (sf / Year)
HeatPumpModel_v31	F,A	Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] (Houses / Year)
HeatPumpModel_v31	F,A	Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
HeatPumpModel_v31	C	No Turnover Switch (dmnl )
.housingagingchain v8	C	Noise Correlation Time (Year)
.housingagingchain v8	C	Noise Correlation Time 0 (Year)
HeatPumpModel_v31	C	Noise Correlation Time 1 (Year)
.housingagingchain v8	C	Noise Standard Deviation (Dimensionless)
.housingagingchain v8	C	Noise Standard Deviation 0 (Dimensionless)
HeatPumpModel_v31	C	Noise Standard Deviation 1 (Dimensionless)
.housingagingchain v8	C	Noise Start Time (Year)
.housingagingchain v8	C	Noise Start Time 0 (Year)
HeatPumpModel_v31	C	Noise Start Time 1 (Year)
HeatPumpModel_v31	A,T	Oil COP TABLE (dmnl)
HeatPumpModel_v31	A	Optimal Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	C	Optimal Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] (kBTU / (Year * House))
HeatPumpModel_v31	A	Optimal Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	A	Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
HeatPumpModel_v31	A	Optimal Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	A	Optimal Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
HeatPumpModel_v31	A	Optimal U Across All Housing (kBTU / (sf * F * Year))
.housingagingchain v18	A	Optimal U for New Homes[Cohort,Heating and Cooling System] (kBTU / (sf * Year * F))
HeatPumpModel_v31	A	Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
.housingagingchain v4 testing	A	Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Optimal U Value with No EEHIC Proportional Subsidy[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Peak Cooling Load on Grid (kWH / Day)
HeatPumpModel_v31	A	Peak Heating Load on Grid (kWH / Day)
HeatPumpModel_v31	C	Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Fossil Fuel Heating,Retrofitting Status] (kWH / Day)
HeatPumpModel_v31	C	Peak Load from Heat Pumps on Hottest Days per Group[Cohort,No AC Cooling,Retrofitting Status] (kWH / Day)
HeatPumpModel_v31	C	Peak Load from Non Heating or Cooling Sources (kWH / Day )
HeatPumpModel_v31	A	Perceived Cost of Not Retrofitting[Cohort,Heating and Cooling System] (Dollar / (House * Year))
HeatPumpModel_v31	A	Perceived Cost of Retrofitting[Cohort,Heating and Cooling System] (Dollar / (House * Year))
HeatPumpModel_v31	C	Pounds per Ton (lb CO2 / tCO2)
.housingagingchain v5 testing	C	Present Value of Cooling Operating Costs[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] (Dollars / (House))
.housingagingchain v5 testing	A	Present Value of Heating Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / (House))
HeatPumpModel_v31	A	Present Value of Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / (House) )
HeatPumpModel_v31	C	Present Value Replacement Cost[No AC Cooling] (Dollar / House)
HeatPumpModel_v31	C	Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )
HeatPumpModel_v31	C	Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
.housingagingchain v15	C	Proportional MassSave Subsidy Implementation Year for Retrofits (Year )
.housingagingchain v15	C	Proportional Subsidy Switch for Retrofits (dmnl )
.housingagingchain v8	C	Pulse Time (Year)
.housingagingchain v8	C	Pulse Time 0 (Year)
HeatPumpModel_v31	C	Pulse Time 1 (Year)
.housingagingchain v8	C	Ramp End Time (Year)
.housingagingchain v8	C	Ramp End Time 0 (Year)
HeatPumpModel_v31	C	Ramp End Time 1 (Year)
.housingagingchain v8	C	Ramp Start Time (Year)
.housingagingchain v8	C	Ramp Start Time 0 (Year)
HeatPumpModel_v31	C	Ramp Start Time 1 (Year)
HeatPumpModel_v31	C	Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )
.housingagingchain v5 testing	C	Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )
HeatPumpModel_v31	C	Reference Retrofit Cost (Dollar / (House * Year) )
.housingagingchain v9	C	Reference U Value (kBTU / (sf * Year * F) )
HeatPumpModel_v31	C	Retrofit Delay (Year )
HeatPumpModel_v31	F,A	Retrofitting[Cohort,Heating and Cooling System] (House * kBTU / (sf * F* Year) / Year)
HeatPumpModel_v31	A	Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
HeatPumpModel_v31	C	Sensitivity of Affinity to Cost (dmnl )
.housingagingchain v5 testing	C	Sensitivity of Marginal Cost to U Value (dmnl )
HeatPumpModel_v31	C	Sensitivity of Retrofits to Cost (dmnl )
.housingagingchain v8	C	Sine Amplitude (Dimensionless)
.housingagingchain v8	C	Sine Amplitude 0 (Dimensionless)
HeatPumpModel_v31	C	Sine Amplitude 1 (Dimensionless)
.housingagingchain v8	C	Sine Period (Year)
.housingagingchain v8	C	Sine Period 0 (Year)
HeatPumpModel_v31	C	Sine Period 1 (Year)
HeatPumpModel_v31	A	Soft Costs of Retrofitting (Dollar / Home)
.housingagingchain v8	C	Step Time (Year)
.housingagingchain v8	C	Step Time 0 (Year)
HeatPumpModel_v31	C	Step Time 1 (Year)
HeatPumpModel_v31	A	Subsidized Cost of Heat Pumps (Dollar / House)
.housingagingchain v15	A	Subsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar /House)
HeatPumpModel_v31	C	System Switching SWITCH (dmnl )
HeatPumpModel_v31	C	Time to Decide to Retrofit (Year )
.housingagingchain v8	L	Total Age[Cohort,Open to Retrofitting] (House * Year)
HeatPumpModel_v31	A	Total Area (sf)
HeatPumpModel_v31	A	Total Cooling Cost (Dollar / Year)
HeatPumpModel_v31	A	Total Cooling Energy Use (kBTU/ Year)
HeatPumpModel_v31	A	Total Cost of Ownership of Average Home[Cohort,Heating and Cooling System] (Dollar / (Year * House))
HeatPumpModel_v31	A	Total Cost of Ownership of Retrofitted Homes[Cohort,Heating and Cooling System] (Dollar / (House * Year))
HeatPumpModel_v31	A	Total Energy Use (kBTU / Year)
HeatPumpModel_v31	A	Total Heat Pump Sales (House / Year)
HeatPumpModel_v31	A	Total Heating Cost (Dollar / Year)
HeatPumpModel_v31	A	Total Heating Energy Use (kBTU/ Year)
HeatPumpModel_v31	A	Total Housing Starts (House/ Year)
.housingagingchain v4 testing	A	Total Housing Stock (House)
HeatPumpModel_v31	C	Total Initial Homes (Houses )
HeatPumpModel_v31	C	Total Initial Housing Starts (Houses / Year )
HeatPumpModel_v31	A	Total Present Value of Cost[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / House)
HeatPumpModel_v31	L	Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] (House * kBTU / (Year * F * sf) )
HeatPumpModel_v31	A	Total U Value Across All Groupings (House * kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Total U Value by Cohort[Cohort] (House * kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Total U Value by Heating and Cooling System[Heating and Cooling System] (House * kBTU / (sf * F * Year))
HeatPumpModel_v31	A	U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] (kBTU / (F * sf * Year))
HeatPumpModel_v31	A	U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	U Value Increase from Source Switching[Heating and Cooling System] (kBTUHouse/(YearYearsfF))
HeatPumpModel_v31	F,A	U Value Loss from Demolition[Cohort,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf) / Year)
.housingagingchain v18	A	U Value of Housing Starts[Cohort,Heating and Cooling System] (kBTU / (Year * F * sf))
HeatPumpModel_v31	A	U Value of Retrofitting Homes[Cohort,Heating and Cooling System] (kBTU / (sf * Year * F))
HeatPumpModel_v31	L	U Value Retrofitted Away (House * kBTU / (Year * F * sf))
HeatPumpModel_v31	F,A	U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf) / Year)
HeatPumpModel_v31	A,T	Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)
HeatPumpModel_v31	A	Unsubsidized Cost of Heat Pumps (Dollar / House)
.housingagingchain v8	A	Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar / House)
.housingagingchain v5 testing	A	Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] (Dollar / sf)
HeatPumpModel_v31	C	Weight on Upfront Cost (dmnl )
.housingagingchain v8	A	White Noise (Dimensionless)
.housingagingchain v8	A	White Noise 0 (Dimensionless)
HeatPumpModel_v31	A	White Noise 1 (Dimensionless)
.Control	C	FINAL TIME (Year)
.Control	C	INITIAL TIME (Year)
.Control	A	SAVEPER (Year )
.Control	C	TIME STEP (Year )

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_v31	InOutLinks	Housing (House)	6 \| 30	0.20	3\| 1\| 2	25\| 4\| 1
HeatPumpModel_v31	InOutLinks	Average Area (sf / House)	2 \| 16	0.12	2\| 0\| 0	16\| 0\| 0
HeatPumpModel_v31	InOutLinks	Input 1 (Dimensionless)	15 \| 1	15.00	11\| 0\| 4	1\| 0\| 0
.housingagingchain v8	InOutLinks	Input 0 (Dimensionless)	15 \| 1	15.00	11\| 0\| 4	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	U Value by Grouping (kBTU / (sf * F * Year))	2 \| 13	0.15	1\| 1\| 0	12\| 0\| 1
.housingagingchain v4 testing	InOutLinks	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 v8	InOutLinks	Input (Dimensionless)	15 \| 0	Infinite	10\| 1\| 4	0\| 0\| 0
.housingagingchain v4 testing	InOutLinks	Total Housing Stock (House)	1 \| 11	0.09	1\| 0\| 0	7\| 4\| 0
HeatPumpModel_v31	InOutLinks	U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))	8 \| 2	4.00	5\| 3\| 0	2\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Unsubsidized Retrofit Cost Intensity (Dollar / sf)	6 \| 3	2.00	1\| 4\| 1	3\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total U Value (House * kBTU / (Year * F * sf) )	6 \| 3	2.00	2\| 2\| 2	3\| 0\| 0
HeatPumpModel_v31	InOutLinks	Housing Starts (Houses / Year)	4 \| 5	0.80	3\| 1\| 0	5\| 0\| 0
.housingagingchain v15	InOutLinks	Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))	2 \| 7	0.29	2\| 0\| 0	5\| 2\| 0
.housingagingchain v15	InOutLinks	Delay in Changing Subsidy Expectations (Year )	0 \| 9	0.00	0\| 0\| 0	9\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cooling System Efficiency (dmnl)	4 \| 5	0.80	4\| 0\| 0	0\| 5\| 0
HeatPumpModel_v31	InOutLinks	Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)	7 \| 1	7.00	4\| 3\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)	7 \| 1	7.00	4\| 3\| 0	1\| 0\| 0
.housingagingchain v18	InOutLinks	Optimal U for New Homes (kBTU / (sf * Year * F))	6 \| 2	3.00	4\| 2\| 0	1\| 1\| 0
HeatPumpModel_v31	InOutLinks	Heating System Efficiency (dmnl)	4 \| 4	1.00	4\| 0\| 0	0\| 4\| 0
.housingagingchain v15	InOutLinks	Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)	3 \| 5	0.60	3\| 0\| 0	2\| 3\| 0
HeatPumpModel_v31	InOutLinks	Energy Use by Grouping (kBTU / Year)	2 \| 6	0.33	2\| 0\| 0	6\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Heating Energy Use (kBTU / (Year * House))	4 \| 4	1.00	3\| 1\| 0	4\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Cooling Energy Use (kBTU / (Year * House))	4 \| 4	1.00	3\| 1\| 0	4\| 0\| 0
.housingagingchain v15	InOutLinks	Additional Cost of Building to U Value (Dollar / sf)	7 \| 1	7.00	3\| 4\| 0	0\| 0\| 1
.housingagingchain v5 testing	InOutLinks	Sensitivity of Marginal Cost to U Value (dmnl )	0 \| 7	0.00	0\| 0\| 0	4\| 3\| 0
HeatPumpModel_v31	InOutLinks	Retrofitting (House * kBTU / (sf * F* Year) / Year)	4 \| 3	1.33	2\| 2\| 0	2\| 1\| 0
.housingagingchain v9	InOutLinks	Reference U Value (kBTU / (sf * Year * F) )	0 \| 7	0.00	0\| 0\| 0	4\| 2\| 1
HeatPumpModel_v31	InOutLinks	Net Change in Homes Retrofitting (Houses / Year)	3 \| 4	0.75	2\| 1\| 0	3\| 0\| 1
HeatPumpModel_v31	InOutLinks	MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)	5 \| 2	2.50	2\| 0\| 3	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Houses Switching Sources (House / Year)	3 \| 4	0.75	3\| 0\| 0	3\| 0\| 1
.housingagingchain v15	InOutLinks	Expected Subsidy for Retrofits (Dollar / House)	6 \| 1	6.00	4\| 0\| 2	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Demolitions (House / Year)	3 \| 4	0.75	2\| 1\| 0	3\| 1\| 0
.housingagingchain v8	InOutLinks	Area (sf)	5 \| 2	2.50	4\| 1\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Unsubsidized Cost of Heat Pumps (Dollar / House)	2 \| 4	0.50	0\| 2\| 0	4\| 0\| 0
.housingagingchain v8	InOutLinks	Total Age (House * Year)	4 \| 2	2.00	2\| 1\| 1	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Present Value Replacement Cost (Dollar / House)	5 \| 1	5.00	2\| 3\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))	5 \| 1	5.00	3\| 2\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Optimal U Value for Existing Homes (kBTU / (sf * F * Year))	5 \| 1	5.00	3\| 0\| 2	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Optimal Heating Energy Use (kBTU / (House * Year))	4 \| 2	2.00	3\| 1\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Optimal Cooling Energy Use (kBTU / (Year * House))	4 \| 2	2.00	3\| 1\| 0	2\| 0\| 0
.housingagingchain v15	InOutLinks	MassSave Expected Subsidy for Retrofits (Dollar / House)	5 \| 1	5.00	5\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)	4 \| 2	2.00	1\| 0\| 3	2\| 0\| 0
.housingagingchain v15	InOutLinks	Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)	4 \| 2	2.00	1\| 0\| 3	2\| 0\| 0
.housingagingchain v15	InOutLinks	Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)	4 \| 2	2.00	1\| 0\| 3	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)	4 \| 2	2.00	1\| 0\| 3	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)	4 \| 2	2.00	1\| 0\| 3	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)	4 \| 2	2.00	1\| 0\| 3	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Houses Retrofitting per Year (House / Year)	4 \| 2	2.00	1\| 1\| 2	2\| 0\| 0
.housingagingchain v15	InOutLinks	HOMES Implemented Lower Subsidy (Dollar / House)	4 \| 2	2.00	1\| 0\| 3	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	HOMES Implemented High Subsidy (Dollar / House)	4 \| 2	2.00	1\| 0\| 3	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Heating Energy Use Under Alternatives (kBTU / (House * Year))	5 \| 1	5.00	4\| 1\| 0	1\| 0\| 0
.housingagingchain v15	InOutLinks	Expected Heating Energy Price (Dollar / kBTU)	2 \| 4	0.50	2\| 0\| 0	4\| 0\| 0
HeatPumpModel_v31	InOutLinks	Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)	3 \| 3	1.00	3\| 0\| 0	2\| 1\| 0
HeatPumpModel_v31	InOutLinks	Expected Cooling Energy Price (Dollar / kBTU)	2 \| 4	0.50	2\| 0\| 0	4\| 0\| 0
HeatPumpModel_v31	InOutLinks	EEHIC Expected Subsidy for Retrofits (Dollar / House)	5 \| 1	5.00	5\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cooling Energy Use Under Alternatives (kBTU / (House * Year))	5 \| 1	5.00	4\| 1\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Area of Housing Starts (sf / House)	4 \| 2	2.00	2\| 2\| 0	1\| 1\| 0
.housingagingchain v8	InOutLinks	Active Cohort Indicator (dmnl)	5 \| 1	5.00	0\| 0\| 5	1\| 0\| 0
.housingagingchain v8	InOutLinks	Unsubsidized Retrofit Cost (Dollar / House)	2 \| 3	0.67	2\| 0\| 0	3\| 0\| 0
.housingagingchain v15	InOutLinks	Subsidized Retrofit Cost (Dollar /House)	3 \| 2	1.50	2\| 1\| 0	2\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Present Value of Heating Operating Costs (Dollar / (House))	4 \| 1	4.00	3\| 1\| 0	1\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Present Value of Cooling Operating Costs (Dollars / (House))	4 \| 1	4.00	3\| 1\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	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_v31	InOutLinks	Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)	2 \| 3	0.67	1\| 1\| 0	0\| 2\| 1
HeatPumpModel_v31	InOutLinks	IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)	4 \| 1	4.00	4\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Housing by Heating and Cooling System (House)	1 \| 4	0.25	1\| 0\| 0	4\| 0\| 0
HeatPumpModel_v31	InOutLinks	Housing by Cohort and Retrofitting Status (House)	1 \| 4	0.25	1\| 0\| 0	3\| 0\| 1
HeatPumpModel_v31	InOutLinks	Federal Annual Retrofit Subsidy (Dollar / Year)	3 \| 2	1.50	3\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Discount Rate (1 / Year )	0 \| 5	0.00	0\| 0\| 0	1\| 4\| 0
.housingagingchain v18	InOutLinks	Code U (kBTU / (sf * Year * F))	2 \| 3	0.67	1\| 1\| 0	3\| 0\| 0
HeatPumpModel_v31	InOutLinks	Actual HOMES Subsidy for Retrofits (Dollar/ Home)	4 \| 1	4.00	2\| 0\| 2	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	White Noise 1 (Dimensionless)	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	White Noise 0 (Dimensionless)	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	White Noise (Dimensionless)	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)	2 \| 2	1.00	2\| 0\| 0	1\| 0\| 1
.housingagingchain v18	InOutLinks	U Value of Housing Starts (kBTU / (Year * F * sf))	3 \| 1	3.00	2\| 0\| 1	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Present Value of Cost (Dollar / House)	3 \| 1	3.00	3\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Heat Pump Sales (House / Year)	1 \| 3	0.33	1\| 0\| 0	3\| 0\| 0
HeatPumpModel_v31	InOutLinks	Subsidized Cost of Heat Pumps (Dollar / House)	2 \| 2	1.00	1\| 1\| 0	2\| 0\| 0
.housingagingchain v15	InOutLinks	Proportional Subsidy Switch for Retrofits (dmnl )	0 \| 4	0.00	0\| 0\| 0	4\| 0\| 0
HeatPumpModel_v31	InOutLinks	Perceived Cost of Retrofitting (Dollar / (House * Year))	3 \| 1	3.00	3\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Massachusetts Annual Retrofit Subsidy (Dollar / Year)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
.housingagingchain v15	InOutLinks	Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)	2 \| 2	1.00	2\| 0\| 0	1\| 1\| 0
HeatPumpModel_v31	InOutLinks	Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	IRA Actual Subsidy for Heat Pumps (Dollar / House)	3 \| 1	3.00	3\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Initial Age (House * Year)	3 \| 1	3.00	0\| 0\| 3	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Indicated Homes Retrofitting (House)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
.housingagingchain v15	InOutLinks	HOMES Expected Lower Lump Sum Subsidy (Dollar / House)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Heating Degree Days (F )	0 \| 4	0.00	0\| 0\| 0	4\| 0\| 0
HeatPumpModel_v31	InOutLinks	Federal Annual Heat Pump Subsidy (Dollar / Year)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)	3 \| 1	3.00	3\| 0\| 0	1\| 0\| 0
.housingagingchain v15	InOutLinks	Expected Fixed Cost (Dollar / House)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)	2 \| 2	1.00	2\| 0\| 0	1\| 1\| 0
HeatPumpModel_v31	InOutLinks	Energy Savings (dmnl)	2 \| 2	1.00	2\| 0\| 0	0\| 0\| 2
HeatPumpModel_v31	InOutLinks	Emissions by Grouping (tCO2 / Year)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
.housingagingchain v15	InOutLinks	Cost of Switching Heating and Cooling Systems (Dollar / House)	3 \| 1	3.00	3\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Cooling Degree Days (F )	0 \| 4	0.00	0\| 0\| 0	4\| 0\| 0
HeatPumpModel_v31	InOutLinks	Change in AC Noise 1 (1/Year)	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Change in AC Noise 0 (1/Year)	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Change in AC Noise (1/Year)	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Average Heating Cost (Dollar / (Year * House))	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Energy Use (kBTU / (Year * House))	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Emissions from Heating by Grouping (tCO2 / (House * Year))	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Emissions from Cooling by Grouping (tCO2 / (House * Year))	3 \| 1	3.00	2\| 1\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Cooling Cost (Dollar / (Year * House))	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
.housingagingchain v8	InOutLinks	Average Age (Year)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Annual Retrofit Subsidy (Dollar / Year)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Annual Heat Pump Subsidy (Dollar / Year)	2 \| 2	1.00	2\| 0\| 0	2\| 0\| 0
.housingagingchain v15	InOutLinks	Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))	2 \| 2	1.00	1\| 1\| 0	2\| 0\| 0
.housingagingchain v4 testing	InOutLinks	Affinity of Retrofitting (dmnl)	3 \| 1	3.00	1\| 2\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Affinity of Not Retrofitting (dmnl)	3 \| 1	3.00	1\| 2\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Affinity of Heating and Cooling Systems (dmnl)	3 \| 1	3.00	1\| 2\| 0	0\| 0\| 1
HeatPumpModel_v31	InOutLinks	Actual MassSave Subsidy for Retrofits (Dollar / House)	3 \| 1	3.00	3\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Actual EEHIC Subsidy for Retrofits (Dollar / House)	3 \| 1	3.00	3\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	U Value of Retrofitting Homes (kBTU / (sf * Year * F))	1 \| 2	0.50	1\| 0\| 0	1\| 1\| 0
HeatPumpModel_v31	InOutLinks	U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)	2 \| 1	2.00	2\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Total Heating Energy Use (kBTU/ Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Heating Cost (Dollar / Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Cooling Energy Use (kBTU/ Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Cooling Cost (Dollar / Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Soft Costs of Retrofitting (Dollar / Home)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Present Value of Operating Costs (Dollar / (House) )	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Perceived Cost of Not Retrofitting (Dollar / (House * Year))	2 \| 1	2.00	1\| 1\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Optimal U Across All Housing (kBTU / (sf * F * Year))	3 \| 0	Infinite	2\| 1\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Optimal Heating Cost (Dollar / (Year * House))	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Optimal Energy Cost (Dollar / (Year * House))	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Optimal Cooling Cost (Dollar / (Year * House))	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	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 v8	InOutLinks	Net Area Shift by System (sf / Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Net Age Shift by System (Year * House / Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	MassSave Subsidy for Retrofits Final Year (Year)	1 \| 2	0.50	1\| 0\| 0	0\| 0\| 2
HeatPumpModel_v31	InOutLinks	MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
.housingagingchain v15	InOutLinks	Initial U Value (House * kBTU / (Year * F * sf))	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Initial Homes Retrofitting (Houses)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Initial Homes Not Retrofitting (House)	2 \| 1	2.00	1\| 1\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Indicated Fraction of Homes Retrofitting (dmnl)	2 \| 1	2.00	1\| 1\| 0	1\| 0\| 0
.housingagingchain v18	InOutLinks	Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Houses Considering Switching System (Houses / Year)	2 \| 1	2.00	1\| 1\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	HOMES Expected Higher Subsidy (Dollar / House)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Heating Energy Price (Dollar / (kBTU))	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Fraction of Houses in Each Heating and Cooling System (dmnl)	3 \| 0	Infinite	3\| 0\| 0	0\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Fixed Cost per Unit Area (Dollar / sf)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Expected Subsidy for Heat Pumps (Dollar / House)	2 \| 1	2.00	2\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
.housingagingchain v15	InOutLinks	Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
.housingagingchain v15	InOutLinks	Expected Lump Sum Subsidy Intensity (Dollar / sf)	2 \| 1	2.00	1\| 1\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Emissions (tCO2 / Year)	1 \| 2	0.50	1\| 0\| 0	2\| 0\| 0
.housingagingchain v18	InOutLinks	Decrease in Code U (kBTU / (sf * Year * F) / Year)	2 \| 1	2.00	2\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Days per Year (Day / Year )	0 \| 3	0.00	0\| 0\| 0	0\| 3\| 0
HeatPumpModel_v31	InOutLinks	Cost of Heating System Replacement (Dollar / House )	1 \| 2	0.50	1\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cost of Cooling System Replacement (Dollar / House)	1 \| 2	0.50	1\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cooling Energy Price (Dollar / kBTU)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))	3 \| 0	Infinite	3\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Lifetime of Cooling Technology (Years)	1 \| 2	0.50	1\| 0\| 0	1\| 1\| 0
HeatPumpModel_v31	InOutLinks	Average EUI by Grouping (kBTU / (sf * Year))	3 \| 0	Infinite	3\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Energy Use in All Housing (kBTU / Year / House)	2 \| 1	2.00	1\| 1\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Energy Cost (Dollar / (Year * House))	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Emissions by Grouping (tCO2 / (Year * House))	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Average Area in All Housing (sf/ House)	2 \| 1	2.00	2\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Autocorrelated Noise 1 (Dimensionless)	1 \| 2	0.50	1\| 0\| 0	1\| 1\| 0
.housingagingchain v8	InOutLinks	Autocorrelated Noise 0 (Dimensionless)	1 \| 2	0.50	1\| 0\| 0	1\| 1\| 0
.housingagingchain v8	InOutLinks	Autocorrelated Noise (Dimensionless)	1 \| 2	0.50	1\| 0\| 0	1\| 1\| 0
.housingagingchain v8	InOutLinks	Area Removal (sf /Year)	2 \| 1	2.00	2\| 0\| 0	0\| 1\| 0
.housingagingchain v8	InOutLinks	Area of New Homes (sf / Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Annual MA Subsidies (Dollar / Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Annual Federal Subsidies (Dollar / Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Aging (House * Year / Year)	2 \| 1	2.00	2\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Age Removal (House * Year /Year)	2 \| 1	2.00	2\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Weight on Upfront Cost (dmnl )	0 \| 2	0.00	0\| 0\| 0	1\| 1\| 0
HeatPumpModel_v31	InOutLinks	U Value Increase from Source Switching (kBTUHouse/(YearYearsfF))	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total U Value by Cohort (House * kBTU / (sf * F * Year))	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total U Value Across All Groupings (House * kBTU / (sf * F * Year))	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Energy Use (kBTU / Year)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Cost of Ownership of Average Home (Dollar / (Year * House))	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Area (sf)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Sensitivity of Retrofits to Cost (dmnl )	0 \| 2	0.00	0\| 0\| 0	0\| 2\| 0
HeatPumpModel_v31	InOutLinks	Retrofit Delay (Year )	0 \| 2	0.00	0\| 0\| 0	1\| 1\| 0
HeatPumpModel_v31	InOutLinks	Reference Retrofit Cost (Dollar / (House * Year) )	0 \| 2	0.00	0\| 0\| 0	2\| 0\| 0
.housingagingchain v15	InOutLinks	Proportional MassSave Subsidy Implementation Year for Retrofits (Year )	0 \| 2	0.00	0\| 0\| 0	0\| 0\| 2
HeatPumpModel_v31	InOutLinks	Proportional IRA Subsidy Switch for Heat Pumps (dmnl )	0 \| 2	0.00	0\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )	0 \| 2	0.00	0\| 0\| 0	0\| 0\| 2
HeatPumpModel_v31	InOutLinks	Pounds per Ton (lb CO2 / tCO2)	0 \| 2	0.00	0\| 0\| 0	0\| 2\| 0
HeatPumpModel_v31	InOutLinks	Optimal Energy Use (kBTU / (House * Year))	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Noise Correlation Time 1 (Year)	0 \| 2	0.00	0\| 0\| 0	2\| 0\| 0
.housingagingchain v8	InOutLinks	Noise Correlation Time 0 (Year)	0 \| 2	0.00	0\| 0\| 0	2\| 0\| 0
.housingagingchain v8	InOutLinks	Noise Correlation Time (Year)	0 \| 2	0.00	0\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	No Turnover Switch (dmnl )	0 \| 2	0.00	0\| 0\| 0	0\| 2\| 0
HeatPumpModel_v31	InOutLinks	Net Area Shift due to Retrofit Status Switching (sf / Year)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Net Age Shift from Retrofitting Status Shifting (House * Year / Year)	1 \| 1	1.00	1\| 0\| 0	0\| 0\| 1
HeatPumpModel_v31	InOutLinks	Monthly Total Heat Pump Sales (Houses/ Month)	2 \| 0	Infinite	1\| 1\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	kBTU per kWH (kBTU / kWH )	0 \| 2	0.00	0\| 0\| 0	0\| 2\| 0
HeatPumpModel_v31	InOutLinks	IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )	0 \| 2	0.00	0\| 0\| 0	0\| 0\| 2
HeatPumpModel_v31	InOutLinks	IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )	0 \| 2	0.00	0\| 0\| 0	0\| 0\| 2
HeatPumpModel_v31	InOutLinks	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_v31	InOutLinks	Initial Fraction of Homes Retrofitting (dmnl )	0 \| 2	0.00	0\| 0\| 0	1\| 1\| 0
HeatPumpModel_v31	InOutLinks	Housing Starts In Each Cohort (House / Year)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Housing by Retrofitting Status (House)	1 \| 1	1.00	1\| 0\| 0	0\| 0\| 1
HeatPumpModel_v31	InOutLinks	Housing by Cohort and Heating and Cooling System (Houses)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Houses Switching Into Sources (Houses / Year)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
.housingagingchain v15	InOutLinks	HOMES Subsidy Implementation Year (Year )	0 \| 2	0.00	0\| 0\| 0	0\| 0\| 2
HeatPumpModel_v31	InOutLinks	HOMES Subsidy Final Year (Year)	0 \| 2	0.00	0\| 0\| 0	0\| 0\| 2
HeatPumpModel_v31	InOutLinks	HOMES Cut Off for Savings (dmnl )	0 \| 2	0.00	0\| 0\| 0	0\| 0\| 2
HeatPumpModel_v31	InOutLinks	Fraction Retrofitting by Cohort (dmnl)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Fraction of Housing by Heating and Cooling System (dmnl)	2 \| 0	Infinite	1\| 1\| 0	0\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Fraction of Houses Switching (dmnl)	1 \| 1	1.00	0\| 0\| 1	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Emissions by Heating and Cooling System (tCO2 / Year)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	EEHIC Subsidy for Retrofits Final Year (Year)	0 \| 2	0.00	0\| 0\| 0	0\| 0\| 2
.housingagingchain v15	InOutLinks	Delay in Forming Expectations of Retrofit Costs (Year )	0 \| 2	0.00	0\| 0\| 0	2\| 0\| 0
.housingagingchain v15	InOutLinks	Delay in Forming Expectations of Energy Price (Year )	0 \| 2	0.00	0\| 0\| 0	2\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cumulative Subsidy for Retrofits (Dollar)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cumulative Subsidies for Heat Pumps (Dollar)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cumulative Subsidies (Dollar)	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
.housingagingchain v8	InOutLinks	Cohort Duration (Year )	0 \| 2	0.00	0\| 0\| 0	0\| 0\| 2
.housingagingchain v4 testing	InOutLinks	Average U Value in All Housing (kBTU / (sf * F * Year))	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Subsidized Retrofit Cost (Dollar / House)	2 \| 0	Infinite	1\| 0\| 1	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Lifetime of Heating Technology (Year)	0 \| 2	0.00	0\| 0\| 0	1\| 1\| 0
HeatPumpModel_v31	InOutLinks	Average Indicated Fraction of Homes Retrofitting (dmnl)	2 \| 0	Infinite	1\| 1\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Heating Energy Use Across All Homes (kBTU / (Year * House))	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Heating Cost Across All Homes (Dollar / Year / House)	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average EUI in All Housing (kBTU / (sf * Year))	2 \| 0	Infinite	1\| 1\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Energy Use by Heating and Cooling System (kBTU / (House * Year))	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
.housingagingchain v8	InOutLinks	Average Energy Costs if Retrofitted (Dollar/(Year*House))	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
.housingagingchain v15	InOutLinks	Average Energy Costs for Retrofitting Home (Dollar / Year / House)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Emissions by Heating and Cooling System (tCO2 / Year / House)	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Emissions (tCO2 / House / Year)	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Daily Load from Heat Pumps (kBTU / Day)	2 \| 0	Infinite	1\| 1\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Cooling Energy Use Across All Homes (kBTU / Year / House)	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Cooling Cost Across All Homes (Dollar / House/ Year)	2 \| 0	Infinite	1\| 1\| 0	0\| 0\| 0
.housingagingchain v8	InOutLinks	Average Age in All Housing (Year)	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Annual Subsidies (Dollar / Year)	2 \| 0	Infinite	2\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Annual Load from Heat Pumps (kBTU / Year)	1 \| 1	1.00	1\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)	0 \| 1	0.00	0\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	U Value Retrofitted Away (House * kBTU / (Year * F * sf))	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Initial Housing Starts (Houses / Year )	0 \| 1	0.00	0\| 0\| 0	0\| 0\| 1
HeatPumpModel_v31	InOutLinks	Total Housing Starts (House/ Year)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Time to Decide to Retrofit (Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	System Switching SWITCH (dmnl )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Step Time 1 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Step Time 0 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Step Time (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Sine Period 1 (Year)	0 \| 1	0.00	0\| 0\| 0	0\| 0\| 1
.housingagingchain v8	InOutLinks	Sine Period 0 (Year)	0 \| 1	0.00	0\| 0\| 0	0\| 0\| 1
.housingagingchain v8	InOutLinks	Sine Period (Year)	0 \| 1	0.00	0\| 0\| 0	0\| 0\| 1
HeatPumpModel_v31	InOutLinks	Sine Amplitude 1 (Dimensionless)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Sine Amplitude 0 (Dimensionless)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Sine Amplitude (Dimensionless)	0 \| 1	0.00	0\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Sensitivity of Affinity to Cost (dmnl )	0 \| 1	0.00	0\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Ramp Start Time 1 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Ramp Start Time 0 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Ramp Start Time (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Ramp End Time 1 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Ramp End Time 0 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Ramp End Time (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Pulse Time 1 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Pulse Time 0 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Pulse Time (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Peak Heating Load on Grid (kWH / Day)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Peak Cooling Load on Grid (kWH / Day)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Oil COP TABLE (dmnl)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Noise Start Time 1 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Noise Start Time 0 (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Noise Start Time (Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Noise Standard Deviation 1 (Dimensionless)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Noise Standard Deviation 0 (Dimensionless)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Noise Standard Deviation (Dimensionless)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Months per Year (Month / Year )	0 \| 1	0.00	0\| 0\| 0	0\| 1\| 0
.housingagingchain v15	InOutLinks	MassSave Maximum Subsidy for Retrofits (Dollar / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )	0 \| 1	0.00	0\| 0\| 0	0\| 0\| 1
HeatPumpModel_v31	InOutLinks	MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)	0 \| 1	0.00	0\| 0\| 0	0\| 0\| 1
HeatPumpModel_v31	InOutLinks	MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v15	InOutLinks	Mass Save Proportional Subsidy Rate for Retrofits (dmnl )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	IRA Proportional Subsidy Rate for Heat Pumps (dmnl )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Initial Heating Energy Price (Dollar / (kBTU))	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Initial Cooling Energy Price (Dollar / kBTU)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Initial Code U Value (kBTU / (sf * F * Year))	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Initial Average U Value (kBTU/(YearsfF))	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Initial Average Area of Housing Starts (sf / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Initial Area (sf)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Increase in Area per Year (sf / Year / House )	0 \| 1	0.00	0\| 0\| 0	0\| 1\| 0
.housingagingchain v8	InOutLinks	Housing Starts Step Height (Dimensionless )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Housing Starts Ramp Slope (1/Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Housing Starts Pulse Quantity (Dimensionless*Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Housing Starts Exponential Growth Rate (1/Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Housing Starts Across Cohorts ()	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Housing Fractional Growth Rate (1 / Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Housing by Cohort (House)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Houses Retrofitting (Houses)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
.housingagingchain v15	InOutLinks	HOMES Lower Subsidy Amount (Dollar / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	HOMES High Subsidy Amount (Dollar / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Homeowner Hours Spent Retrofitting (Hour )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Heating Emissions Factors (lb CO2 / kBTU)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Heat Pump Heating COP TABLE (dmnl)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Heat Pump COP on Coldest Days (dmnl )	0 \| 1	0.00	0\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Heat Pump Cooling COP TABLE (dmnl)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	HDD on Coldest Day (F )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Gas COP TABLE (dmnl)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Fractional Decrease in Code U (1 / Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Fraction Retrofitting by System and Cohort (dmnl)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Fraction Retrofitting (dmnl)	1 \| 0	Infinite	0\| 0\| 1	0\| 0\| 0
.housingagingchain v5 testing	InOutLinks	Fixed Cost (Dollar / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Energy Use by Oil Houses (kBTU / Year)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Energy Use by Heat Pump Houses (kBTU / Year)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Energy Use by Gas Houses (kBTU/ Year)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
.housingagingchain v8	InOutLinks	Energy Price Step Height (Dimensionless )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Energy Price Ramp Slope 1 (1/Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Energy Price Ramp Slope (1/Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Energy Price Pulse Quantity 1 (Dimensionless*Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Energy Price Pulse Quantity (Dimensionless*Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Energy Price Exponential Growth Rate 1 (1/Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
.housingagingchain v8	InOutLinks	Energy Price Exponential Growth Rate (1/Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Effect of Air Leakage from Window AC on Efficiency (dmnl)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	EEHIC Proportional Subsidy Rate for Retrofits (dmnl )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	EEHIC Maximum Subsidy for Retrofits (Dollar / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Demolition Hazard Rate (1 / Year )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cumulative MA Subsidy (Dollar)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cumulative Federal Subsidy (Dollar)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cumulative Emissions (tCO2)	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cost of Bad Air Conditioning (Dollar / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cooling Energy Price Step Height 1 (Dimensionless )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Cooling Emissions Factor (lb CO2 / kBTU)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	CDD on Coldest Day (F )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Average Time To Consider Switching (Year )	0 \| 1	0.00	0\| 0\| 0	0\| 1\| 0
HeatPumpModel_v31	InOutLinks	Average Income (Dollar / Hour / House )	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Amoritization Period (Year )	0 \| 1	0.00	0\| 0\| 0	0\| 1\| 0
.housingagingchain v8	InOutLinks	Aging per Year (Year / Year)	0 \| 1	0.00	0\| 0\| 0	1\| 0\| 0
HeatPumpModel_v31	InOutLinks	Total Initial Homes (Houses )	( 0\| 0)	Infinite	0\| 0\| 0	0\| 0\| 0
HeatPumpModel_v31	InOutLinks	Peak Load from Non Heating or Cooling Sources (kWH / Day )	( 0\| 0)	Infinite	0\| 0\| 0	0\| 0\| 0
.housingagingchain v8	InOutLinks	Maximum Energy Price (Dollar / kBTU)	( 0\| 0)	Infinite	0\| 0\| 0	0\| 0\| 0
.Control	InOutLinks	TIME STEP (Year )	0 \| 7	0.00	0\| 0\| 0	1\| 3\| 3
.Control	InOutLinks	INITIAL TIME (Year)	0 \| 5	0.00	0\| 0\| 0	0\| 1\| 4
.Control	InOutLinks	SAVEPER (Year )	1 \| 0	Infinite	1\| 0\| 0	0\| 0\| 0
.Control	InOutLinks	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_v31	Sub	Backup Heating ()
HeatPumpModel_v31	Sub	Central AC Cooling ()
.	Sub	Cohort ()
HeatPumpModel_v31	Sub	Fossil Fuel Heating ()
HeatPumpModel_v31	Sub	Gas and Window or No AC ()
HeatPumpModel_v31	Sub	Gas Heating ()
HeatPumpModel_v31	Sub	Heating ()
HeatPumpModel_v31	Sub	Heating and Cooling System ()
HeatPumpModel_v31	C	kBTU per kWH (kBTU / kWH )
HeatPumpModel_v31	Sub	New Cohorts ()
HeatPumpModel_v31	Sub	No AC Cooling ()
HeatPumpModel_v31	Sub	Oil and Window or No AC ()
HeatPumpModel_v31	Sub	Oil Heating ()
.housingagingchain v8	Sub	Preexisting Cohorts ()
HeatPumpModel_v31	Sub	Retrofit Cost ()
HeatPumpModel_v31	Sub	Retrofitting Status ()
HeatPumpModel_v31	Sub	Traditional Cooling ()
HeatPumpModel_v31	Sub	Window AC Cooling ()

Supplementary Variables (0 Variables + 0 Control Variables)

Group

Type

Variable

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_v31	A	Annual Subsidies (Dollar / Year)
.housingagingchain v8	A	Average Age in All Housing (Year)
HeatPumpModel_v31	A	Average Cooling Cost Across All Homes (Dollar / House/ Year)
HeatPumpModel_v31	A	Average Cooling Energy Use Across All Homes (kBTU / Year / House)
HeatPumpModel_v31	A	Average Daily Load from Heat Pumps (kBTU / Day)
HeatPumpModel_v31	A	Average Emissions (tCO2 / House / Year)
HeatPumpModel_v31	A	Average Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year / House)
HeatPumpModel_v31	A	Average Energy Use by Heating and Cooling System[Heating and Cooling System] (kBTU / (House * Year))
HeatPumpModel_v31	A	Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * Year))
HeatPumpModel_v31	A	Average EUI in All Housing (kBTU / (sf * Year))
HeatPumpModel_v31	A	Average Heating Cost Across All Homes (Dollar / Year / House)
HeatPumpModel_v31	A	Average Heating Energy Use Across All Homes (kBTU / (Year * House))
HeatPumpModel_v31	A	Average Indicated Fraction of Homes Retrofitting (dmnl)
HeatPumpModel_v31	A	Average Subsidized Retrofit Cost (Dollar / House)
HeatPumpModel_v31	A	Average U Value by Heating and Cooling System[Heating and Cooling System] (kBTU / (sf * F * Year))
.housingagingchain v4 testing	A	Average U Value in All Housing (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Average U Value of Houses Switching Into Sources[Heating and Cooling System] (kBTU / (sf * F * Year))
HeatPumpModel_v31	Sub	Backup Heating ()
HeatPumpModel_v31	L	Cumulative Emissions (tCO2)
HeatPumpModel_v31	L	Cumulative Federal Subsidy (Dollar)
HeatPumpModel_v31	L	Cumulative MA Subsidy (Dollar)
HeatPumpModel_v31	A	Cumulative Subsidies (Dollar)
HeatPumpModel_v31	A	Energy Use by Gas Houses (kBTU/ Year)
HeatPumpModel_v31	A	Energy Use by Heat Pump Houses (kBTU / Year)
HeatPumpModel_v31	A	Energy Use by Oil Houses (kBTU / Year)
HeatPumpModel_v31	A	Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Fraction of Housing by Heating and Cooling System[Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Fraction Retrofitting (dmnl)
HeatPumpModel_v31	A	Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	Sub	Heating ()
HeatPumpModel_v31	A	Houses Retrofitting[Cohort,Heating and Cooling System] (Houses)
HeatPumpModel_v31	A	Housing by Cohort[Cohort] (House)
HeatPumpModel_v31	A	Housing Starts Across Cohorts ()
.	A	Initial Housing Starts[Heating and Cooling System] (House/Year)
.housingagingchain v8	A	Input (Dimensionless)
.housingagingchain v8	C	Maximum Energy Price (Dollar / kBTU)
HeatPumpModel_v31	A	Monthly Total Heat Pump Sales (Houses/ Month)
HeatPumpModel_v31	Sub	New Cohorts ()
HeatPumpModel_v31	A	Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
HeatPumpModel_v31	A	Optimal U Across All Housing (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Peak Cooling Load on Grid (kWH / Day)
HeatPumpModel_v31	A	Peak Heating Load on Grid (kWH / Day)
HeatPumpModel_v31	C	Peak Load from Non Heating or Cooling Sources (kWH / Day )
HeatPumpModel_v31	A	Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
HeatPumpModel_v31	Sub	Technology ()
HeatPumpModel_v31	A	Total Housing Starts (House/ Year)
HeatPumpModel_v31	C	Total Initial Homes (Houses )
HeatPumpModel_v31	L	U Value Retrofitted Away (House * kBTU / (Year * F * sf))

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Stock Variables (14 Variables + 0 Control Variables)

Group	Type	Variable
.housingagingchain v8	L	Area[Preexisting Cohorts,Open to Retrofitting] (sf)
.housingagingchain v8	L	Autocorrelated Noise (Dimensionless)
.housingagingchain v8	L	Autocorrelated Noise 0 (Dimensionless)
HeatPumpModel_v31	L	Autocorrelated Noise 1 (Dimensionless)
.housingagingchain v18	L	Code U (kBTU / (sf * Year * F))
HeatPumpModel_v31	L	Cumulative Emissions (tCO2)
HeatPumpModel_v31	L	Cumulative Federal Subsidy (Dollar)
HeatPumpModel_v31	L	Cumulative MA Subsidy (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidies for Heat Pumps (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidy for Retrofits (Dollar)
HeatPumpModel_v31	L	Housing[Cohort,Heating and Cooling System,Open to Retrofitting] (House)
.housingagingchain v8	L	Total Age[Cohort,Open to Retrofitting] (House * Year)
HeatPumpModel_v31	L	Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] (House * kBTU / (Year * F * sf) )
HeatPumpModel_v31	L	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 v8	L	Autocorrelated Noise (Dimensionless)
.housingagingchain v8	L	Autocorrelated Noise 0 (Dimensionless)
HeatPumpModel_v31	L	Autocorrelated Noise 1 (Dimensionless)
HeatPumpModel_v31	L	Cumulative Emissions (tCO2)
HeatPumpModel_v31	L	Cumulative Federal Subsidy (Dollar)
HeatPumpModel_v31	L	Cumulative MA Subsidy (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidies for Heat Pumps (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidy for Retrofits (Dollar)
.housingagingchain v8	A	Input (Dimensionless)
.housingagingchain v8	A	Input 0 (Dimensionless)
HeatPumpModel_v31	A	Input 1 (Dimensionless)
HeatPumpModel_v31	A	U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] (kBTU / (F * sf * Year))
HeatPumpModel_v31	A	U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * F * Year))
HeatPumpModel_v31	L	U Value Retrofitted Away (House * kBTU / (Year * F * sf))
.housingagingchain v5 testing	A	Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] (Dollar / sf)
.housingagingchain v8	A	White Noise (Dimensionless)
.housingagingchain v8	A	White Noise 0 (Dimensionless)
HeatPumpModel_v31	A	White Noise 1 (Dimensionless)

Nonmonotonic Lookup Functions (0 Variables + 0 Control Variables)

Group

Type

Variable

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

Group	Type	Variable	Non-Zero
HeatPumpModel_v31	Non-Zero	Gas COP TABLE (dmnl)	Left
HeatPumpModel_v31	Non-Zero	Heat Pump Cooling COP TABLE (dmnl)	Both
HeatPumpModel_v31	Non-Zero	Heat Pump Heating COP TABLE (dmnl)	Both
HeatPumpModel_v31	Non-Zero	Oil COP TABLE (dmnl)	Left
HeatPumpModel_v31	Non-Zero	Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)	Both

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 v8	A	Input (Dimensionless)
.housingagingchain v8	A	Input 0 (Dimensionless)
HeatPumpModel_v31	A	Input 1 (Dimensionless)

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

Group	Type	Variable
HeatPumpModel_v31	A	Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar/ Home)
HeatPumpModel_v31	A	Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
.housingagingchain v15	A	Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
HeatPumpModel_v31	A	HOMES Implemented High Subsidy (Dollar / House)
.housingagingchain v15	A	HOMES Implemented Lower Subsidy (Dollar / House)
HeatPumpModel_v31	A	Houses Retrofitting per Year[Cohort,Heating and Cooling System] (House / Year)
HeatPumpModel_v31	A	Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
HeatPumpModel_v31	A	Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
HeatPumpModel_v31	A	Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	A	Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
.housingagingchain v15	A	Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
HeatPumpModel_v31	A	IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
HeatPumpModel_v31	A	MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
HeatPumpModel_v31	A	Net Age Shift by System[Cohort,Heating and Cooling System] (Year * House / Year)
.housingagingchain v8	A	Net Area Shift by System[Cohort,Heating and Cooling System] (sf / Year)
HeatPumpModel_v31	F,A	Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
HeatPumpModel_v31	A	Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] (kBTU / (F * sf * Year))
HeatPumpModel_v31	A	U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * F * Year))
.housingagingchain v18	A	U Value of Housing Starts[Cohort,Heating and Cooling System] (kBTU / (Year * F * sf))
.housingagingchain v5 testing	A	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_v31	A	Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
HeatPumpModel_v31	A	Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
HeatPumpModel_v31	A	Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
HeatPumpModel_v31	A	EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
HeatPumpModel_v31	A	Energy Savings[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
HeatPumpModel_v31	A	IRA Actual Subsidy for Heat Pumps (Dollar / House)
HeatPumpModel_v31	A	IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	A	MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
HeatPumpModel_v31	A	MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
HeatPumpModel_v31	F,A	Retrofitting[Cohort,Heating and Cooling System] (House * kBTU / (sf * F* Year) / Year)
HeatPumpModel_v31	A	Subsidized Cost of Heat Pumps (Dollar / House)
.housingagingchain v5 testing	A	Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] (Dollar / sf)

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

Group	Type	Variable	Complexity
HeatPumpModel_v31	Complexity	Actual HOMES Subsidy for Retrofits (Dollar/ Home)	4
HeatPumpModel_v31	Complexity	Affinity of Heating and Cooling Systems (dmnl)	4
.housingagingchain v8	Complexity	Area (sf)	4
HeatPumpModel_v31	Complexity	Average Area of Housing Starts (sf / House)	4
HeatPumpModel_v31	Complexity	Average Heating Energy Use (kBTU / (Year * House))	4
HeatPumpModel_v31	Complexity	HOMES Implemented High Subsidy (Dollar / House)	4
.housingagingchain v15	Complexity	HOMES Implemented Lower Subsidy (Dollar / House)	4
HeatPumpModel_v31	Complexity	Houses Retrofitting per Year (House / Year)	4
HeatPumpModel_v31	Complexity	Housing Starts (Houses / Year)	4
HeatPumpModel_v31	Complexity	Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)	4
HeatPumpModel_v31	Complexity	Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)	4
HeatPumpModel_v31	Complexity	Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)	4
.housingagingchain v15	Complexity	Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)	4
.housingagingchain v15	Complexity	Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)	4
HeatPumpModel_v31	Complexity	IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)	4
HeatPumpModel_v31	Complexity	IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)	4
HeatPumpModel_v31	Complexity	Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))	4
HeatPumpModel_v31	Complexity	Optimal Heating Energy Use (kBTU / (House * Year))	4
.housingagingchain v5 testing	Complexity	Present Value of Heating Operating Costs (Dollar / (House))	4
HeatPumpModel_v31	Complexity	Retrofitting (House * kBTU / (sf * F* Year) / Year)	4
.housingagingchain v8	Complexity	Total Age (House * Year)	4
HeatPumpModel_v31	Complexity	Cooling Energy Use Under Alternatives (kBTU / (House * Year))	5
HeatPumpModel_v31	Complexity	EEHIC Expected Subsidy for Retrofits (Dollar / House)	5
HeatPumpModel_v31	Complexity	Heating Energy Use Under Alternatives (kBTU / (House * Year))	5
HeatPumpModel_v31	Complexity	Housing (House)	5
.housingagingchain v15	Complexity	MassSave Expected Subsidy for Retrofits (Dollar / House)	5
HeatPumpModel_v31	Complexity	MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)	5
HeatPumpModel_v31	Complexity	Optimal U Value for Existing Homes (kBTU / (sf * F * Year))	5
HeatPumpModel_v31	Complexity	Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))	5
.housingagingchain v15	Complexity	Expected Subsidy for Retrofits (Dollar / House)	6
.housingagingchain v18	Complexity	Optimal U for New Homes (kBTU / (sf * Year * F))	6
.housingagingchain v4 testing	Complexity	Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))	6
HeatPumpModel_v31	Complexity	Total U Value (House * kBTU / (Year * F * sf) )	6
.housingagingchain v5 testing	Complexity	Unsubsidized Retrofit Cost Intensity (Dollar / sf)	6
.housingagingchain v15	Complexity	Additional Cost of Building to U Value (Dollar / sf)	7
HeatPumpModel_v31	Complexity	U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))	8
.housingagingchain v8	Complexity	Input (Dimensionless)	15
.housingagingchain v8	Complexity	Input 0 (Dimensionless)	15
HeatPumpModel_v31	Complexity	Input 1 (Dimensionless)	15

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 v8	L	Area[Preexisting Cohorts,Open to Retrofitting] (sf)
.housingagingchain v8	L	Autocorrelated Noise (Dimensionless)
.housingagingchain v8	L	Autocorrelated Noise 0 (Dimensionless)
HeatPumpModel_v31	L	Autocorrelated Noise 1 (Dimensionless)
.housingagingchain v18	L	Code U (kBTU / (sf * Year * F))
HeatPumpModel_v31	L	Cumulative Emissions (tCO2)
HeatPumpModel_v31	L	Cumulative Federal Subsidy (Dollar)
HeatPumpModel_v31	L	Cumulative MA Subsidy (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidies for Heat Pumps (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidy for Retrofits (Dollar)
HeatPumpModel_v31	SM,A	Expected Cooling Energy Price (Dollar / kBTU)
HeatPumpModel_v31	SM,A	Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
HeatPumpModel_v31	SM,A	Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
.housingagingchain v15	SM,A	Expected Fixed Cost (Dollar / House)
.housingagingchain v15	SM,A	Expected Heating Energy Price[Heating and Cooling System] (Dollar / kBTU)
HeatPumpModel_v31	SM,A	Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
.housingagingchain v15	SM,A	Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
.housingagingchain v15	SM,A	Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
HeatPumpModel_v31	SM,A	Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	SM,A	Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
HeatPumpModel_v31	SM,A	HOMES Expected Higher Subsidy (Dollar / House)
.housingagingchain v15	SM,A	HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
HeatPumpModel_v31	L	Housing[Cohort,Heating and Cooling System,Open to Retrofitting] (House)
HeatPumpModel_v31	SM,A	MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v8	L	Total Age[Cohort,Open to Retrofitting] (House * Year)
HeatPumpModel_v31	L	Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] (House * kBTU / (Year * F * sf) )
HeatPumpModel_v31	L	U Value Retrofitted Away (House * kBTU / (Year * F * sf))

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 v8	C	Active Cohort Indicator[Preexisting Cohorts] (dmnl)
HeatPumpModel_v31	A	Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Affinity of Not Retrofitting[Cohort,Heating and Cooling System] (dmnl)
.housingagingchain v4 testing	A	Affinity of Retrofitting[Cohort,Heating and Cooling System] (dmnl)
.housingagingchain v8	C	Aging per Year (Year / Year)
.housingagingchain v8	L	Autocorrelated Noise (Dimensionless)
.housingagingchain v8	L	Autocorrelated Noise 0 (Dimensionless)
HeatPumpModel_v31	L	Autocorrelated Noise 1 (Dimensionless)
HeatPumpModel_v31	A	Average Indicated Fraction of Homes Retrofitting (dmnl)
HeatPumpModel_v31	C	Cooling Energy Price Step Height 1 (Dimensionless )
HeatPumpModel_v31	A	Cooling System Efficiency[No AC Cooling] (dmnl)
HeatPumpModel_v31	C	EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
HeatPumpModel_v31	C	Effect of Air Leakage from Window AC on Efficiency (dmnl)
.housingagingchain v8	C	Energy Price Step Height (Dimensionless )
HeatPumpModel_v31	A	Energy Savings[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	SM,A	Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
HeatPumpModel_v31	SM,A	Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
.housingagingchain v15	SM,A	Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
HeatPumpModel_v31	A	Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] (dmnl)
.housingagingchain v5 testing	A	Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Fraction of Housing by Heating and Cooling System[Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Fraction Retrofitting (dmnl)
HeatPumpModel_v31	LI,A	Fraction Retrofitting by Cohort[Cohort] (dmnl)
HeatPumpModel_v31	A	Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A,T	Gas COP TABLE (dmnl)
HeatPumpModel_v31	A,T	Heat Pump Cooling COP TABLE (dmnl)
HeatPumpModel_v31	C	Heat Pump COP on Coldest Days (dmnl )
HeatPumpModel_v31	A,T	Heat Pump Heating COP TABLE (dmnl)
HeatPumpModel_v31	A	Heating System Efficiency[Oil Heating] (dmnl)
HeatPumpModel_v31	C	HOMES Cut Off for Savings (dmnl )
.housingagingchain v8	C	Housing Starts Step Height (Dimensionless )
HeatPumpModel_v31	A	Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
.housingagingchain v15	A	Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
HeatPumpModel_v31	A	Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	C	Initial Fraction of Homes Retrofitting (dmnl )
.housingagingchain v8	A	Input (Dimensionless)
.housingagingchain v8	A	Input 0 (Dimensionless)
HeatPumpModel_v31	A	Input 1 (Dimensionless)
HeatPumpModel_v31	A	IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
HeatPumpModel_v31	C	IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
.housingagingchain v15	C	Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
HeatPumpModel_v31	C	No Turnover Switch (dmnl )
.housingagingchain v8	C	Noise Standard Deviation (Dimensionless)
.housingagingchain v8	C	Noise Standard Deviation 0 (Dimensionless)
HeatPumpModel_v31	C	Noise Standard Deviation 1 (Dimensionless)
HeatPumpModel_v31	A,T	Oil COP TABLE (dmnl)
HeatPumpModel_v31	C	Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
.housingagingchain v15	C	Proportional Subsidy Switch for Retrofits (dmnl )
HeatPumpModel_v31	C	Sensitivity of Affinity to Cost (dmnl )
.housingagingchain v5 testing	C	Sensitivity of Marginal Cost to U Value (dmnl )
HeatPumpModel_v31	C	Sensitivity of Retrofits to Cost (dmnl )
.housingagingchain v8	C	Sine Amplitude (Dimensionless)
.housingagingchain v8	C	Sine Amplitude 0 (Dimensionless)
HeatPumpModel_v31	C	Sine Amplitude 1 (Dimensionless)
HeatPumpModel_v31	C	System Switching SWITCH (dmnl )
HeatPumpModel_v31	C	Weight on Upfront Cost (dmnl )
.housingagingchain v8	A	White Noise (Dimensionless)
.housingagingchain v8	A	White Noise 0 (Dimensionless)
HeatPumpModel_v31	A	White Noise 1 (Dimensionless)

Quick Links:

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

Group	Type	Variable
.housingagingchain v8	C	Active Cohort Indicator[Preexisting Cohorts] (dmnl)
HeatPumpModel_v31	A	Actual EEHIC Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
HeatPumpModel_v31	A	Actual HOMES Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar/ Home)
HeatPumpModel_v31	A	Actual MassSave Subsidy for Retrofits[Cohort,Heating and Cooling System] (Dollar / House)
.housingagingchain v15	A	Additional Cost of Building to U Value[Cohort,Heating and Cooling System] (Dollar / sf)
HeatPumpModel_v31	A	Affinity of Heating and Cooling Systems[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Affinity of Not Retrofitting[Cohort,Heating and Cooling System] (dmnl)
.housingagingchain v4 testing	A	Affinity of Retrofitting[Cohort,Heating and Cooling System] (dmnl)
.housingagingchain v8	F,A	Age Removal[Cohort,Retrofitting Status] (House * Year /Year)
.housingagingchain v8	F,A	Aging[Cohort,Retrofitting Status] (House * Year / Year)
.housingagingchain v8	C	Aging per Year (Year / Year)
HeatPumpModel_v31	C	Amoritization Period (Year )
.housingagingchain v15	A	Amoritized Subsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar / (House * Year))
HeatPumpModel_v31	F,A	Annual Federal Subsidies (Dollar / Year)
HeatPumpModel_v31	F,A	Annual Heat Pump Subsidy (Dollar / Year)
HeatPumpModel_v31	A	Annual Load from Heat Pumps (kBTU / Year)
HeatPumpModel_v31	F,A	Annual MA Subsidies (Dollar / Year)
HeatPumpModel_v31	F,A	Annual Retrofit Subsidy (Dollar / Year)
HeatPumpModel_v31	A	Annual Subsidies (Dollar / Year)
.housingagingchain v8	L	Area[Preexisting Cohorts,Open to Retrofitting] (sf)
.housingagingchain v8	F,A	Area of New Homes[Cohort] (sf / Year)
.housingagingchain v8	F,A	Area Removal[Cohort,Retrofitting Status] (sf /Year)
.housingagingchain v8	L	Autocorrelated Noise (Dimensionless)
.housingagingchain v8	L	Autocorrelated Noise 0 (Dimensionless)
HeatPumpModel_v31	L	Autocorrelated Noise 1 (Dimensionless)
.housingagingchain v8	A	Average Age[Cohort,Retrofitting Status] (Year)
.housingagingchain v8	A	Average Age in All Housing (Year)
HeatPumpModel_v31	A	Average Area[Cohort,Retrofitting Status] (sf / House)
.housingagingchain v8	A	Average Area in All Housing (sf/ House)
HeatPumpModel_v31	A	Average Area of Housing Starts (sf / House)
HeatPumpModel_v31	A	Average Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	A	Average Cooling Cost Across All Homes (Dollar / House/ Year)
HeatPumpModel_v31	C	Average Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] (kBTU / (Year * House))
HeatPumpModel_v31	A	Average Cooling Energy Use Across All Homes (kBTU / Year / House)
HeatPumpModel_v31	A	Average Daily Load from Heat Pumps (kBTU / Day)
HeatPumpModel_v31	A	Average Emissions (tCO2 / House / Year)
HeatPumpModel_v31	A	Average Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (Year * House))
HeatPumpModel_v31	A	Average Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year / House)
HeatPumpModel_v31	A	Average Emissions from Cooling by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (House * Year))
HeatPumpModel_v31	A	Average Emissions from Heating by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / (House * Year))
HeatPumpModel_v31	A	Average Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
.housingagingchain v15	A	Average Energy Costs for Retrofitting Home[Cohort,Heating and Cooling System] (Dollar / Year / House)
.housingagingchain v8	A	Average Energy Costs if Retrofitted[Cohort,Heating and Cooling System] (Dollar/(Year*House))
HeatPumpModel_v31	A	Average Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (Year * House))
HeatPumpModel_v31	A	Average Energy Use by Heating and Cooling System[Heating and Cooling System] (kBTU / (House * Year))
HeatPumpModel_v31	A	Average Energy Use in All Housing (kBTU / Year / House)
HeatPumpModel_v31	A	Average EUI by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * Year))
HeatPumpModel_v31	A	Average EUI in All Housing (kBTU / (sf * Year))
.housingagingchain v5 testing	A	Average Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	A	Average Heating Cost Across All Homes (Dollar / Year / House)
HeatPumpModel_v31	A	Average Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (Year * House))
HeatPumpModel_v31	A	Average Heating Energy Use Across All Homes (kBTU / (Year * House))
HeatPumpModel_v31	C	Average Income (Dollar / Hour / House )
HeatPumpModel_v31	A	Average Indicated Fraction of Homes Retrofitting (dmnl)
HeatPumpModel_v31	A	Average Lifetime of Cooling Technology[No AC Cooling] (Years)
HeatPumpModel_v31	C	Average Lifetime of Heating Technology[Oil Heating] (Year)
HeatPumpModel_v31	A	Average Subsidized Retrofit Cost (Dollar / House)
HeatPumpModel_v31	C	Average Time To Consider Switching (Year )
HeatPumpModel_v31	A	Average U Value by Heating and Cooling System[Heating and Cooling System] (kBTU / (sf * F * Year))
.housingagingchain v4 testing	A	Average U Value in All Housing (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Average U Value of Houses Switching Into Sources[Heating and Cooling System] (kBTU / (sf * F * Year))
HeatPumpModel_v31	C	CDD on Coldest Day (F )
.housingagingchain v8	F,A	Change in AC Noise (1/Year)
.housingagingchain v8	F,A	Change in AC Noise 0 (1/Year)
HeatPumpModel_v31	F,A	Change in AC Noise 1 (1/Year)
.housingagingchain v18	L	Code U (kBTU / (sf * Year * F))
.housingagingchain v8	C	Cohort Duration (Year )
HeatPumpModel_v31	C	Cooling Degree Days (F )
HeatPumpModel_v31	C	Cooling Emissions Factor (lb CO2 / kBTU)
HeatPumpModel_v31	A	Cooling Energy Price (Dollar / kBTU)
HeatPumpModel_v31	C	Cooling Energy Price Step Height 1 (Dimensionless )
HeatPumpModel_v31	A	Cooling Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
HeatPumpModel_v31	A	Cooling System Efficiency[No AC Cooling] (dmnl)
HeatPumpModel_v31	C	Cost of Bad Air Conditioning[No AC Cooling] (Dollar / House )
HeatPumpModel_v31	C	Cost of Cooling System Replacement[No AC Cooling] (Dollar / House)
HeatPumpModel_v31	C	Cost of Heating System Replacement[Oil Heating] (Dollar / House )
.housingagingchain v15	A	Cost of Switching Heating and Cooling Systems[Cohort,Heat Pump and Oil,Retrofitting Status,Heat Pump and Oil] (Dollar / House)
HeatPumpModel_v31	L	Cumulative Emissions (tCO2)
HeatPumpModel_v31	L	Cumulative Federal Subsidy (Dollar)
HeatPumpModel_v31	L	Cumulative MA Subsidy (Dollar)
HeatPumpModel_v31	A	Cumulative Subsidies (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidies for Heat Pumps (Dollar)
HeatPumpModel_v31	L	Cumulative Subsidy for Retrofits (Dollar)
HeatPumpModel_v31	C	Days per Year (Day / Year )
.housingagingchain v18	F,A	Decrease in Code U (kBTU / (sf * Year * F) / Year)
.housingagingchain v15	C	Delay in Changing Subsidy Expectations (Year )
.housingagingchain v15	C	Delay in Forming Expectations of Energy Price (Year )
.housingagingchain v15	C	Delay in Forming Expectations of Retrofit Costs (Year )
HeatPumpModel_v31	C	Demolition Hazard Rate (1 / Year )
HeatPumpModel_v31	F,A	Demolitions[Cohort,Heating and Cooling System,Retrofitting Status] (House / Year)
HeatPumpModel_v31	C	Discount Rate (1 / Year )
HeatPumpModel_v31	A	EEHIC Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
HeatPumpModel_v31	C	EEHIC Maximum Subsidy for Retrofits (Dollar / House )
HeatPumpModel_v31	C	EEHIC Proportional Subsidy Rate for Retrofits (dmnl )
HeatPumpModel_v31	C	EEHIC Subsidy for Retrofits Final Year (Year)
HeatPumpModel_v31	C	Effect of Air Leakage from Window AC on Efficiency (dmnl)
HeatPumpModel_v31	F,A	Emissions (tCO2 / Year)
HeatPumpModel_v31	A	Emissions by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (tCO2 / Year)
HeatPumpModel_v31	A	Emissions by Heating and Cooling System[Heating and Cooling System] (tCO2 / Year)
.housingagingchain v8	C	Energy Price Exponential Growth Rate (1/Year )
HeatPumpModel_v31	C	Energy Price Exponential Growth Rate 1 (1/Year )
.housingagingchain v8	C	Energy Price Pulse Quantity (Dimensionless*Year)
HeatPumpModel_v31	C	Energy Price Pulse Quantity 1 (Dimensionless*Year)
.housingagingchain v8	C	Energy Price Ramp Slope (1/Year )
HeatPumpModel_v31	C	Energy Price Ramp Slope 1 (1/Year )
.housingagingchain v8	C	Energy Price Step Height (Dimensionless )
HeatPumpModel_v31	A	Energy Savings[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Energy Use by Gas Houses (kBTU/ Year)
HeatPumpModel_v31	A	Energy Use by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / Year)
HeatPumpModel_v31	A	Energy Use by Heat Pump Houses (kBTU / Year)
HeatPumpModel_v31	A	Energy Use by Oil Houses (kBTU / Year)
HeatPumpModel_v31	SM,A	Expected Cooling Energy Price (Dollar / kBTU)
HeatPumpModel_v31	SM,A	Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)
HeatPumpModel_v31	SM,A	Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)
.housingagingchain v15	SM,A	Expected Fixed Cost (Dollar / House)
.housingagingchain v15	SM,A	Expected Heating Energy Price[Heating and Cooling System] (Dollar / kBTU)
HeatPumpModel_v31	SM,A	Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)
.housingagingchain v15	A	Expected Lump Sum Subsidy Intensity[Retrofit Cost] (Dollar / sf)
.housingagingchain v15	SM,A	Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)
.housingagingchain v15	SM,A	Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)
HeatPumpModel_v31	SM,A	Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	SM,A	Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))
HeatPumpModel_v31	A	Expected Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	A	Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
HeatPumpModel_v31	A	Federal Annual Heat Pump Subsidy (Dollar / Year)
HeatPumpModel_v31	A	Federal Annual Retrofit Subsidy (Dollar / Year)
.housingagingchain v5 testing	C	Fixed Cost (Dollar / House )
.housingagingchain v5 testing	A	Fixed Cost per Unit Area[Cohort] (Dollar / sf)
HeatPumpModel_v31	A	Fraction of Houses in Each Heating and Cooling System[Heating and Cooling System] (dmnl)
.housingagingchain v5 testing	A	Fraction of Houses Switching[Cohort,Oil Heating,Retrofitting Status,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Fraction of Housing by Heating and Cooling System[Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Fraction Retrofitting (dmnl)
HeatPumpModel_v31	LI,A	Fraction Retrofitting by Cohort[Cohort] (dmnl)
HeatPumpModel_v31	A	Fraction Retrofitting by System and Cohort[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	C	Fractional Decrease in Code U (1 / Year )
HeatPumpModel_v31	A,T	Gas COP TABLE (dmnl)
HeatPumpModel_v31	C	HDD on Coldest Day (F )
HeatPumpModel_v31	A,T	Heat Pump Cooling COP TABLE (dmnl)
HeatPumpModel_v31	C	Heat Pump COP on Coldest Days (dmnl )
HeatPumpModel_v31	A,T	Heat Pump Heating COP TABLE (dmnl)
HeatPumpModel_v31	C	Heating Degree Days (F )
HeatPumpModel_v31	C	Heating Emissions Factors[Oil Heating] (lb CO2 / kBTU)
.housingagingchain v5 testing	A	Heating Energy Price[Heating and Cooling System] (Dollar / (kBTU))
HeatPumpModel_v31	A	Heating Energy Use Under Alternatives[Cohort,Fossil Fuel Heating,Open to Retrofitting,Heating and Cooling System] (kBTU / (House * Year))
HeatPumpModel_v31	A	Heating System Efficiency[Oil Heating] (dmnl)
HeatPumpModel_v31	C	Homeowner Hours Spent Retrofitting (Hour )
HeatPumpModel_v31	C	HOMES Cut Off for Savings (dmnl )
HeatPumpModel_v31	SM,A	HOMES Expected Higher Subsidy (Dollar / House)
.housingagingchain v15	SM,A	HOMES Expected Lower Lump Sum Subsidy (Dollar / House)
HeatPumpModel_v31	C	HOMES High Subsidy Amount (Dollar / House )
HeatPumpModel_v31	A	HOMES Implemented High Subsidy (Dollar / House)
.housingagingchain v15	A	HOMES Implemented Lower Subsidy (Dollar / House)
.housingagingchain v15	C	HOMES Lower Subsidy Amount (Dollar / House )
HeatPumpModel_v31	C	HOMES Subsidy Final Year (Year)
.housingagingchain v15	C	HOMES Subsidy Implementation Year (Year )
HeatPumpModel_v31	A	Houses Considering Switching System[Cohort,Heating and Cooling System,Retrofitting Status] (Houses / Year)
HeatPumpModel_v31	A	Houses Retrofitting[Cohort,Heating and Cooling System] (Houses)
HeatPumpModel_v31	A	Houses Retrofitting per Year[Cohort,Heating and Cooling System] (House / Year)
HeatPumpModel_v31	A	Houses Switching Into Sources[Heating and Cooling System] (Houses / Year)
HeatPumpModel_v31	F,A	Houses Switching Sources[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (House / Year)
HeatPumpModel_v31	L	Housing[Cohort,Heating and Cooling System,Open to Retrofitting] (House)
HeatPumpModel_v31	A	Housing by Cohort[Cohort] (House)
HeatPumpModel_v31	A	Housing by Cohort and Heating and Cooling System[Cohort,Heating and Cooling System] (Houses)
HeatPumpModel_v31	A	Housing by Cohort and Retrofitting Status[Cohort,Retrofitting Status] (House)
HeatPumpModel_v31	A	Housing by Heating and Cooling System[Heating and Cooling System] (House)
HeatPumpModel_v31	A	Housing by Retrofitting Status[Retrofitting Status] (House)
HeatPumpModel_v31	C	Housing Fractional Growth Rate (1 / Year )
HeatPumpModel_v31	F,A	Housing Starts[Cohort,Heating and Cooling System] (Houses / Year)
HeatPumpModel_v31	A	Housing Starts Across Cohorts ()
.housingagingchain v8	C	Housing Starts Exponential Growth Rate (1/Year )
HeatPumpModel_v31	A	Housing Starts In Each Cohort[Cohort] (House / Year)
.housingagingchain v8	C	Housing Starts Pulse Quantity (Dimensionless*Year)
.housingagingchain v8	C	Housing Starts Ramp Slope (1/Year )
.housingagingchain v8	C	Housing Starts Step Height (Dimensionless )
HeatPumpModel_v31	A	Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)
HeatPumpModel_v31	A	Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)
HeatPumpModel_v31	A	Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	A	Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)
.housingagingchain v15	A	Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)
HeatPumpModel_v31	C	Increase in Area per Year (sf / Year / House )
.housingagingchain v18	F,A	Increase in U Value from Housing Starts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
HeatPumpModel_v31	A	Indicated Fraction of Homes Retrofitting[Cohort,Heating and Cooling System] (dmnl)
HeatPumpModel_v31	A	Indicated Homes Retrofitting[Cohort,Heating and Cooling System] (House)
.housingagingchain v8	LI,A	Initial Age[Preexisting Cohorts,Retrofitting Status] (House * Year)
HeatPumpModel_v31	LI,C	Initial Area[Cohort] (sf)
HeatPumpModel_v31	C	Initial Average Area of Housing Starts (sf / House )
HeatPumpModel_v31	C	Initial Average U Value[Cohort] (kBTU/(YearsfF))
HeatPumpModel_v31	LI,C	Initial Code U Value (kBTU / (sf * F * Year))
HeatPumpModel_v31	C	Initial Cooling Energy Price (Dollar / kBTU)
HeatPumpModel_v31	C	Initial Fraction of Homes Retrofitting (dmnl )
.housingagingchain v5 testing	C	Initial Heating Energy Price[Oil Heating] (Dollar / (kBTU))
.housingagingchain v5 testing	LI,A	Initial Homes Not Retrofitting[Preexisting Cohorts,Heating and Cooling System] (House)
.housingagingchain v5 testing	LI,A	Initial Homes Retrofitting[Preexisting Cohorts,Heating and Cooling System] (Houses)
HeatPumpModel_v31	C	Initial Housing[Cohort,Heating and Cooling System] (House)
.	A	Initial Housing Starts[Heating and Cooling System] (House/Year)
.housingagingchain v15	LI,A	Initial U Value[Preexisting Cohorts,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf))
.housingagingchain v8	A	Input (Dimensionless)
.housingagingchain v8	A	Input 0 (Dimensionless)
HeatPumpModel_v31	A	Input 1 (Dimensionless)
HeatPumpModel_v31	A	IRA Actual Subsidy for Heat Pumps (Dollar / House)
HeatPumpModel_v31	A	IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)
HeatPumpModel_v31	A	IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)
HeatPumpModel_v31	C	IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )
HeatPumpModel_v31	C	IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )
HeatPumpModel_v31	C	IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )
HeatPumpModel_v31	C	IRA Proportional Subsidy Rate for Heat Pumps (dmnl )
HeatPumpModel_v31	C	kBTU per kWH (kBTU / kWH )
HeatPumpModel_v31	A	Lifetime Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] (Dollar * Year * F / kBTU)
HeatPumpModel_v31	A	Marginal Cooling Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / (kBTU))
HeatPumpModel_v31	A	Marginal Cost at Binding U Value without EEHIC[Cohort,Heating and Cooling System] ((Dollar / sf) / (kBTU / (sf * F * Year)))
.housingagingchain v15	A	Marginal Cost Reductions from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / kBTU)
.housingagingchain v5 testing	A	Marginal Heating Cost Reduction from Retrofitting[Cohort,Heating and Cooling System] (Dollar * F / (kBTU))
.housingagingchain v15	C	Mass Save Proportional Subsidy Rate for Retrofits (dmnl )
HeatPumpModel_v31	A	Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)
HeatPumpModel_v31	A	Massachusetts Annual Retrofit Subsidy (Dollar / Year)
HeatPumpModel_v31	SM,A	MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)
.housingagingchain v15	A	MassSave Expected Subsidy for Retrofits[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / House)
HeatPumpModel_v31	A	MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)
HeatPumpModel_v31	C	MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )
HeatPumpModel_v31	C	MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)
HeatPumpModel_v31	C	MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )
.housingagingchain v15	C	MassSave Maximum Subsidy for Retrofits (Dollar / House )
HeatPumpModel_v31	A	MassSave Subsidy for Retrofits Final Year (Year)
.housingagingchain v8	C	Maximum Energy Price (Dollar / kBTU)
HeatPumpModel_v31	A	Monthly Total Heat Pump Sales (Houses/ Month)
HeatPumpModel_v31	C	Months per Year (Month / Year )
HeatPumpModel_v31	A	Net Age Shift by System[Cohort,Heating and Cooling System] (Year * House / Year)
HeatPumpModel_v31	F,A	Net Age Shift from Retrofitting Status Shifting[Cohort] (House * Year / Year)
.housingagingchain v8	A	Net Area Shift by System[Cohort,Heating and Cooling System] (sf / Year)
HeatPumpModel_v31	F,A	Net Area Shift due to Retrofit Status Switching[Cohort] (sf / Year)
HeatPumpModel_v31	F,A	Net Change in Homes Retrofitting[Cohort,Heating and Cooling System] (Houses / Year)
HeatPumpModel_v31	F,A	Net U Value Change from Retrofitting Home Shifts[Cohort,Heating and Cooling System] (House * kBTU / (Year * F * sf) / Year)
HeatPumpModel_v31	C	No Turnover Switch (dmnl )
.housingagingchain v8	C	Noise Correlation Time (Year)
.housingagingchain v8	C	Noise Correlation Time 0 (Year)
HeatPumpModel_v31	C	Noise Correlation Time 1 (Year)
.housingagingchain v8	C	Noise Standard Deviation (Dimensionless)
.housingagingchain v8	C	Noise Standard Deviation 0 (Dimensionless)
HeatPumpModel_v31	C	Noise Standard Deviation 1 (Dimensionless)
.housingagingchain v8	C	Noise Start Time (Year)
.housingagingchain v8	C	Noise Start Time 0 (Year)
HeatPumpModel_v31	C	Noise Start Time 1 (Year)
HeatPumpModel_v31	A,T	Oil COP TABLE (dmnl)
HeatPumpModel_v31	A	Optimal Cooling Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	C	Optimal Cooling Energy Use[Cohort,No AC Cooling,Retrofitting Status] (kBTU / (Year * House))
HeatPumpModel_v31	A	Optimal Energy Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	A	Optimal Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
HeatPumpModel_v31	A	Optimal Heating Cost[Cohort,Heating and Cooling System,Retrofitting Status] (Dollar / (Year * House))
HeatPumpModel_v31	A	Optimal Heating Energy Use[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (House * Year))
HeatPumpModel_v31	A	Optimal U Across All Housing (kBTU / (sf * F * Year))
.housingagingchain v18	A	Optimal U for New Homes[Cohort,Heating and Cooling System] (kBTU / (sf * Year * F))
HeatPumpModel_v31	A	Optimal U Value for Existing Homes[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
.housingagingchain v4 testing	A	Optimal U Value for Existing Homes if no EEHIC Cap[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Optimal U Value with No EEHIC Proportional Subsidy[Cohort,Heating and Cooling System] (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Peak Cooling Load on Grid (kWH / Day)
HeatPumpModel_v31	A	Peak Heating Load on Grid (kWH / Day)
HeatPumpModel_v31	C	Peak Load from Heat Pumps on Coldest Days per Group[Cohort,Fossil Fuel Heating,Retrofitting Status] (kWH / Day)
HeatPumpModel_v31	C	Peak Load from Heat Pumps on Hottest Days per Group[Cohort,No AC Cooling,Retrofitting Status] (kWH / Day)
HeatPumpModel_v31	C	Peak Load from Non Heating or Cooling Sources (kWH / Day )
HeatPumpModel_v31	A	Perceived Cost of Not Retrofitting[Cohort,Heating and Cooling System] (Dollar / (House * Year))
HeatPumpModel_v31	A	Perceived Cost of Retrofitting[Cohort,Heating and Cooling System] (Dollar / (House * Year))
HeatPumpModel_v31	C	Pounds per Ton (lb CO2 / tCO2)
.housingagingchain v5 testing	C	Present Value of Cooling Operating Costs[Cohort,Heating and Cooling System,Retrofitting Status,No AC Cooling] (Dollars / (House))
.housingagingchain v5 testing	A	Present Value of Heating Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / (House))
HeatPumpModel_v31	A	Present Value of Operating Costs[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / (House) )
HeatPumpModel_v31	C	Present Value Replacement Cost[No AC Cooling] (Dollar / House)
HeatPumpModel_v31	C	Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )
HeatPumpModel_v31	C	Proportional IRA Subsidy Switch for Heat Pumps (dmnl )
.housingagingchain v15	C	Proportional MassSave Subsidy Implementation Year for Retrofits (Year )
.housingagingchain v15	C	Proportional Subsidy Switch for Retrofits (dmnl )
.housingagingchain v8	C	Pulse Time (Year)
.housingagingchain v8	C	Pulse Time 0 (Year)
HeatPumpModel_v31	C	Pulse Time 1 (Year)
.housingagingchain v8	C	Ramp End Time (Year)
.housingagingchain v8	C	Ramp End Time 0 (Year)
HeatPumpModel_v31	C	Ramp End Time 1 (Year)
.housingagingchain v8	C	Ramp Start Time (Year)
.housingagingchain v8	C	Ramp Start Time 0 (Year)
HeatPumpModel_v31	C	Ramp Start Time 1 (Year)
HeatPumpModel_v31	C	Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )
.housingagingchain v5 testing	C	Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )
HeatPumpModel_v31	C	Reference Retrofit Cost (Dollar / (House * Year) )
.housingagingchain v9	C	Reference U Value (kBTU / (sf * Year * F) )
HeatPumpModel_v31	C	Retrofit Delay (Year )
HeatPumpModel_v31	F,A	Retrofitting[Cohort,Heating and Cooling System] (House * kBTU / (sf * F* Year) / Year)
HeatPumpModel_v31	A	Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))
HeatPumpModel_v31	C	Sensitivity of Affinity to Cost (dmnl )
.housingagingchain v5 testing	C	Sensitivity of Marginal Cost to U Value (dmnl )
HeatPumpModel_v31	C	Sensitivity of Retrofits to Cost (dmnl )
.housingagingchain v8	C	Sine Amplitude (Dimensionless)
.housingagingchain v8	C	Sine Amplitude 0 (Dimensionless)
HeatPumpModel_v31	C	Sine Amplitude 1 (Dimensionless)
.housingagingchain v8	C	Sine Period (Year)
.housingagingchain v8	C	Sine Period 0 (Year)
HeatPumpModel_v31	C	Sine Period 1 (Year)
HeatPumpModel_v31	A	Soft Costs of Retrofitting (Dollar / Home)
.housingagingchain v8	C	Step Time (Year)
.housingagingchain v8	C	Step Time 0 (Year)
HeatPumpModel_v31	C	Step Time 1 (Year)
HeatPumpModel_v31	A	Subsidized Cost of Heat Pumps (Dollar / House)
.housingagingchain v15	A	Subsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar /House)
HeatPumpModel_v31	C	System Switching SWITCH (dmnl )
HeatPumpModel_v31	C	Time to Decide to Retrofit (Year )
.housingagingchain v8	L	Total Age[Cohort,Open to Retrofitting] (House * Year)
HeatPumpModel_v31	A	Total Area (sf)
HeatPumpModel_v31	A	Total Cooling Cost (Dollar / Year)
HeatPumpModel_v31	A	Total Cooling Energy Use (kBTU/ Year)
HeatPumpModel_v31	A	Total Cost of Ownership of Average Home[Cohort,Heating and Cooling System] (Dollar / (Year * House))
HeatPumpModel_v31	A	Total Cost of Ownership of Retrofitted Homes[Cohort,Heating and Cooling System] (Dollar / (House * Year))
HeatPumpModel_v31	A	Total Energy Use (kBTU / Year)
HeatPumpModel_v31	A	Total Heat Pump Sales (House / Year)
HeatPumpModel_v31	A	Total Heating Cost (Dollar / Year)
HeatPumpModel_v31	A	Total Heating Energy Use (kBTU/ Year)
HeatPumpModel_v31	A	Total Housing Starts (House/ Year)
.housingagingchain v4 testing	A	Total Housing Stock (House)
HeatPumpModel_v31	C	Total Initial Homes (Houses )
HeatPumpModel_v31	C	Total Initial Housing Starts (Houses / Year )
HeatPumpModel_v31	A	Total Present Value of Cost[Cohort,Fossil Fuel Heating,Retrofitting Status,Heating and Cooling System] (Dollar / House)
HeatPumpModel_v31	L	Total U Value[Cohort,Heating and Cooling System,Open to Retrofitting] (House * kBTU / (Year * F * sf) )
HeatPumpModel_v31	A	Total U Value Across All Groupings (House * kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Total U Value by Cohort[Cohort] (House * kBTU / (sf * F * Year))
HeatPumpModel_v31	A	Total U Value by Heating and Cooling System[Heating and Cooling System] (House * kBTU / (sf * F * Year))
HeatPumpModel_v31	A	U Value at Which EEHIC Cap Binds[Cohort,Heating and Cooling System] (kBTU / (F * sf * Year))
HeatPumpModel_v31	A	U Value by Grouping[Cohort,Heating and Cooling System,Retrofitting Status] (kBTU / (sf * F * Year))
HeatPumpModel_v31	A	U Value Increase from Source Switching[Heating and Cooling System] (kBTUHouse/(YearYearsfF))
HeatPumpModel_v31	F,A	U Value Loss from Demolition[Cohort,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf) / Year)
.housingagingchain v18	A	U Value of Housing Starts[Cohort,Heating and Cooling System] (kBTU / (Year * F * sf))
HeatPumpModel_v31	A	U Value of Retrofitting Homes[Cohort,Heating and Cooling System] (kBTU / (sf * Year * F))
HeatPumpModel_v31	L	U Value Retrofitted Away (House * kBTU / (Year * F * sf))
HeatPumpModel_v31	F,A	U Value Shift from Source Switching[Cohort,Fossil Fuel Heating,Heating and Cooling System,Retrofitting Status] (House * kBTU / (Year * F * sf) / Year)
HeatPumpModel_v31	A,T	Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)
HeatPumpModel_v31	A	Unsubsidized Cost of Heat Pumps (Dollar / House)
.housingagingchain v8	A	Unsubsidized Retrofit Cost[Cohort,Heating and Cooling System] (Dollar / House)
.housingagingchain v5 testing	A	Unsubsidized Retrofit Cost Intensity[Cohort,Heating and Cooling System] (Dollar / sf)
HeatPumpModel_v31	C	Weight on Upfront Cost (dmnl )
.housingagingchain v8	A	White Noise (Dimensionless)
.housingagingchain v8	A	White Noise 0 (Dimensionless)
HeatPumpModel_v31	A	White Noise 1 (Dimensionless)
.Control	C	FINAL TIME (Year)
.Control	C	INITIAL TIME (Year)
.Control	A	SAVEPER (Year )
.Control	C	TIME STEP (Year )

Function Sensitivity Parameters (0 Variables + 0 Control Variables)

Group

Type

Variable

Data Lookup Tables (0 Variables + 0 Control Variables)

Group

Type

Variable

Variables Using Macros (0 Variables + 0 Control Variables)

Group

Type

Variable

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Quick Links:

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

Group	Type	Variable
.housingagingchain v8	C	Maximum Energy Price (Dollar / kBTU)
.Control	A	SAVEPER (Year )

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

Group	Type	Variable	Units
HeatPumpModel_v31	Units	Heating System Efficiency (dmnl)	Lhs Units: (Dmnl) Rhs Units: LOOKUP Used With Dimensioned Argument < (Year) > Complete Rhs Units: LOOKUP ( Dmnl , Year )
HeatPumpModel_v31	Units	Housing Starts Across Cohorts ()	Lhs Units: None Specified
HeatPumpModel_v31	Units	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_v31	Units	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
DollarFYear/kBTU	Combined	[(Dollar/sf)/(kBTU/(sf * F * Year))]
Dollar*F/kBTU	Combined	[Dollar * F/(kBTU), Dollar * F/kBTU]
DollarYearF/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]
HousekBTU/sfF*Year	Combined	[House * kBTU/(sf * F * Year)]
HousekBTU/sfFYearYear	Combined	[House * kBTU/(sf * F* Year)/Year]
HousekBTU/YearF*sf	Combined	[House * kBTU/(Year * F * sf)]
HousekBTU/YearYearFsf	Combined	[House * kBTU/(Year * F * sf)/Year]
HousekBTU/YearYearsfF	Combined	[House * kBTU/( Year * Year * sf * F)]
House*Year	Combined	[House * Year]
House/Month	Combined	[Houses/Month]
House/Year	Combined	[Houses/Year]
kBTUHouse/YearYearsfF	Combined	[kBTUHouse/(YearYearsfF)]
kBTU/Day	Combined
kBTU/FsfYear	Combined	[kBTU/(F * sf * Year)]
kBTU/House*Year	Combined	[kBTU/(House * Year)]
kBTU/kWH	Combined
kBTU/sfFYear	Combined	[kBTU/(sf * F * Year)]
kBTU/sf*Year	Combined	[kBTU/(sf * Year)]
kBTU/sfYearF	Combined	[kBTU/(sf * Year * F)]
kBTU/sfYearYear*F	Combined	[kBTU/(sf * Year * F)/Year]
kBTU/Year	Combined
kBTU/YearFsf	Combined	[kBTU/(Year * F * sf)]
kBTU/Year*House	Combined	[kBTU/(Year * House), kBTU/Year/House]
kBTU/YearsfF	Combined	[kBTU/(YearsfF)]
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]

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

Group

Type

Variable

Loops

+/- Ratio

Loops (IVV)

+/- Ratio

Feedback...

Housing (House)

5 (29.4%)

3 [ 2, 4]

2 [ 2, 2]

1.50

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Total U Value (House * kBTU / (Year * F * sf) )

4 (23.5%)

2 [ 3, 3]

1.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

U Value by Grouping (kBTU / (sf * F * Year))

4 (23.5%)

2 [ 3, 3]

1.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Area (sf)

2 (11.8%)

1 [ 4, 4]

1 [ 3, 3]

1.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Age (Year)

2 (11.8%)

1 [ 4, 4]

1 [ 3, 3]

1.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Area (sf / House)

2 (11.8%)

1 [ 4, 4]

1 [ 3, 3]

1.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

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]

Feedback...

Total Age (House * Year)

2 (11.8%)

1 [ 4, 4]

1 [ 3, 3]

1.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Age Removal (House * Year /Year)

1 (5.9%)

0 [ 0, 0]

1 [ 3, 3]

0.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Area Removal (sf /Year)

1 (5.9%)

0 [ 0, 0]

1 [ 3, 3]

0.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Autocorrelated Noise (Dimensionless)

1 (5.9%)

0 [ 0, 0]

1 [ 2, 2]

0.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Autocorrelated Noise 0 (Dimensionless)

1 (5.9%)

0 [ 0, 0]

1 [ 2, 2]

0.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Autocorrelated Noise 1 (Dimensionless)

1 (5.9%)

0 [ 0, 0]

1 [ 2, 2]

0.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

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]

Feedback...

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]

Feedback...

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]

Feedback...

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]

Feedback...

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]

Feedback...

Demolitions (House / Year)

1 (5.9%)

0 [ 0, 0]

1 [ 2, 2]

0.00

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Houses Considering Switching System (Houses / Year)

1 (5.9%)

1 [ 3, 3]

0 [ 0, 0]

Infinite

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Houses Switching Sources (House / Year)

1 (5.9%)

1 [ 3, 3]

0 [ 0, 0]

Infinite

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

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]

Feedback...

Housing Starts (Houses / Year)

1 (5.9%)

1 [ 2, 2]

0 [ 0, 0]

Infinite

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Indicated Homes Retrofitting (House)

1 (5.9%)

1 [ 4, 4]

0 [ 0, 0]

Infinite

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

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]

Feedback...

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]

Feedback...

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]

Feedback...

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]

Feedback...

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]

Feedback...

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]

Feedback...

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]

Feedback...

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]

Feedback...

Active Cohort Indicator (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Actual EEHIC Subsidy for Retrofits (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Actual HOMES Subsidy for Retrofits (Dollar/ Home)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Actual MassSave Subsidy for Retrofits (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Additional Cost of Building to U Value (Dollar / sf)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Affinity of Heating and Cooling Systems (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Affinity of Not Retrofitting (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Affinity of Retrofitting (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Aging per Year (Year / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Aging (House * Year / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Amoritization Period (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Annual Federal Subsidies (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Annual Heat Pump Subsidy (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Annual Load from Heat Pumps (kBTU / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Annual MA Subsidies (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Annual Retrofit Subsidy (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Annual Subsidies (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Area of New Homes (sf / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Age in All Housing (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Area in All Housing (sf/ House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Area of Housing Starts (sf / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Cooling Cost Across All Homes (Dollar / House/ Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Cooling Cost (Dollar / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Cooling Energy Use Across All Homes (kBTU / Year / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Cooling Energy Use (kBTU / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Daily Load from Heat Pumps (kBTU / Day)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Emissions (tCO2 / House / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Emissions by Grouping (tCO2 / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Emissions by Heating and Cooling System (tCO2 / Year / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Emissions from Cooling by Grouping (tCO2 / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Emissions from Heating by Grouping (tCO2 / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Energy Cost (Dollar / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Energy Costs for Retrofitting Home (Dollar / Year / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Energy Costs if Retrofitted (Dollar/(Year*House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Energy Use by Heating and Cooling System (kBTU / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Energy Use in All Housing (kBTU / Year / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Energy Use (kBTU / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average EUI by Grouping (kBTU / (sf * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average EUI in All Housing (kBTU / (sf * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Heating Cost Across All Homes (Dollar / Year / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Heating Cost (Dollar / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Heating Energy Use Across All Homes (kBTU / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average Heating Energy Use (kBTU / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Income (Dollar / Hour / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Indicated Fraction of Homes Retrofitting (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Lifetime of Cooling Technology (Years)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Lifetime of Heating Technology (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Subsidized Retrofit Cost (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average Time To Consider Switching (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average U Value in All Housing (kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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CDD on Coldest Day (F )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cohort Duration (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cooling Degree Days (F )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cooling Emissions Factor (lb CO2 / kBTU)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cooling Energy Price (Dollar / kBTU)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cooling Energy Price Step Height 1 (Dimensionless )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cooling Energy Use Under Alternatives (kBTU / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cooling System Efficiency (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cost of Bad Air Conditioning (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cost of Cooling System Replacement (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Cost of Heating System Replacement (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cost of Switching Heating and Cooling Systems (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cumulative Emissions (tCO2)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cumulative Federal Subsidy (Dollar)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cumulative MA Subsidy (Dollar)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cumulative Subsidies (Dollar)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cumulative Subsidies for Heat Pumps (Dollar)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Cumulative Subsidy for Retrofits (Dollar)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Days per Year (Day / Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Delay in Changing Subsidy Expectations (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Delay in Forming Expectations of Energy Price (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Delay in Forming Expectations of Retrofit Costs (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Demolition Hazard Rate (1 / Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Discount Rate (1 / Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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EEHIC Expected Subsidy for Retrofits (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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EEHIC Maximum Subsidy for Retrofits (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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EEHIC Proportional Subsidy Rate for Retrofits (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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EEHIC Subsidy for Retrofits Final Year (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Effect of Air Leakage from Window AC on Efficiency (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Emissions (tCO2 / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Emissions by Grouping (tCO2 / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Emissions by Heating and Cooling System (tCO2 / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Energy Price Exponential Growth Rate (1/Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Energy Price Exponential Growth Rate 1 (1/Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Energy Price Pulse Quantity (Dimensionless*Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Energy Price Pulse Quantity 1 (Dimensionless*Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Energy Price Ramp Slope (1/Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Energy Price Ramp Slope 1 (1/Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Energy Price Step Height (Dimensionless )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Energy Savings (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Energy Use by Gas Houses (kBTU/ Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Energy Use by Grouping (kBTU / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Energy Use by Heat Pump Houses (kBTU / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Energy Use by Oil Houses (kBTU / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Expected Cooling Energy Price (Dollar / kBTU)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Expected Fixed Cost (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Expected Heating Energy Price (Dollar / kBTU)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Expected Lump Sum Subsidy Intensity (Dollar / sf)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Expected Subsidy for Heat Pumps (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Expected Subsidy for Retrofits (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Federal Annual Heat Pump Subsidy (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Federal Annual Retrofit Subsidy (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Fixed Cost (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Fixed Cost per Unit Area (Dollar / sf)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Fraction of Houses in Each Heating and Cooling System (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Fraction of Houses Switching (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Fraction of Housing by Heating and Cooling System (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Fraction Retrofitting (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Fraction Retrofitting by Cohort (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Fraction Retrofitting by System and Cohort (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Fractional Decrease in Code U (1 / Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Gas COP TABLE (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HDD on Coldest Day (F )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Heat Pump Cooling COP TABLE (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Heat Pump COP on Coldest Days (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Heat Pump Heating COP TABLE (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Heating Degree Days (F )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Heating Emissions Factors (lb CO2 / kBTU)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Heating Energy Price (Dollar / (kBTU))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Heating Energy Use Under Alternatives (kBTU / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Heating System Efficiency (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Homeowner Hours Spent Retrofitting (Hour )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HOMES Cut Off for Savings (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HOMES Expected Higher Subsidy (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HOMES Expected Lower Lump Sum Subsidy (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HOMES High Subsidy Amount (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HOMES Implemented High Subsidy (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HOMES Implemented Lower Subsidy (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HOMES Lower Subsidy Amount (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HOMES Subsidy Final Year (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

HOMES Subsidy Implementation Year (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Houses Retrofitting per Year (House / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Houses Retrofitting (Houses)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Houses Switching Into Sources (Houses / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing by Cohort and Retrofitting Status (House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing by Cohort (House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing by Heating and Cooling System (House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing by Retrofitting Status (House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing Fractional Growth Rate (1 / Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing Starts Across Cohorts ()

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing Starts Exponential Growth Rate (1/Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing Starts In Each Cohort (House / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing Starts Pulse Quantity (Dimensionless*Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing Starts Ramp Slope (1/Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Housing Starts Step Height (Dimensionless )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Increase in Area per Year (sf / Year / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Indicated Fraction of Homes Retrofitting (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Age (House * Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Area (sf)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Average Area of Housing Starts (sf / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Average U Value (kBTU/(Year*sf*F))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Code U Value (kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Cooling Energy Price (Dollar / kBTU)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Fraction of Homes Retrofitting (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Heating Energy Price (Dollar / (kBTU))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Homes Not Retrofitting (House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Homes Retrofitting (Houses)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Housing Starts (House/Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial Housing (House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Initial U Value (House * kBTU / (Year * F * sf))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Input (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Input 0 (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Input 1 (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

IRA Actual Subsidy for Heat Pumps (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

IRA Proportional Subsidy Rate for Heat Pumps (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

kBTU per kWH (kBTU / kWH )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Mass Save Proportional Subsidy Rate for Retrofits (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Massachusetts Annual Retrofit Subsidy (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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MassSave Expected Subsidy for Retrofits (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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MassSave Maximum Subsidy for Retrofits (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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MassSave Subsidy for Retrofits Final Year (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Maximum Energy Price (Dollar / kBTU)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Monthly Total Heat Pump Sales (Houses/ Month)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Months per Year (Month / Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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No Turnover Switch (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Noise Correlation Time (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Noise Correlation Time 0 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Noise Correlation Time 1 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Noise Standard Deviation (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Noise Standard Deviation 0 (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Noise Standard Deviation 1 (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Noise Start Time (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Noise Start Time 0 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Noise Start Time 1 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Oil COP TABLE (dmnl)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Optimal Cooling Cost (Dollar / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Optimal Cooling Energy Use (kBTU / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Optimal Energy Cost (Dollar / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Optimal Energy Use (kBTU / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Optimal Heating Cost (Dollar / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Optimal Heating Energy Use (kBTU / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Optimal U Across All Housing (kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Optimal U for New Homes (kBTU / (sf * Year * F))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Optimal U Value for Existing Homes (kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Peak Cooling Load on Grid (kWH / Day)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Peak Heating Load on Grid (kWH / Day)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Peak Load from Non Heating or Cooling Sources (kWH / Day )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Perceived Cost of Not Retrofitting (Dollar / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Perceived Cost of Retrofitting (Dollar / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Pounds per Ton (lb CO2 / tCO2)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Present Value of Cooling Operating Costs (Dollars / (House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Present Value of Heating Operating Costs (Dollar / (House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Present Value of Operating Costs (Dollar / (House) )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Present Value Replacement Cost (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Proportional IRA Subsidy Switch for Heat Pumps (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Proportional MassSave Subsidy Implementation Year for Retrofits (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Proportional Subsidy Switch for Retrofits (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Pulse Time (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Pulse Time 0 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Pulse Time 1 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Ramp End Time (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Ramp End Time 0 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Ramp End Time 1 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Ramp Start Time (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Ramp Start Time 0 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Ramp Start Time 1 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Reference Retrofit Cost (Dollar / (House * Year) )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

.housingagingchain v9

Feedback...

Reference U Value (kBTU / (sf * Year * F) )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Retrofit Delay (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Sensitivity of Affinity to Cost (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Sensitivity of Marginal Cost to U Value (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Sensitivity of Retrofits to Cost (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Sine Amplitude (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Sine Amplitude 0 (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Sine Amplitude 1 (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Sine Period (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Sine Period 0 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Sine Period 1 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Soft Costs of Retrofitting (Dollar / Home)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Step Time (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Step Time 0 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Step Time 1 (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Subsidized Cost of Heat Pumps (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Subsidized Retrofit Cost (Dollar /House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

System Switching SWITCH (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Time to Decide to Retrofit (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Area (sf)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Cooling Cost (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Cooling Energy Use (kBTU/ Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Cost of Ownership of Average Home (Dollar / (Year * House))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Energy Use (kBTU / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Heat Pump Sales (House / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Heating Cost (Dollar / Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Heating Energy Use (kBTU/ Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Housing Starts (House/ Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Housing Stock (House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Initial Homes (Houses )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Initial Housing Starts (Houses / Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total Present Value of Cost (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Total U Value Across All Groupings (House * kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Total U Value by Cohort (House * kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Feedback...

Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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U Value Increase from Source Switching (kBTU*House/(Year*Year*sf*F))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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U Value of Housing Starts (kBTU / (Year * F * sf))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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U Value of Retrofitting Homes (kBTU / (sf * Year * F))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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U Value Retrofitted Away (House * kBTU / (Year * F * sf))

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Unsubsidized Cost of Heat Pumps (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Unsubsidized Retrofit Cost Intensity (Dollar / sf)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Unsubsidized Retrofit Cost (Dollar / House)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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Weight on Upfront Cost (dmnl )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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White Noise (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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White Noise 0 (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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White Noise 1 (Dimensionless)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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FINAL TIME (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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INITIAL TIME (Year)

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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SAVEPER (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

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TIME STEP (Year )

0 ( 0%)

0 [ 0, 0]

0 ( 0%)

0 [ 0, 0]

Exogenous Variables Analysis (160 Variables + 4 Control Variables)

Group	Type	Variable	Variable Number	Data Source
.housingagingchain v8	Exogenous	Active Cohort Indicator (dmnl)	1	3 Exogenous
.housingagingchain v8	Exogenous	Aging per Year (Year / Year)	2	Hardcoded
HeatPumpModel_v31	Exogenous	Amoritization Period (Year )	3	Hardcoded
HeatPumpModel_v31	Exogenous	Average Area of Housing Starts (sf / House)	4	4 Exogenous
HeatPumpModel_v31	Exogenous	Average Income (Dollar / Hour / House )	5	Hardcoded
HeatPumpModel_v31	Exogenous	Average Lifetime of Cooling Technology (Years)	6	1 Exogenous
HeatPumpModel_v31	Exogenous	Average Lifetime of Heating Technology (Year)	7	Hardcoded
HeatPumpModel_v31	Exogenous	Average Time To Consider Switching (Year )	8	Hardcoded
HeatPumpModel_v31	Exogenous	CDD on Coldest Day (F )	9	Hardcoded
.housingagingchain v8	Exogenous	Cohort Duration (Year )	10	Hardcoded
HeatPumpModel_v31	Exogenous	Cooling Degree Days (F )	11	Hardcoded
HeatPumpModel_v31	Exogenous	Cooling Emissions Factor (lb CO2 / kBTU)	12	Hardcoded
HeatPumpModel_v31	Exogenous	Cooling Energy Price Step Height 1 (Dimensionless )	13	Hardcoded
HeatPumpModel_v31	Exogenous	Cooling System Efficiency (dmnl)	14	4 Exogenous
HeatPumpModel_v31	Exogenous	Cost of Bad Air Conditioning (Dollar / House )	15	Hardcoded
HeatPumpModel_v31	Exogenous	Cost of Cooling System Replacement (Dollar / House)	16	1 Exogenous
HeatPumpModel_v31	Exogenous	Cost of Heating System Replacement (Dollar / House )	17	1 Exogenous
HeatPumpModel_v31	Exogenous	Days per Year (Day / Year )	18	Hardcoded
.housingagingchain v15	Exogenous	Delay in Changing Subsidy Expectations (Year )	19	Hardcoded
.housingagingchain v15	Exogenous	Delay in Forming Expectations of Energy Price (Year )	20	Hardcoded
.housingagingchain v15	Exogenous	Delay in Forming Expectations of Retrofit Costs (Year )	21	Hardcoded
HeatPumpModel_v31	Exogenous	Demolition Hazard Rate (1 / Year )	22	Hardcoded
HeatPumpModel_v31	Exogenous	Discount Rate (1 / Year )	23	Hardcoded
HeatPumpModel_v31	Exogenous	EEHIC Maximum Subsidy for Retrofits (Dollar / House )	24	Hardcoded
HeatPumpModel_v31	Exogenous	EEHIC Proportional Subsidy Rate for Retrofits (dmnl )	25	Hardcoded
HeatPumpModel_v31	Exogenous	EEHIC Subsidy for Retrofits Final Year (Year)	26	Hardcoded
HeatPumpModel_v31	Exogenous	Effect of Air Leakage from Window AC on Efficiency (dmnl)	27	Hardcoded
.housingagingchain v8	Exogenous	Energy Price Exponential Growth Rate (1/Year )	28	Hardcoded
HeatPumpModel_v31	Exogenous	Energy Price Exponential Growth Rate 1 (1/Year )	29	Hardcoded
.housingagingchain v8	Exogenous	Energy Price Pulse Quantity (Dimensionless*Year)	30	Hardcoded
HeatPumpModel_v31	Exogenous	Energy Price Pulse Quantity 1 (Dimensionless*Year)	31	Hardcoded
.housingagingchain v8	Exogenous	Energy Price Ramp Slope (1/Year )	32	Hardcoded
HeatPumpModel_v31	Exogenous	Energy Price Ramp Slope 1 (1/Year )	33	Hardcoded
.housingagingchain v8	Exogenous	Energy Price Step Height (Dimensionless )	34	Hardcoded
HeatPumpModel_v31	Exogenous	Expected EEHIC Maximum Subsidy for Retrofits (Dollar / House)	35	2 Exogenous
HeatPumpModel_v31	Exogenous	Expected EEHIC Proportional Subsidy Rate for Retrofits (dmnl)	36	3 Exogenous
.housingagingchain v15	Exogenous	Expected Fixed Cost (Dollar / House)	37	2 Exogenous
HeatPumpModel_v31	Exogenous	Expected IRA Proportional Subsidy Rate for Heat Pumps (dmnl)	38	3 Exogenous
.housingagingchain v15	Exogenous	Expected Lump Sum Subsidy Intensity (Dollar / sf)	39	2 Exogenous
.housingagingchain v15	Exogenous	Expected MassSave Maximum Subsidy for Retrofits (Dollar / House)	40	2 Exogenous
.housingagingchain v15	Exogenous	Expected MassSave Proportional Subsidy Rate for Retrofits (dmnl)	41	3 Exogenous
HeatPumpModel_v31	Exogenous	Expected Maximum IRA Proportional Subsidy for Heat Pumps (Dollar / House)	42	2 Exogenous
.housingagingchain v15	Exogenous	Expected Reference Marginal Cost ((Dollar / sf) / (kBTU / (sf * Year * F)))	43	2 Exogenous
HeatPumpModel_v31	Exogenous	Expected Subsidy for Heat Pumps (Dollar / House)	44	2 Exogenous
.housingagingchain v5 testing	Exogenous	Fixed Cost (Dollar / House )	45	Hardcoded
HeatPumpModel_v31	Exogenous	Fractional Decrease in Code U (1 / Year )	46	Hardcoded
HeatPumpModel_v31	Exogenous	Gas COP TABLE (dmnl)	47	Hardcoded
HeatPumpModel_v31	Exogenous	HDD on Coldest Day (F )	48	Hardcoded
HeatPumpModel_v31	Exogenous	Heat Pump Cooling COP TABLE (dmnl)	49	Hardcoded
HeatPumpModel_v31	Exogenous	Heat Pump COP on Coldest Days (dmnl )	50	Hardcoded
HeatPumpModel_v31	Exogenous	Heat Pump Heating COP TABLE (dmnl)	51	Hardcoded
HeatPumpModel_v31	Exogenous	Heating Degree Days (F )	52	Hardcoded
HeatPumpModel_v31	Exogenous	Heating Emissions Factors (lb CO2 / kBTU)	53	Hardcoded
HeatPumpModel_v31	Exogenous	Heating System Efficiency (dmnl)	54	4 Exogenous
HeatPumpModel_v31	Exogenous	Homeowner Hours Spent Retrofitting (Hour )	55	Hardcoded
HeatPumpModel_v31	Exogenous	HOMES Cut Off for Savings (dmnl )	56	Hardcoded
HeatPumpModel_v31	Exogenous	HOMES Expected Higher Subsidy (Dollar / House)	57	2 Exogenous
.housingagingchain v15	Exogenous	HOMES Expected Lower Lump Sum Subsidy (Dollar / House)	58	2 Exogenous
HeatPumpModel_v31	Exogenous	HOMES High Subsidy Amount (Dollar / House )	59	Hardcoded
HeatPumpModel_v31	Exogenous	HOMES Implemented High Subsidy (Dollar / House)	60	4 Exogenous
.housingagingchain v15	Exogenous	HOMES Implemented Lower Subsidy (Dollar / House)	61	4 Exogenous
.housingagingchain v15	Exogenous	HOMES Lower Subsidy Amount (Dollar / House )	62	Hardcoded
HeatPumpModel_v31	Exogenous	HOMES Subsidy Final Year (Year)	63	Hardcoded
.housingagingchain v15	Exogenous	HOMES Subsidy Implementation Year (Year )	64	Hardcoded
HeatPumpModel_v31	Exogenous	Housing Fractional Growth Rate (1 / Year )	65	Hardcoded
.housingagingchain v8	Exogenous	Housing Starts Exponential Growth Rate (1/Year )	66	Hardcoded
.housingagingchain v8	Exogenous	Housing Starts Pulse Quantity (Dimensionless*Year)	67	Hardcoded
.housingagingchain v8	Exogenous	Housing Starts Ramp Slope (1/Year )	68	Hardcoded
.housingagingchain v8	Exogenous	Housing Starts Step Height (Dimensionless )	69	Hardcoded
HeatPumpModel_v31	Exogenous	Implemented EEHIC Maximum Subsidy for Retrofits (Dollar / House)	70	4 Exogenous
HeatPumpModel_v31	Exogenous	Implemented EEHIC Subsidy Proportional Rate for Retrofits (dmnl)	71	4 Exogenous
HeatPumpModel_v31	Exogenous	Implemented IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House)	72	4 Exogenous
.housingagingchain v15	Exogenous	Implemented MassSave Maximum Subsidy for Retrofits (Dollar / House)	73	4 Exogenous
.housingagingchain v15	Exogenous	Implemented MassSave Subsidy Proportional Rate for Retrofits (dmnl)	74	4 Exogenous
HeatPumpModel_v31	Exogenous	Increase in Area per Year (sf / Year / House )	75	Hardcoded
HeatPumpModel_v31	Exogenous	Initial Area (sf)	76	Hardcoded
HeatPumpModel_v31	Exogenous	Initial Average Area of Housing Starts (sf / House )	77	Hardcoded
HeatPumpModel_v31	Exogenous	Initial Average U Value (kBTU/(YearsfF))	78	Hardcoded
HeatPumpModel_v31	Exogenous	Initial Code U Value (kBTU / (sf * F * Year))	79	Hardcoded
HeatPumpModel_v31	Exogenous	Initial Cooling Energy Price (Dollar / kBTU)	80	Hardcoded
HeatPumpModel_v31	Exogenous	Initial Fraction of Homes Retrofitting (dmnl )	81	Hardcoded
.housingagingchain v5 testing	Exogenous	Initial Heating Energy Price (Dollar / (kBTU))	82	Hardcoded
.housingagingchain v5 testing	Exogenous	Initial Homes Not Retrofitting (House)	83	2 Exogenous
.housingagingchain v5 testing	Exogenous	Initial Homes Retrofitting (Houses)	84	2 Exogenous
.	Exogenous	Initial Housing Starts (House/Year)	85	1 Exogenous
HeatPumpModel_v31	Exogenous	Initial Housing (House)	86	Hardcoded
HeatPumpModel_v31	Exogenous	IRA Actual Subsidy for Heat Pumps (Dollar / House)	87	3 Exogenous
HeatPumpModel_v31	Exogenous	IRA Expected Proportional Subsidy for Heat Pumps (Dollar / House)	88	4 Exogenous
HeatPumpModel_v31	Exogenous	IRA Implemented Subsidy Proportional Rate for Heat Pumps (dmnl)	89	4 Exogenous
HeatPumpModel_v31	Exogenous	IRA Lump Sum Subsidy for Heat Pumps Final Year (Year )	90	Hardcoded
HeatPumpModel_v31	Exogenous	IRA Maximum Proportional Subsidy for Heat Pumps (Dollar / House )	91	Hardcoded
HeatPumpModel_v31	Exogenous	IRA Proportional Subsidy Implementation Year for Heat Pumps (Year )	92	Hardcoded
HeatPumpModel_v31	Exogenous	IRA Proportional Subsidy Rate for Heat Pumps (dmnl )	93	Hardcoded
HeatPumpModel_v31	Exogenous	kBTU per kWH (kBTU / kWH )	94	Hardcoded
.housingagingchain v15	Exogenous	Mass Save Proportional Subsidy Rate for Retrofits (dmnl )	95	Hardcoded
HeatPumpModel_v31	Exogenous	MassSave Expected Lump Sum Subsidy for Heat Pumps (Dollar / House)	96	2 Exogenous
HeatPumpModel_v31	Exogenous	MassSave Implemented Lump Sum Subsidy for Heat Pumps (Dollar / House)	97	5 Exogenous
HeatPumpModel_v31	Exogenous	MassSave Lump Sum Subsidy Amount for Heat Pumps (Dollar / House )	98	Hardcoded
HeatPumpModel_v31	Exogenous	MassSave Lump Sum Subsidy for Heat Pumps Final Year (Year)	99	Hardcoded
HeatPumpModel_v31	Exogenous	MassSave Lump Sum Subsidy Implementation Year for Heat Pumps (Year )	100	Hardcoded
.housingagingchain v15	Exogenous	MassSave Maximum Subsidy for Retrofits (Dollar / House )	101	Hardcoded
HeatPumpModel_v31	Exogenous	MassSave Subsidy for Retrofits Final Year (Year)	102	1 Exogenous
.housingagingchain v8	Exogenous	Maximum Energy Price (Dollar / kBTU)	103	Hardcoded
HeatPumpModel_v31	Exogenous	Months per Year (Month / Year )	104	Hardcoded
HeatPumpModel_v31	Exogenous	No Turnover Switch (dmnl )	105	Hardcoded
.housingagingchain v8	Exogenous	Noise Correlation Time (Year)	106	Hardcoded
.housingagingchain v8	Exogenous	Noise Correlation Time 0 (Year)	107	Hardcoded
HeatPumpModel_v31	Exogenous	Noise Correlation Time 1 (Year)	108	Hardcoded
.housingagingchain v8	Exogenous	Noise Standard Deviation (Dimensionless)	109	Hardcoded
.housingagingchain v8	Exogenous	Noise Standard Deviation 0 (Dimensionless)	110	Hardcoded
HeatPumpModel_v31	Exogenous	Noise Standard Deviation 1 (Dimensionless)	111	Hardcoded
.housingagingchain v8	Exogenous	Noise Start Time (Year)	112	Hardcoded
.housingagingchain v8	Exogenous	Noise Start Time 0 (Year)	113	Hardcoded
HeatPumpModel_v31	Exogenous	Noise Start Time 1 (Year)	114	Hardcoded
HeatPumpModel_v31	Exogenous	Oil COP TABLE (dmnl)	115	Hardcoded
HeatPumpModel_v31	Exogenous	Peak Load from Non Heating or Cooling Sources (kWH / Day )	116	Hardcoded
HeatPumpModel_v31	Exogenous	Pounds per Ton (lb CO2 / tCO2)	117	Hardcoded
HeatPumpModel_v31	Exogenous	Present Value Replacement Cost (Dollar / House)	118	5 Exogenous
HeatPumpModel_v31	Exogenous	Proportional EEHIC Subsidy Implementation Year for Retrofits (Year )	119	Hardcoded
HeatPumpModel_v31	Exogenous	Proportional IRA Subsidy Switch for Heat Pumps (dmnl )	120	Hardcoded
.housingagingchain v15	Exogenous	Proportional MassSave Subsidy Implementation Year for Retrofits (Year )	121	Hardcoded
.housingagingchain v15	Exogenous	Proportional Subsidy Switch for Retrofits (dmnl )	122	Hardcoded
.housingagingchain v8	Exogenous	Pulse Time (Year)	123	Hardcoded
.housingagingchain v8	Exogenous	Pulse Time 0 (Year)	124	Hardcoded
HeatPumpModel_v31	Exogenous	Pulse Time 1 (Year)	125	Hardcoded
.housingagingchain v8	Exogenous	Ramp End Time (Year)	126	Hardcoded
.housingagingchain v8	Exogenous	Ramp End Time 0 (Year)	127	Hardcoded
HeatPumpModel_v31	Exogenous	Ramp End Time 1 (Year)	128	Hardcoded
.housingagingchain v8	Exogenous	Ramp Start Time (Year)	129	Hardcoded
.housingagingchain v8	Exogenous	Ramp Start Time 0 (Year)	130	Hardcoded
HeatPumpModel_v31	Exogenous	Ramp Start Time 1 (Year)	131	Hardcoded
HeatPumpModel_v31	Exogenous	Reference Lifetime Cost of Heating and Cooling Systems (Dollar / House )	132	Hardcoded
.housingagingchain v5 testing	Exogenous	Reference Marginal Cost (Dollar / sf / (kBTU / (sf * Year * F)) )	133	Hardcoded
HeatPumpModel_v31	Exogenous	Reference Retrofit Cost (Dollar / (House * Year) )	134	Hardcoded
.housingagingchain v9	Exogenous	Reference U Value (kBTU / (sf * Year * F) )	135	Hardcoded
HeatPumpModel_v31	Exogenous	Retrofit Delay (Year )	136	Hardcoded
HeatPumpModel_v31	Exogenous	Sensitivity of Affinity to Cost (dmnl )	137	Hardcoded
.housingagingchain v5 testing	Exogenous	Sensitivity of Marginal Cost to U Value (dmnl )	138	Hardcoded
HeatPumpModel_v31	Exogenous	Sensitivity of Retrofits to Cost (dmnl )	139	Hardcoded
.housingagingchain v8	Exogenous	Sine Amplitude (Dimensionless)	140	Hardcoded
.housingagingchain v8	Exogenous	Sine Amplitude 0 (Dimensionless)	141	Hardcoded
HeatPumpModel_v31	Exogenous	Sine Amplitude 1 (Dimensionless)	142	Hardcoded
.housingagingchain v8	Exogenous	Sine Period (Year)	143	Hardcoded
.housingagingchain v8	Exogenous	Sine Period 0 (Year)	144	Hardcoded
HeatPumpModel_v31	Exogenous	Sine Period 1 (Year)	145	Hardcoded
HeatPumpModel_v31	Exogenous	Soft Costs of Retrofitting (Dollar / Home)	146	2 Exogenous
.housingagingchain v8	Exogenous	Step Time (Year)	147	Hardcoded
.housingagingchain v8	Exogenous	Step Time 0 (Year)	148	Hardcoded
HeatPumpModel_v31	Exogenous	Step Time 1 (Year)	149	Hardcoded
HeatPumpModel_v31	Exogenous	Subsidized Cost of Heat Pumps (Dollar / House)	150	2 Exogenous
HeatPumpModel_v31	Exogenous	System Switching SWITCH (dmnl )	151	Hardcoded
HeatPumpModel_v31	Exogenous	Time to Decide to Retrofit (Year )	152	Hardcoded
HeatPumpModel_v31	Exogenous	Total Initial Homes (Houses )	153	Hardcoded
HeatPumpModel_v31	Exogenous	Total Initial Housing Starts (Houses / Year )	154	Hardcoded
HeatPumpModel_v31	Exogenous	Unsubsidized Cost of Heat Pump Over Time TABLE (Dollar/ House)	155	Hardcoded
HeatPumpModel_v31	Exogenous	Unsubsidized Cost of Heat Pumps (Dollar / House)	156	2 Exogenous
HeatPumpModel_v31	Exogenous	Weight on Upfront Cost (dmnl )	157	Hardcoded
.housingagingchain v8	Exogenous	White Noise (Dimensionless)	158	3 Exogenous
.housingagingchain v8	Exogenous	White Noise 0 (Dimensionless)	159	3 Exogenous
HeatPumpModel_v31	Exogenous	White Noise 1 (Dimensionless)	160	3 Exogenous
.Control	Exogenous	FINAL TIME (Year)	161	Hardcoded
.Control	Exogenous	INITIAL TIME (Year)	162	Hardcoded
.Control	Exogenous	SAVEPER (Year )	163	1 Exogenous
.Control	Exogenous	TIME STEP (Year )	164	Hardcoded

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 v8	Endogenous	Input (Dimensionless)	1	15	14	93.3	2	3	3.50	3.50	4	150	16
.housingagingchain v8	Endogenous	Input 0 (Dimensionless)	2	15	14	93.3	2	3	3.50	3.50	4	150	16
HeatPumpModel_v31	Endogenous	Input 1 (Dimensionless)	3	15	14	93.3	2	3	3.50	3.50	4	150	16
.housingagingchain v18	Endogenous	Optimal U for New Homes (kBTU / (sf * Year * F))	4	6	5	83.3	17	2	3.41	4.00	5	144	22
.housingagingchain v4 testing	Endogenous	Optimal U Value for Existing Homes if no EEHIC Cap (kBTU / (sf * F * Year))	5	6	5	83.3	19	2	3.53	3.00	5	142	24
HeatPumpModel_v31	Endogenous	Optimal U Value with No EEHIC Proportional Subsidy (kBTU / (sf * F * Year))	6	5	4	80.0	16	2	3.62	4.00	5	146	20
HeatPumpModel_v31	Endogenous	Actual HOMES Subsidy for Retrofits (Dollar/ Home)	7	4	3	75.0	25	2	4.16	5.00	5	138	28
HeatPumpModel_v31	Endogenous	Housing Starts (Houses / Year)	8	4	3	75.0	10	2	3.30	3.00	5	153	13
HeatPumpModel_v31	Endogenous	Marginal Cost at Binding U Value without EEHIC ((Dollar / sf) / (kBTU / (sf * F * Year)))	9	4	3	75.0	10	2	3.30	3.50	4	153	13
HeatPumpModel_v31	Endogenous	U Value at Which EEHIC Cap Binds (kBTU / (F * sf * Year))	10	8	6	75.0	22	2	3.86	5.00	5	138	28
.housingagingchain v15	Endogenous	Additional Cost of Building to U Value (Dollar / sf)	11	7	5	71.4	24	2	3.50	3.50	5	137	29
HeatPumpModel_v31	Endogenous	Actual EEHIC Subsidy for Retrofits (Dollar / House)	12	3	2	66.7	11	2	3.27	3.00	5	153	13
HeatPumpModel_v31	Endogenous	Actual MassSave Subsidy for Retrofits (Dollar / House)	13	3	2	66.7	11	2	3.36	3.00	5	153	13
HeatPumpModel_v31	Endogenous	Affinity of Heating and Cooling Systems (dmnl)	14	3	2	66.7	4	3	4.00	4.00	5	160	6
HeatPumpModel_v31	Endogenous	Affinity of Not Retrofitting (dmnl)	15	3	2	66.7	1	2	2.00	2.00	2	163	3
.housingagingchain v4 testing	Endogenous	Affinity of Retrofitting (dmnl)	16	3	2	66.7	5	2	4.00	5.00	5	159	7
HeatPumpModel_v31	Endogenous	Average Emissions from Cooling by Grouping (tCO2 / (House * Year))	17	3	2	66.7	13	2	4.38	5.00	5	151	15
HeatPumpModel_v31	Endogenous	Average Emissions from Heating by Grouping (tCO2 / (House * Year))	18	3	2	66.7	14	2	4.29	5.00	5	150	16
.housingagingchain v8	Endogenous	Change in AC Noise (1/Year)	19	3	2	66.7	2	2	2.00	2.00	2	162	4
.housingagingchain v8	Endogenous	Change in AC Noise 0 (1/Year)	20	3	2	66.7	2	2	2.00	2.00	2	162	4
HeatPumpModel_v31	Endogenous	Change in AC Noise 1 (1/Year)	21	3	2	66.7	2	2	2.00	2.00	2	162	4
.housingagingchain v15	Endogenous	Cost of Switching Heating and Cooling Systems (Dollar / House)	22	3	2	66.7	9	2	4.11	5.00	5	155	11
HeatPumpModel_v31	Endogenous	Demolitions (House / Year)	23	3	2	66.7	10	3	3.70	3.50	5	154	12
HeatPumpModel_v31	Endogenous	Marginal Cooling Cost Reduction from Retrofitting (Dollar * F / (kBTU))	24	3	2	66.7	17	2	3.59	4.00	4	147	19
.housingagingchain v5 testing	Endogenous	Marginal Heating Cost Reduction from Retrofitting (Dollar * F / (kBTU))	25	3	2	66.7	18	2	3.50	4.00	4	146	20
HeatPumpModel_v31	Endogenous	Total Present Value of Cost (Dollar / House)	26	3	2	66.7	15	2	4.40	5.00	5	149	17
HeatPumpModel_v31	Endogenous	EEHIC Expected Subsidy for Retrofits (Dollar / House)	27	5	3	60.0	22	2	3.86	4.00	5	141	25
.housingagingchain v15	Endogenous	MassSave Expected Subsidy for Retrofits (Dollar / House)	28	5	3	60.0	22	2	3.91	4.00	5	141	25
HeatPumpModel_v31	Endogenous	Peak Load from Heat Pumps on Coldest Days per Group (kWH / Day)	29	7	4	57.1	19	3	3.89	4.00	5	143	23
HeatPumpModel_v31	Endogenous	Peak Load from Heat Pumps on Hottest Days per Group (kWH / Day)	30	7	4	57.1	21	2	3.71	4.00	5	141	25
.housingagingchain v8	Endogenous	Aging (House * Year / Year)	31	2	1	50.0	12	3	3.58	3.00	5	153	13
.housingagingchain v15	Endogenous	Amoritized Subsidized Retrofit Cost (Dollar / (House * Year))	32	2	1	50.0	14	3	4.29	4.50	5	151	15
.housingagingchain v8	Endogenous	Area of New Homes (sf / Year)	33	2	1	50.0	12	2	3.17	3.50	5	153	13
HeatPumpModel_v31	Endogenous	Average Cooling Energy Use (kBTU / (Year * House))	34	4	2	50.0	19	2	4.11	4.00	5	145	21
HeatPumpModel_v31	Endogenous	Average Daily Load from Heat Pumps (kBTU / Day)	35	2	1	50.0	9	5	5.00	5.00	5	156	10
HeatPumpModel_v31	Endogenous	Average Heating Energy Use (kBTU / (Year * House))	36	4	2	50.0	20	2	4.00	4.00	5	144	22
.housingagingchain v18	Endogenous	Code U (kBTU / (sf * Year * F))	37	2	1	50.0	1	2	2.00	2.00	2	164	2
HeatPumpModel_v31	Endogenous	Cooling Energy Price (Dollar / kBTU)	38	2	1	50.0	15	2	2.33	2.00	5	150	16
.housingagingchain v18	Endogenous	Decrease in Code U (kBTU / (sf * Year * F) / Year)	39	2	1	50.0	1	2	2.00	2.00	2	164	2
HeatPumpModel_v31	Endogenous	Expected Cooling Energy Price (Dollar / kBTU)	40	2	1	50.0	15	2	3.07	3.00	5	150	16
.housingagingchain v15	Endogenous	Expected Heating Energy Price (Dollar / kBTU)	41	2	1	50.0	15	2	3.07	3.00	5	150	16
.housingagingchain v15	Endogenous	Expected Subsidy for Retrofits (Dollar / House)	42	6	3	50.0	30	2	4.03	4.00	5	133	33
HeatPumpModel_v31	Endogenous	Federal Annual Heat Pump Subsidy (Dollar / Year)	43	2	1	50.0	9	3	3.56	3.00	5	156	10
.housingagingchain v5 testing	Endogenous	Fixed Cost per Unit Area (Dollar / sf)	44	2	1	50.0	13	2	4.38	5.00	5	152	14
.housingagingchain v5 testing	Endogenous	Heating Energy Price (Dollar / (kBTU))	45	2	1	50.0	15	2	2.33	2.00	5	150	16
HeatPumpModel_v31	Endogenous	Houses Considering Switching System (Houses / Year)	46	2	1	50.0	11	3	3.55	3.00	5	154	12
.housingagingchain v8	Endogenous	Initial Age (House * Year)	47	2	1	50.0	9	4	4.22	4.00	5	156	10
.housingagingchain v15	Endogenous	Initial U Value (House * kBTU / (Year * F * sf))	48	2	1	50.0	12	3	3.58	3.00	5	153	13
HeatPumpModel_v31	Endogenous	Lifetime Marginal Cost Reductions from Retrofitting (Dollar * Year * F / kBTU)	49	2	1	50.0	10	3	4.00	4.00	5	155	11
HeatPumpModel_v31	Endogenous	Massachusetts Annual Heat Pumps Subsidy (Dollar / Year)	50	2	1	50.0	8	2	3.25	3.00	5	157	9
HeatPumpModel_v31	Endogenous	Monthly Total Heat Pump Sales (Houses/ Month)	51	2	1	50.0	4	3	4.25	4.50	5	161	5
HeatPumpModel_v31	Endogenous	Optimal Cooling Energy Use (kBTU / (Year * House))	52	4	2	50.0	27	2	3.93	4.00	5	137	29
HeatPumpModel_v31	Endogenous	Optimal Heating Energy Use (kBTU / (House * Year))	53	4	2	50.0	28	2	3.86	4.00	5	136	30
HeatPumpModel_v31	Endogenous	Perceived Cost of Not Retrofitting (Dollar / (House * Year))	54	2	1	50.0	0	NA	NA	NA	NA	165	1
.housingagingchain v5 testing	Endogenous	Present Value of Cooling Operating Costs (Dollars / (House))	55	4	2	50.0	39	2	4.13	4.00	5	125	41
.housingagingchain v5 testing	Endogenous	Present Value of Heating Operating Costs (Dollar / (House))	56	4	2	50.0	40	2	4.10	4.00	5	124	42
.housingagingchain v5 testing	Endogenous	Unsubsidized Retrofit Cost Intensity (Dollar / sf)	57	6	3	50.0	24	2	4.46	5.00	5	139	27
HeatPumpModel_v31	Endogenous	Cooling Energy Use Under Alternatives (kBTU / (House * Year))	58	5	2	40.0	31	2	3.77	4.00	5	133	33
HeatPumpModel_v31	Endogenous	Heating Energy Use Under Alternatives (kBTU / (House * Year))	59	5	2	40.0	32	2	3.72	4.00	5	132	34
HeatPumpModel_v31	Endogenous	Average EUI by Grouping (kBTU / (sf * Year))	60	3	1	33.3	18	3	4.39	5.00	5	147	19
HeatPumpModel_v31	Endogenous	Average U Value of Houses Switching Into Sources (kBTU / (sf * F * Year))	61	3	1	33.3	4	3	4.25	4.50	5	161	5
HeatPumpModel_v31	Endogenous	Fraction of Houses in Each Heating and Cooling System (dmnl)	62	3	1	33.3	10	4	4.30	4.00	5	155	11
HeatPumpModel_v31	Endogenous	Houses Switching Sources (House / Year)	63	3	1	33.3	12	2	3.92	4.00	5	153	13
HeatPumpModel_v31	Endogenous	Housing (House)	64	6	2	33.3	14	2	2.93	2.50	5	150	16
HeatPumpModel_v31	Endogenous	Net Change in Homes Retrofitting (Houses / Year)	65	3	1	33.3	14	3	3.79	4.00	5	151	15
HeatPumpModel_v31	Endogenous	Perceived Cost of Retrofitting (Dollar / (House * Year))	66	3	1	33.3	8	2	4.25	4.50	5	157	9
.housingagingchain v15	Endogenous	Subsidized Retrofit Cost (Dollar /House)	67	3	1	33.3	23	2	3.96	4.00	5	142	24
HeatPumpModel_v31	Endogenous	Houses Retrofitting per Year (House / Year)	68	4	1	25.0	28	2	3.61	3.50	5	137	29
HeatPumpModel_v31	Endogenous	Retrofitting (House * kBTU / (sf * F* Year) / Year)	69	4	1	25.0	28	2	3.61	3.50	5	137	29
.housingagingchain v8	Endogenous	Area (sf)	70	5	1	20.0	12	3	3.58	3.50	5	153	13
.housingagingchain v8	Endogenous	Age Removal (House * Year /Year)	71	2	0	0.0	11	2	3.82	4.00	5	155	11
HeatPumpModel_v31	Endogenous	Annual Federal Subsidies (Dollar / Year)	72	2	0	0.0	30	3	4.33	4.00	5	136	30
HeatPumpModel_v31	Endogenous	Annual Heat Pump Subsidy (Dollar / Year)	73	2	0	0.0	10	3	3.80	4.00	5	156	10
HeatPumpModel_v31	Endogenous	Annual Load from Heat Pumps (kBTU / Year)	74	1	0	0.0	17	4	4.47	4.00	5	149	17
HeatPumpModel_v31	Endogenous	Annual MA Subsidies (Dollar / Year)	75	2	0	0.0	24	3	4.38	5.00	5	142	24
HeatPumpModel_v31	Endogenous	Annual Retrofit Subsidy (Dollar / Year)	76	2	0	0.0	28	3	4.39	4.00	5	138	28
HeatPumpModel_v31	Endogenous	Annual Subsidies (Dollar / Year)	77	2	0	0.0	24	4	4.79	5.00	5	142	24
.housingagingchain v8	Endogenous	Area Removal (sf /Year)	78	2	0	0.0	13	2	4.00	4.00	5	153	13
.housingagingchain v8	Endogenous	Autocorrelated Noise (Dimensionless)	79	1	0	0.0	3	2	2.67	3.00	3	163	3
.housingagingchain v8	Endogenous	Autocorrelated Noise 0 (Dimensionless)	80	1	0	0.0	3	2	2.67	3.00	3	163	3
HeatPumpModel_v31	Endogenous	Autocorrelated Noise 1 (Dimensionless)	81	1	0	0.0	3	2	2.67	3.00	3	163	3
.housingagingchain v8	Endogenous	Average Age in All Housing (Year)	82	2	0	0.0	11	3	4.00	4.00	5	155	11
.housingagingchain v8	Endogenous	Average Age (Year)	83	2	0	0.0	11	3	4.00	4.00	5	155	11
.housingagingchain v8	Endogenous	Average Area in All Housing (sf/ House)	84	2	0	0.0	13	3	4.31	4.00	5	153	13
HeatPumpModel_v31	Endogenous	Average Area (sf / House)	85	2	0	0.0	13	2	4.00	4.00	5	153	13
HeatPumpModel_v31	Endogenous	Average Cooling Cost Across All Homes (Dollar / House/ Year)	86	2	0	0.0	17	3	3.88	4.00	5	149	17
HeatPumpModel_v31	Endogenous	Average Cooling Cost (Dollar / (Year * House))	87	2	0	0.0	28	2	4.07	4.00	5	138	28
HeatPumpModel_v31	Endogenous	Average Cooling Energy Use Across All Homes (kBTU / Year / House)	88	2	0	0.0	14	3	4.21	4.00	5	152	14
HeatPumpModel_v31	Endogenous	Average Emissions (tCO2 / House / Year)	89	2	0	0.0	13	4	4.46	4.00	5	153	13
HeatPumpModel_v31	Endogenous	Average Emissions by Grouping (tCO2 / (Year * House))	90	2	0	0.0	11	2	3.36	4.00	5	155	11
HeatPumpModel_v31	Endogenous	Average Emissions by Heating and Cooling System (tCO2 / Year / House)	91	2	0	0.0	13	4	4.46	4.00	5	153	13
HeatPumpModel_v31	Endogenous	Average Energy Cost (Dollar / (Year * House))	92	2	0	0.0	35	3	4.63	5.00	5	131	35
.housingagingchain v15	Endogenous	Average Energy Costs for Retrofitting Home (Dollar / Year / House)	93	1	0	0.0	10	4	4.70	5.00	5	156	10
.housingagingchain v8	Endogenous	Average Energy Costs if Retrofitted (Dollar/(Year*House))	94	1	0	0.0	12	4	4.75	5.00	5	154	12
HeatPumpModel_v31	Endogenous	Average Energy Use by Heating and Cooling System (kBTU / (House * Year))	95	2	0	0.0	19	3	4.00	4.00	5	147	19
HeatPumpModel_v31	Endogenous	Average Energy Use in All Housing (kBTU / Year / House)	96	2	0	0.0	12	4	4.42	4.00	5	154	12
HeatPumpModel_v31	Endogenous	Average Energy Use (kBTU / (Year * House))	97	2	0	0.0	17	2	4.00	5.00	5	149	17
HeatPumpModel_v31	Endogenous	Average EUI in All Housing (kBTU / (sf * Year))	98	2	0	0.0	8	4	4.88	5.00	5	158	8
HeatPumpModel_v31	Endogenous	Average Heating Cost Across All Homes (Dollar / Year / House)	99	2	0	0.0	18	3	3.94	4.00	5	148	18
.housingagingchain v5 testing	Endogenous	Average Heating Cost (Dollar / (Year * House))	100	2	0	0.0	29	2	4.03	4.00	5	137	29
HeatPumpModel_v31	Endogenous	Average Heating Energy Use Across All Homes (kBTU / (Year * House))	101	2	0	0.0	15	3	4.20	4.00	5	151	15
HeatPumpModel_v31	Endogenous	Average Indicated Fraction of Homes Retrofitting (dmnl)	102	2	0	0.0	13	4	4.31	4.00	5	153	13
HeatPumpModel_v31	Endogenous	Average Subsidized Retrofit Cost (Dollar / House)	103	2	0	0.0	26	3	3.96	4.00	5	140	26
HeatPumpModel_v31	Endogenous	Average U Value by Heating and Cooling System (kBTU / (sf * F * Year))	104	2	0	0.0	14	4	4.36	4.00	5	152	14
.housingagingchain v4 testing	Endogenous	Average U Value in All Housing (kBTU / (sf * F * Year))	105	2	0	0.0	12	4	4.42	4.00	5	154	12
HeatPumpModel_v31	Endogenous	Cumulative Emissions (tCO2)	106	1	0	0.0	10	5	5.00	5.00	5	156	10
HeatPumpModel_v31	Endogenous	Cumulative Federal Subsidy (Dollar)	107	1	0	0.0	18	4	4.89	5.00	5	148	18
HeatPumpModel_v31	Endogenous	Cumulative MA Subsidy (Dollar)	108	1	0	0.0	11	4	4.64	5.00	5	155	11
HeatPumpModel_v31	Endogenous	Cumulative Subsidies (Dollar)	109	2	0	0.0	5	5	5.00	5.00	5	161	5
HeatPumpModel_v31	Endogenous	Cumulative Subsidies for Heat Pumps (Dollar)	110	1	0	0.0	9	4	4.67	5.00	5	157	9
HeatPumpModel_v31	Endogenous	Cumulative Subsidy for Retrofits (Dollar)	111	1	0	0.0	15	4	4.87	5.00	5	151	15
HeatPumpModel_v31	Endogenous	Emissions (tCO2 / Year)	112	1	0	0.0	15	4	4.33	4.00	5	151	15
HeatPumpModel_v31	Endogenous	Emissions by Grouping (tCO2 / Year)	113	2	0	0.0	22	3	3.86	4.00	5	144	22
HeatPumpModel_v31	Endogenous	Emissions by Heating and Cooling System (tCO2 / Year)	114	1	0	0.0	15	4	4.33	4.00	5	151	15
HeatPumpModel_v31	Endogenous	Energy Savings (dmnl)	115	2	0	0.0	27	2	3.89	4.00	5	139	27
HeatPumpModel_v31	Endogenous	Energy Use by Gas Houses (kBTU/ Year)	116	1	0	0.0	17	4	4.47	4.00	5	149	17
HeatPumpModel_v31	Endogenous	Energy Use by Grouping (kBTU / Year)	117	2	0	0.0	20	3	3.70	4.00	5	146	20
HeatPumpModel_v31	Endogenous	Energy Use by Heat Pump Houses (kBTU / Year)	118	1	0	0.0	17	4	4.47	4.00	5	149	17
HeatPumpModel_v31	Endogenous	Energy Use by Oil Houses (kBTU / Year)	119	1	0	0.0	17	4	4.47	4.00	5	149	17
HeatPumpModel_v31	Endogenous	Federal Annual Retrofit Subsidy (Dollar / Year)	120	3	0	0.0	31	2	3.77	4.00	5	135	31
.housingagingchain v5 testing	Endogenous	Fraction of Houses Switching (dmnl)	121	1	0	0.0	5	2	3.60	4.00	5	161	5
HeatPumpModel_v31	Endogenous	Fraction of Housing by Heating and Cooling System (dmnl)	122	2	0	0.0	10	4	4.30	4.00	5	156	10
HeatPumpModel_v31	Endogenous	Fraction Retrofitting (dmnl)	123	1	0	0.0	7	5	5.00	5.00	5	159	7
HeatPumpModel_v31	Endogenous	Fraction Retrofitting by Cohort (dmnl)	124	1	0	0.0	12	3	3.58	3.00	5	154	12
HeatPumpModel_v31	Endogenous	Fraction Retrofitting by System and Cohort (dmnl)	125	1	0	0.0	12	3	3.58	3.00	5	154	12
HeatPumpModel_v31	Endogenous	Houses Retrofitting (Houses)	126	1	0	0.0	12	3	3.58	3.00	5	154	12
HeatPumpModel_v31	Endogenous	Houses Switching Into Sources (Houses / Year)	127	1	0	0.0	10	2	4.30	5.00	5	156	10
HeatPumpModel_v31	Endogenous	Housing by Cohort and Heating and Cooling System (Houses)	128	1	0	0.0	12	3	3.58	3.00	5	154	12
HeatPumpModel_v31	Endogenous	Housing by Cohort and Retrofitting Status (House)	129	1	0	0.0	12	3	3.58	3.00	5	154	12
HeatPumpModel_v31	Endogenous	Housing by Cohort (House)	130	1	0	0.0	12	3	3.58	3.00	5	154	12
HeatPumpModel_v31	Endogenous	Housing by Heating and Cooling System (House)	131	1	0	0.0	12	3	3.58	3.00	5	154	12
HeatPumpModel_v31	Endogenous	Housing by Retrofitting Status (House)	132	1	0	0.0	10	4	4.30	4.00	5	156	10
HeatPumpModel_v31	Endogenous	Housing Starts Across Cohorts ()	133	1	0	0.0	9	3	4.33	5.00	5	157	9
HeatPumpModel_v31	Endogenous	Housing Starts In Each Cohort (House / Year)	134	1	0	0.0	10	2	3.50	4.00	5	156	10
.housingagingchain v18	Endogenous	Increase in U Value from Housing Starts (House * kBTU / (Year * F * sf) / Year)	135	2	0	0.0	25	2	3.88	4.00	5	141	25
HeatPumpModel_v31	Endogenous	Indicated Fraction of Homes Retrofitting (dmnl)	136	2	0	0.0	4	2	2.75	2.50	4	162	4
HeatPumpModel_v31	Endogenous	Indicated Homes Retrofitting (House)	137	2	0	0.0	14	3	4.14	4.00	5	152	14
.housingagingchain v15	Endogenous	Marginal Cost Reductions from Retrofitting (Dollar * F / kBTU)	138	2	0	0.0	34	2	4.41	5.00	5	132	34
HeatPumpModel_v31	Endogenous	Massachusetts Annual Retrofit Subsidy (Dollar / Year)	139	2	0	0.0	27	2	4.04	4.00	5	139	27
HeatPumpModel_v31	Endogenous	Net Age Shift by System (Year * House / Year)	140	2	0	0.0	13	2	4.15	4.00	5	153	13
HeatPumpModel_v31	Endogenous	Net Age Shift from Retrofitting Status Shifting (House * Year / Year)	141	1	0	0.0	9	3	4.78	5.00	5	157	9
.housingagingchain v8	Endogenous	Net Area Shift by System (sf / Year)	142	2	0	0.0	15	2	4.27	4.00	5	151	15
HeatPumpModel_v31	Endogenous	Net Area Shift due to Retrofit Status Switching (sf / Year)	143	1	0	0.0	8	3	4.62	5.00	5	158	8
HeatPumpModel_v31	Endogenous	Net U Value Change from Retrofitting Home Shifts (House * kBTU / (Year * F * sf) / Year)	144	2	0	0.0	16	2	4.31	4.00	5	150	16
HeatPumpModel_v31	Endogenous	Optimal Cooling Cost (Dollar / (Year * House))	145	2	0	0.0	31	2	3.87	4.00	5	135	31
HeatPumpModel_v31	Endogenous	Optimal Energy Cost (Dollar / (Year * House))	146	2	0	0.0	42	3	4.64	5.00	5	124	42
HeatPumpModel_v31	Endogenous	Optimal Energy Use (kBTU / (House * Year))	147	2	0	0.0	20	2	3.70	4.00	5	146	20
HeatPumpModel_v31	Endogenous	Optimal Heating Cost (Dollar / (Year * House))	148	2	0	0.0	32	2	3.84	4.00	5	134	32
HeatPumpModel_v31	Endogenous	Optimal U Across All Housing (kBTU / (sf * F * Year))	149	3	0	0.0	27	2	3.59	3.00	5	139	27
HeatPumpModel_v31	Endogenous	Optimal U Value for Existing Homes (kBTU / (sf * F * Year))	150	5	0	0.0	24	2	3.83	4.00	5	142	24
HeatPumpModel_v31	Endogenous	Peak Cooling Load on Grid (kWH / Day)	151	1	0	0.0	18	2	3.83	4.00	5	148	18
HeatPumpModel_v31	Endogenous	Peak Heating Load on Grid (kWH / Day)	152	1	0	0.0	17	2	3.82	4.00	5	149	17
HeatPumpModel_v31	Endogenous	Present Value of Operating Costs (Dollar / (House) )	153	2	0	0.0	43	2	4.51	5.00	5	123	43
HeatPumpModel_v31	Endogenous	Retrofitting Across Cohorts and Systems (House * kBTU / ( Year * Year * sf * F))	154	1	0	0.0	24	2	4.21	4.00	5	142	24
.housingagingchain v8	Endogenous	Total Age (House * Year)	155	4	0	0.0	11	2	3.64	4.00	5	155	11
HeatPumpModel_v31	Endogenous	Total Area (sf)	156	1	0	0.0	12	2	4.25	4.00	5	154	12
HeatPumpModel_v31	Endogenous	Total Cooling Cost (Dollar / Year)	157	2	0	0.0	30	3	4.20	4.50	5	136	30
HeatPumpModel_v31	Endogenous	Total Cooling Energy Use (kBTU/ Year)	158	2	0	0.0	18	2	3.61	3.00	5	148	18
HeatPumpModel_v31	Endogenous	Total Cost of Ownership of Average Home (Dollar / (Year * House))	159	1	0	0.0	3	5	5.00	5.00	5	163	3
HeatPumpModel_v31	Endogenous	Total Cost of Ownership of Retrofitted Homes (Dollar / (House * Year))	160	2	0	0.0	11	2	4.45	5.00	5	155	11
HeatPumpModel_v31	Endogenous	Total Energy Use (kBTU / Year)	161	1	0	0.0	17	4	4.47	4.00	5	149	17
HeatPumpModel_v31	Endogenous	Total Heat Pump Sales (House / Year)	162	1	0	0.0	10	2	4.30	5.00	5	156	10
HeatPumpModel_v31	Endogenous	Total Heating Cost (Dollar / Year)	163	2	0	0.0	31	3	4.19	4.00	5	135	31
HeatPumpModel_v31	Endogenous	Total Heating Energy Use (kBTU/ Year)	164	2	0	0.0	19	2	3.58	3.00	5	147	19
HeatPumpModel_v31	Endogenous	Total Housing Starts (House/ Year)	165	1	0	0.0	10	2	3.50	4.00	5	156	10
.housingagingchain v4 testing	Endogenous	Total Housing Stock (House)	166	1	0	0.0	12	3	3.58	3.00	5	154	12
HeatPumpModel_v31	Endogenous	Total U Value Across All Groupings (House * kBTU / (sf * F * Year))	167	1	0	0.0	9	4	4.78	5.00	5	157	9
HeatPumpModel_v31	Endogenous	Total U Value by Cohort (House * kBTU / (sf * F * Year))	168	1	0	0.0	20	3	4.45	5.00	5	146	20
HeatPumpModel_v31	Endogenous	Total U Value by Heating and Cooling System (House * kBTU / (sf * F * Year))	169	1	0	0.0	20	3	4.45	5.00	5	146	20
HeatPumpModel_v31	Endogenous	Total U Value (House * kBTU / (Year * F * sf) )	170	6	0	0.0	28	2	3.89	4.00	5	138	28
HeatPumpModel_v31	Endogenous	U Value by Grouping (kBTU / (sf * F * Year))	171	2	0	0.0	22	3	3.95	4.00	5	144	22
HeatPumpModel_v31	Endogenous	U Value Increase from Source Switching (kBTUHouse/(YearYearsfF))	172	1	0	0.0	12	3	4.75	5.00	5	154	12
HeatPumpModel_v31	Endogenous	U Value Loss from Demolition (House * kBTU / (Year * F * sf) / Year)	173	2	0	0.0	14	2	4.07	4.00	5	152	14
.housingagingchain v18	Endogenous	U Value of Housing Starts (kBTU / (Year * F * sf))	174	3	0	0.0	26	2	3.88	4.00	5	140	26
HeatPumpModel_v31	Endogenous	U Value of Retrofitting Homes (kBTU / (sf * Year * F))	175	1	0	0.0	14	4	4.36	4.00	5	152	14
HeatPumpModel_v31	Endogenous	U Value Retrofitted Away (House * kBTU / (Year * F * sf))	176	1	0	0.0	24	2	4.21	4.00	5	142	24
HeatPumpModel_v31	Endogenous	U Value Shift from Source Switching (House * kBTU / (Year * F * sf) / Year)	177	2	0	0.0	16	2	4.06	4.00	5	150	16
.housingagingchain v8	Endogenous	Unsubsidized Retrofit Cost (Dollar / House)	178	2	0	0.0	19	2	4.26	5.00	5	147	19

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Macros (0 Variables)

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Macro Definition

Expanded Macro Definition

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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	+

Quick Links:

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	-

Quick Links:

Function-based Polarity Causal Links (67 Variables)

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