France PV waste_V2.8_sensi5984750b-9b02-41f1-b11f-316f01a2de58isee systems, inc.Stella Architect19922070
16
Export1dmnlunitlessfractiontonyryearPV modules that entered EoL either by aging out of their useful life or through repowering, that are not yet fed into a disposal system. The stock drains when the modules are assigned different EoL pathways: Export or official collection.
Unit: ton.0PV_entering_EoLexportPV_collectiontonEoL modules arrayed by module that are exported each year to outside of France (EU and non-EU). It is assumed that all panels that are not collected are exported.
The unit is ton per year. EoL_PV[Techno]*(1-collection_success_rate)ton/yearPV modules that follow the official collection path, arrayed by module type, depending on the panels that reached end of life and the collection success rate.
Outflow of EoL PV and inflow to PV available for recycling.
UnitEoL_PV[Techno]*collection_success_rateton/yearExponential curve fit of projection of PV panel weight-to-power ratio (t/MW) by IRENA: Weckend et al. 2016 p.27.
The curve represents the decrease in material needed per megawatt of potential production by PV.
Unit: Tons per MegawattNANton/MWSum of all exported panels arrayed by module type.
Unit: ton.
0exportton${Export}
Annual installation in MW based on historical data until and including 2022, afterwards based on goals.
Unit: Megawatt per year. PV_goal_gap/installation_timeMw/yearOld goals set in 2008
https://www.pv-magazine.com/2023/08/08/france-aims-for-48-1-gw-of-solar-by-2030-140-gw-by-2050/ NANMWhttps://www.ecologie.gouv.fr/sites/default/files/documents/23242_Strategie-energie-climat_def2_0.pdf p.19NANMWGap between currently installed PV capacity and the goal for the year.
Unit: Megawatt.MAX(0, PV_installation_scenario-perceived_total_MW)MW${Switch}
0dmnl1yearAnnual installation of PV in MW arrayed by module type (technology) based on the market share.
Unit: Megawatt per year. Array by Technology.annual_PV_installation_in_MW*n_type_shareannual_PV_installation_in_MW*p_type_shareannual_PV_installation_in_MW*Thin_Film_shareannual_PV_installation_in_MW*Tandem_shareMw/yearImports market share of thin-film modules (e.g. CIGS, CdTe) from Excel-File. See supplementary material for sources. Until 2023 historical data is used, afterwards a stable share of 2.5% is assumed. NANdmnlImports market share of N-type modules within the market of c-Si-modules. See supplementary material for sources. NANdmnlShare of P-type c-Si-Silicon modules in the PV market, calculated by subtracting the share of thin film modules and the share of N-type modules.
P-Type modules include modules with mono or polycrystalline silicon that is doped with boron or gallium. It used to be the dominant technology in the past, but is fading out. (1-Thin_Film_share)*(1-N_type_share_of_c_Si_modules)*(1-Tandem_share)dmnlShare of N-type c-Si-Silicon modules in the PV market, calculated by subtracting the share of thin film modules and multiplying the left over share (the share of c-Si-modules) with the share of N-Type modules within the c-Si-market.
N-Type modules include modules with mono or polycrystalline silicon that are doped with phosphorus. Used to be the minority but is now the standard technology. (1-Thin_Film_share)*N_type_share_of_c_Si_modules*(1-Tandem_share)dmnlControl variable, always needs to be one. Sums together the shares of different modules types, check data imput for module types shares if not one. p_type_share+n_type_share+Thin_Film_share+Tandem_sharedmnlShare of aluminum included in an average PV module of a module type (Technology). The value is imported via an external .csv file and changes over time due to technological progress;, see supplementary material for a more detailed explanation and sources.
Unit: dimensionless. Array by: Technology. NANNANNANNANdmnlShare of glass included in an average PV module of a module type depending on the technology used. The value is imported via an external .csv file and changes over time due to technological progress; see supplementary material for a more detailed explanation and sources.
Unit: dimensionless. Array by: Technology. NANNANNANNANdmnlShare of silicon included in an average PV module of a module type. The value is imported via an external .csv file and changes over time due to technological progress; see supplementary material for a more detailed explanation and sources.
Unit: dimensionless. Array by: Technology. 0.050.0500dmnlShare of other material is calculated by subtracting the share of known materials for each module type. Other materials only occur in small amounts and include nickel, lead, and other metals, but also polymers (IRENA: Weckend et al., 2016).
Additional use: Control variable. Other materials should never go negative; otherwise, the external .csv file has an error.
Unit: dimensionless. Array by: Technology. 1-aluminum-glass-copper-silicon-silverdmnlAnnual PV installation in tons arrayed by module and materials calculated by multiplying the annual PV installation in tons, that is arrayed by module with the share of materials also arrayed by module type. The volume of each panel type is therefore further differentiated in different array dimensions that represent the materials the module contains.
It is also the input for inflow to the conveyor belt "PV material in use", it represents the volume of material that is installed each year.
Unit: Tons per Year. annual_PV_installation_in_tons[N]*glass[N]annual_PV_installation_in_tons[N]*aluminum[N]annual_PV_installation_in_tons[N]*silicon[N]annual_PV_installation_in_tons[N]*copper[N]annual_PV_installation_in_tons[N]*silver[N]annual_PV_installation_in_tons[N]*other_materials[N]annual_PV_installation_in_tons[P]*glass[P]annual_PV_installation_in_tons[P]*aluminum[P]annual_PV_installation_in_tons[P]*silicon[P]annual_PV_installation_in_tons[P]*copper[P]annual_PV_installation_in_tons[P]*silver[P]annual_PV_installation_in_tons[P]*other_materials[P]annual_PV_installation_in_tons[Thin]*glass[Thin]annual_PV_installation_in_tons[Thin]*aluminum[Thin]annual_PV_installation_in_tons[Thin]*silicon[Thin]annual_PV_installation_in_tons[Thin]*copper[Thin]annual_PV_installation_in_tons[Thin]*silver[Thin]other_materials[Thin]*annual_PV_installation_in_tons[Thin]annual_PV_installation_in_tons[New]*glass[New]annual_PV_installation_in_tons[New]*aluminum[New]annual_PV_installation_in_tons[New]*silicon[New]copper[New]*annual_PV_installation_in_tons[New]annual_PV_installation_in_tons[New]*silver[New]annual_PV_installation_in_tons[New]*other_materials[New]ton/yearEquivalent to EoL PVs but with additional dimensions for material, as part of the material co-flow structure. Inflows: PV mat enetring EoL and repowering 2. Outflows: material export and material collection.
Unit: ton 0PV_mat_entering_EoLmaterial_exportmaterial_collectiontonEoL modules arrayed by module and material that are exported each year to outside of France (EU and non-EU). It is assumed that all panels that are not collected are exported.
The unit is ton per year. EoL_PV_material*(1-collection_success_rate)ton/yearPV modules that follow the official collection path, arrayed by module type and material, depending on the panels that reached end of life and the collection success rate. Is part of the material co-flow structure and equivalent to PV collection.
Outflow of EoL PV and inflow to PV available for recycling.
UnitEoL_PV_material*collection_success_rateton/yearSum of all exported panels arrayed by module type and material.
Unit: ton. 0material_exporttonShare of a potential new PV technology, included in the model for scenario building in future iterations of the model. Share is zero for this iteration of the model building process. 0.01dmnlShare of copper in an average module type, it is assumed to be approximately stable, since it is mostly present in the junction box.
Unit: dimensionless. Array by: Technology. 0.010.010.010dmnl${Export}
Outflow of PV in use 3 and inflow to EoL PV, represents entering the End of Life.
Unit: Tons per year. SUM(total_annual_waste_stream[Techno,*])ton/year${Export}
Outflow of PV material in use 3 and inflow to EoL PV material, , represents entering of EoL of modules and the material they contain. Is part of the material co-flow structure.
Unit: Tons per year. total_annual_waste_streamTons/YearsShare of silver included in an average PV module of a module type. The value is imported via an external .csv file and changes over time due to technological progress; see supplementary material for a more detailed explanation and sources.
Unit: dimensionless. Array by: Technology. NANNANNANNANdmnlSOREN_waste_stream_projectionton/YEAR0accounting_SORENton${Reference}
Imports the cumulative PV waste volume according to the early loss scenario of IRENA (IRENA: Weckednet al. 2016).
Unit: tonNANton${Reference}
Imports the cumulative PV waste volume according to the regular loss scenario of IRENA (IRENA: Weckednet al. 2016).
Unit: tonNANton${Reference}
The variable imports the annual collection of used PV in tons from Excel. The collection is conducted by the French producer Responsibility organization SOREN and includes all collected EoL PVs,including from oversea departements (SOREN 2023). The variable is used as reference mode.
Unit: Ton per year
NANton/year${Reference}
Imports the annual waste stream projection by Soren, includes all EoL PVs in France (Sorenewable presentation 2023). The variable is used as reference mode.
Unit: Ton per yearNANton/yearPV_mat_entering_EoLton/year0total_PV_entering_EoLtonShare of EoL modules that are collected via official collection points per year. Collection efforts started in 2015. Collection success is assumed to have logarithmic growth until they reach 85% in 2035. The reported collection success from 2015 to 2022 is fluctuating, they report a goal of 85% collection rate. In the model, the assumption is that they will need until 2035 to build up the infrastructure and awareness to reach this goal. Since no evidence is found so far, that module types are handled differently in the collection process, the same collection rate is assumed for all module types.
Unit: Dimensionless per year.TIME0,0.2307,0.2601,0.2882,0.3152,0.3411,0.3659,0.3897,0.4125,0.4343,0.4553,0.4753,0.4946,0.513,0.5307,0.5476,0.5638,0.5794,0.5943,0.6086,0.6223,0.6354,0.648,0.6601,0.6717,0.6827,0.6934,0.7036,0.7133,0.7227,0.7316,0.7402,0.7485,0.7564,0.7639,0.7712,0.7781,0.7848,0.7912,0.7973,0.8032,0.8088,0.8142,0.8194,0.8243,0.8291,0.8336,0.838,0.8422,0.8462,0.85dmnl/yearPERCENT(
SUM(total_PV_entering_EoL [*,glass])//SUM(total_PV_entering_EoL)
)%PERCENT(
SUM(total_PV_entering_EoL[*,alu])//SUM(total_PV_entering_EoL)
)%PERCENT(
SUM(total_PV_entering_EoL [*,silicon])//SUM(total_PV_entering_EoL)
)%PERCENT(
SUM(total_PV_entering_EoL[*,cup])//SUM(total_PV_entering_EoL)
)%PERCENT(
SUM(total_PV_entering_EoL [*,ag])//SUM(total_PV_entering_EoL)
)%PERCENT(
SUM(total_PV_entering_EoL [*,others])//SUM(total_PV_entering_EoL)
)%Control variable should be 0 if no PV modules have entered EoL yet, or 100 if they have. If not, this suggest a mistake in modeling the material array. aluminum_share + copper_share + glass_share + other_material_share + silicon_share + silver_share%PERCENT(
SUM(total_PV_entering_EoL[N,*])//SUM(total_PV_entering_EoL)
)%PERCENT(
SUM(total_PV_entering_EoL[P,*])//SUM(total_PV_entering_EoL)
)%PERCENT(
SUM(total_PV_entering_EoL[Thin,*])//SUM(total_PV_entering_EoL)
)%Control variable should be 0 if no PV modules have entered EoL yet, or 100 if they have. If not, this suggest a mistake in modeling the module array.N_Type_share_in_EoL + P_Type_share_in_EoL + Thin_film_share_in_EoL%Control variable shows difference in volume of module and material co-flow at the entering EoL stage, should be 0. SUM(PV_mat_entering_EoL)-SUM(PV_entering_EoL)ton/yearControl variable summary should be 1, otherwise at least 1 control variable shows a value suggesting a fault in material flow consistency. IF
(control_variable_1 = 0 AND
module_type_control_variable = 1)
AND
((TIME > 2005 AND
control_variable_2 =100 AND
control_variable_3 =100)
OR
TIME <= 2005)
THEN
1
ELSE 0dmnlannual_PV_installation_in_MWMw/year0accounting_mw_installedperceived_mw_wear_outMwDELAY3(total_MW_outflow, Mw_wear_out_account_delay)Mw/year3yearTotal_MW_in_use-perceived_total_MWMwThis is the instantaneous hazard function of the Weibull distribution; the form depends on the "PV lifetime" and the "shape factor Weibull" and changes with PV age, which is modeled by using the array dimension as input to the function. If the shape factor is above 1 the failure rate increases over time.
Unit: dimensionless. Array by: PV age. shape_factor_Weibull*(PV_age/PV_lifetime_1[Techno])^shape_factor_Weibull/PV_agedmnlAverage PV lifetime is an input to "weibull instantaneous hazard". PV lifetime is mostly given as between 25 and 35.
"lifetime_P_&_N_1""lifetime_P_&_N_1"lifetime_thinlifetime_tandem_1dmnlShape factor Weibull, input for "weibull instantaneous hazard". If the shape factor is = 1, the failure rate is constant across the ages., if it is above 1, the failure rate will increase with age.
In literature, the shape factor for the Weibull distribution for PV is mostly between 2.4928 and 14.41. Mostly 2.4928 and 5.3759 are used, representing the early and regular loss scenario in (IRENA: Weckend et al., 2016).
Unit: dimensionless. 2.9
{IRENA: Early loss scenario: 2.4928
Regular loss scenario: 5.3759}dmnlAnnual PV installation arrayed by technology, converted from MW/year to tonnes by multiplying "annual PV installation by module type" with the "panel to power" ratio.
Unit: tons per year. Array by technology. annual_PV_installation_by_module_type*panel_to_power_ratioTons/YearsParallel structure to "PV material in use" tracking the PV power in installation. 0Inflow_3Outflow_3power_wear_outadditional_power_failure1Mw0Mw/yearIF PV_age <= 49 THEN weibull_instantaneous_hazard_1[N,PV_age] ELSE 1MW/yearIF PV_age = 1 THEN
"1st_cohort_power"
ELSE Outflow_3(PV_age-1)Mw/yearSUM(PV_power_in_use_1[*]) + SUM(PV_power_in_use_2[*]) + SUM(PV_power_in_use_3[*])MwOutflow of PV material in use, input for PV mat conveyor flow, as pat of the PV aging process.
Unit: tons/year. Array by: Techno, Materials, PV_age0Tons/YearsLeakage from conveyor "PV material in use" to "PV mat in EoL" contains PV that enters EoL due to wear out. The wear-out is calculated using a Weibull function and is increasing with PV age.
Failure rate per year does not need to be adapted to DT due to the use of a conveyor belt with one-year residence time.
At dimension 50 of the array, the leakage is defined as 1, so that all remaining PV are drained from the conveyor belt. 50 is therefore the defined maximum age a PV panel can reach.
Unit: ton per year. Array by: Techno, Materials, PV_age.IF PV_age <= 49 THEN weibull_instantaneous_hazard_1[Techno,PV_age] ELSE 1Tons/YearsIF PV_age = 1 THEN cohort_1_installation[Techno,Materials]
ELSE
Outflow_PV_mat[Techno,Materials,PV_age-1]Tons/YearsThis conveyor belt with one-year residence time arrayed by PV_age contains the PV modules currently in use. Orginally, the PV-modules enter the conveyor belt at the dimension PV_age 1, and when they leave the conveyor belt via the outflow, they enter at the next dimension of the array via the inflow. This allows the modelling of PVs' aging without cohort blending (Eberlein & Thompson, 2013).
The conveyor belt has two leakages: "infant and constant failure" and "wear out", containing different types of failure modes that affect PVs, which change depending on the PV age. The combination of an age-dependent wear-out distribution and infant and constant failure has been suggested in (Peeters et al., 2017).
Due to PV age having 50 dimensions, this is the maximum age PVs can reach in the model no matter the type of leakage.
Unit: ton. Array by: Techno, Materials, PV_age0PV_mat_conveyor_inflowOutflow_PV_matwear_out_1infant_and_constant_failure_11tonStock containing all PV in EoL, arrayed by Techno(logy), Materials, and PV age; inflows are "infant and constant failure" and "wear out". PV-age shows the age at which the PVs end in EoL, cohorts do mix in this stock.
0wear_out_1infant_and_constant_failure_1ton1ton/MWPULSE(100, 2005, 0)MW/yearLeakage from conveyor "PV material in use" to "PV mat in EoL" contains PV that enters EoL due to infant failure or constant failure (random events). Higher chance of occurrence during the first 3 years and therefore PV age dimensions 1 to 3, afterward, constant (random) failures.
Failure rate per year does not need to be adapted to DT due to the use of a conveyor belt with one-year residence time.
Unit: ton per year. Array by: Techno, Materials, PV_ageadditional_failure_rate[PV_age]Tons/YearsThe additional failure rate covers the yearly rate of PVs reaching EoL due to reasons other than wear out and repowering. This includes early failure and constant or random failures. Before and during the age of 3, infant failure and afterward, constant failure is the driving the additional failure rate. Therefore for the dimensions 1 to 3 of the array PV age, the variable "infant failure" is the input and afterwards "constant failure". IF PV_age <= 3
THEN infant_failure
ELSE constant_failuredmnlThe infant failure rate is the yearly failure rate during the first 3 years after installation. During that time, manufacturing errors or damages that occurred during installation led to breakage.
For simplification, we assume a stable infant failure rate during these first 3 years, despite the failure rate sometimes being modeled as differnetly during the first three years.
In In (Peeters et al., 2017) the failure rate is assumed to be between 0.003% and 0.037%
0.00037
{literature between 0.00003 and 0.00037}dmnlThe constant failure rate relates to failures/decommissioning reasons that occur at any panel age. before age 4, the constant failure rate is integrated into the infant failure.
In (Peeters et al., 2017) the constant failure rate is between 0.0026% and 0.0102%.
Unit: dimensionless.
0.000102
{literature between 0.000026 and 0.000102.}Dimensionlessadditional_failure_rateMW/year27.5dmnl22dmnl20dmnlIF TIME <=2024 THEN
HIS_PV_capacity
ELSE
IF Goal_SWITCH = 0
THEN
France_installation_goals_low
ELSE
France_installation_goals_highMWThis is the instantaneous hazard function of the Weibull distribution; the form depends on the "PV lifetime" and the "shape factor Weibull" and changes with PV age, which is modeled by using the array dimension as input to the function. If the shape factor is above 1 the failure rate increases over time.
Unit: dimensionless. Array by: PV age. shape_factor_Weibull*(PV_age/PV_lifetime_2[Techno])^shape_factor_Weibull/PV_agedmnlAverage PV lifetime is an input to "weibull instantaneous hazard". PV lifetime is mostly given as between 25 and 35.
"lifetime_P_&_N_2""lifetime_P_&_N_2"lifetime_thin_2lifetime_tandem_2dmnlOutflow of PV material in use, input for PV mat conveyor flow, as pat of the PV aging process.
Unit: tons/year. Array by: Techno, Materials, PV_age0Tons/YearsLeakage from conveyor "PV material in use" to "PV mat in EoL" contains PV that enters EoL due to wear out. The wear-out is calculated using a Weibull function and is increasing with PV age.
Failure rate per year does not need to be adapted to DT due to the use of a conveyor belt with one-year residence time.
At dimension 50 of the array, the leakage is defined as 1, so that all remaining PV are drained from the conveyor belt. 50 is therefore the defined maximum age a PV panel can reach.
Unit: ton per year. Array by: Techno, Materials, PV_age.IF PV_age <= 49 THEN weibull_instantaneous_hazard_2[Techno,PV_age] ELSE 1Tons/YearsIF PV_age = 1 THEN "2nd_cohort_installation"[Techno,Materials]
ELSE
Outflow_PV_mat_2[Techno,Materials,PV_age-1]Tons/YearsThis conveyor belt with one-year residence time arrayed by PV_age contains the PV modules currently in use. Orginally, the PV-modules enter the conveyor belt at the dimension PV_age 1, and when they leave the conveyor belt via the outflow, they enter at the next dimension of the array via the inflow. This allows the modelling of PVs' aging without cohort blending (Eberlein & Thompson, 2013).
The conveyor belt has two leakages: "infant and constant failure" and "wear out", containing different types of failure modes that affect PVs, which change depending on the PV age. The combination of an age-dependent wear-out distribution and infant and constant failure has been suggested in (Peeters et al., 2017).
Due to PV age having 50 dimensions, this is the maximum age PVs can reach in the model no matter the type of leakage.
Unit: ton. Array by: Techno, Materials, PV_age0PV_mat_conveyor_inflow_2Outflow_PV_mat_2wear_out_2infant_and_constant_failure_21tonStock containing all PV in EoL, arrayed by Techno(logy), Materials, and PV age; inflows are "infant and constant failure" and "wear out". PV-age shows the age at which the PVs end in EoL, cohorts do mix in this stock.
0wear_out_2infant_and_constant_failure_2tonLeakage from conveyor "PV material in use" to "PV mat in EoL" contains PV that enters EoL due to infant failure or constant failure (random events). Higher chance of occurrence during the first 3 years and therefore PV age dimensions 1 to 3, afterward, constant (random) failures.
Failure rate per year does not need to be adapted to DT due to the use of a conveyor belt with one-year residence time.
Unit: ton per year. Array by: Techno, Materials, PV_ageadditional_failure_rate[PV_age]Tons/Years"lifetime_P_&_N_1"+"2nd_cohort_lifetime_increase"dmnllifetime_thin+"2nd_cohort_lifetime_increase"dmnllifetime_tandem_1dmnlIF TIME < start_2nd_cohort
THEN annual_PV_material_installed
ELSE 0Tons/Years2015yearIF TIME >= start_2nd_cohort AND TIME < start_3rd_cohort
THEN
annual_PV_material_installed
ELSE 0Tons/Years2030yearSUM(infant_and_constant_failure_1[Techno,Materials,*]) + SUM(wear_out_1[Techno,Materials,*]) + SUM(infant_and_constant_failure_2[Techno,Materials,*]) + SUM(wear_out_2[Techno,Materials,*]) + SUM(infant_and_constant_failure_3[Techno,Materials,*]) + SUM(wear_out_3[Techno, Materials, *])Tons/Years3.5dmnlThis is the instantaneous hazard function of the Weibull distribution; the form depends on the "PV lifetime" and the "shape factor Weibull" and changes with PV age, which is modeled by using the array dimension as input to the function. If the shape factor is above 1 the failure rate increases over time.
Unit: dimensionless. Array by: PV age. shape_factor_Weibull*(PV_age/PV_lifetime_3[Techno])^shape_factor_Weibull/PV_agedmnlAverage PV lifetime is an input to "weibull instantaneous hazard". PV lifetime is mostly given as between 25 and 35.
"lifetime_P_&_N_3""lifetime_P_&_N_3"lifetime_thin_3lifetime_tandem_3dmnlOutflow of PV material in use, input for PV mat conveyor flow, as pat of the PV aging process.
Unit: tons/year. Array by: Techno, Materials, PV_age0Tons/YearsLeakage from conveyor "PV material in use" to "PV mat in EoL" contains PV that enters EoL due to wear out. The wear-out is calculated using a Weibull function and is increasing with PV age.
Failure rate per year does not need to be adapted to DT due to the use of a conveyor belt with one-year residence time.
At dimension 50 of the array, the leakage is defined as 1, so that all remaining PV are drained from the conveyor belt. 50 is therefore the defined maximum age a PV panel can reach.
Unit: ton per year. Array by: Techno, Materials, PV_age.IF PV_age <= 49 THEN weibull_instantaneous_hazard_3[Techno,PV_age] ELSE 1Tons/YearsIF PV_age = 1 THEN "3rd_cohort_installation"[Techno,Materials]
ELSE
Outflow_PV_mat_3[Techno,Materials,PV_age-1]Tons/YearsThis conveyor belt with one-year residence time arrayed by PV_age contains the PV modules currently in use. Orginally, the PV-modules enter the conveyor belt at the dimension PV_age 1, and when they leave the conveyor belt via the outflow, they enter at the next dimension of the array via the inflow. This allows the modelling of PVs' aging without cohort blending (Eberlein & Thompson, 2013).
The conveyor belt has two leakages: "infant and constant failure" and "wear out", containing different types of failure modes that affect PVs, which change depending on the PV age. The combination of an age-dependent wear-out distribution and infant and constant failure has been suggested in (Peeters et al., 2017).
Due to PV age having 50 dimensions, this is the maximum age PVs can reach in the model no matter the type of leakage.
Unit: ton. Array by: Techno, Materials, PV_age0PV_mat_conveyor_inflow_3Outflow_PV_mat_3wear_out_3infant_and_constant_failure_31tonStock containing all PV in EoL, arrayed by Techno(logy), Materials, and PV age; inflows are "infant and constant failure" and "wear out". PV-age shows the age at which the PVs end in EoL, cohorts do mix in this stock.
0wear_out_3infant_and_constant_failure_3tonLeakage from conveyor "PV material in use" to "PV mat in EoL" contains PV that enters EoL due to infant failure or constant failure (random events). Higher chance of occurrence during the first 3 years and therefore PV age dimensions 1 to 3, afterward, constant (random) failures.
Failure rate per year does not need to be adapted to DT due to the use of a conveyor belt with one-year residence time.
Unit: ton per year. Array by: Techno, Materials, PV_ageadditional_failure_rate[PV_age]Tons/Years"lifetime_P_&_N_2"+"3rd_cohort_lifetime_increase"dmnllifetime_thin_2+"3rd_cohort_lifetime_increase"dmnllifetime_tandem_2dmnlIF TIME >= start_3rd_cohort
THEN annual_PV_material_installed
ELSE 0Tons/Years5dmnlParallel structure to "PV material in use" tracking the PV power in installation. 0Inflow_4Outflow_4power_wear_out_2additional_power_failure_21Mw0Mw/yearIF PV_age <= 49 THEN weibull_instantaneous_hazard_2[N,PV_age] ELSE 1MW/yearIF PV_age = 1 THEN
"2nd_cohort_power"
ELSE Outflow_4(PV_age-1)Mw/yearadditional_failure_rateMW/yearParallel structure to "PV material in use" tracking the PV power in installation. 0Inflow_5Outflow_5power_wear_out_3additional_power_failure_31Mw0Mw/yearIF PV_age <= 49 THEN weibull_instantaneous_hazard_3[N,PV_age] ELSE 1MW/yearIF PV_age = 1 THEN
"3rd_gen_power"
ELSE Outflow_5(PV_age-1)Mw/yearadditional_failure_rateMW/yearIF TIME < start_2nd_cohort
THEN annual_PV_installation_in_MW
ELSE 0MW/yearIF TIME >= start_2nd_cohort AND TIME < start_3rd_cohort
THEN
annual_PV_installation_in_MW
ELSE 0MW/yearIF TIME >= start_3rd_cohort
THEN annual_PV_installation_in_MW
ELSE 0MW/yearSUM(additional_power_failure[*]) + SUM(power_wear_out[*]) + SUM(additional_power_failure_2[*]) + SUM(power_wear_out_2[*]) + SUM(additional_power_failure_3[*]) + SUM(power_wear_out_3[*])MW/yearSUM(PV_mat_in_EoL)+SUM(PV_mat_in_EoL_1)+SUM(PV_mat_in_EoL_2)tonNANMWSUM(total_annual_waste_stream)Tons/YearsSUM(infant_and_constant_failure_1[*,*,*]) + SUM(infant_and_constant_failure_2[*,*,*]) + SUM(infant_and_constant_failure_3[*, *, *])Tons/YearsPERCENT(infant_and_constnat_failure/summary_annual_waste_stream)dmnlSUM(infant_and_constant_failure_1[*,*,PV_age]) + SUM(wear_out_1[*,*,PV_age]) + SUM(infant_and_constant_failure_2[*,*,PV_age]) + SUM(wear_out_2[*,*,PV_age]) + SUM(infant_and_constant_failure_3[*,*,PV_age]) + SUM(wear_out_3[*, *, PV_age])Tons/YearsSUM(waste_by_age[1:15])Tons/YearsPERCENT(PV_waste_under_15/summary_annual_waste_stream)dmnlPV_power_in_use_1//SUM(PV_material_in_use_1[*,*,PV_age])MW/TonsSUM(PV_material_in_use_1[*,*,*]) + SUM(PV_material_in_use_2[*,*,*]) + SUM(PV_material_in_use_3[*, *, *])tonTotal_MW_in_use//total_tons_in_useMW/TonsEfficency_1/system_efficiencydmnlPV_power_in_use_2//SUM(PV_material_in_use_2[*,*,PV_age])MW/Tonsefficiency_2//system_efficiencydmnlPV_power_in_use_3//SUM(PV_material_in_use_3[*,*,PV_age])MW/TonsEfficiency_3/system_efficiencydmnlNormalized_efficiency_1[1]0.2,0.1964,0.1929,0.1893,0.1857,0.1821,0.1786,0.175,0.1714,0.1679,0.1643,0.1607,0.1571,0.1536,0.15,0.1464,0.1429,0.1393,0.1357,0.1321,0.1286,0.125,0.1214,0.1179,0.1143,0.1107,0.1071,0.1036,0.1,0.09643,0.09286,0.08929,0.08571,0.08214,0.07857,0.075,0.07143,0.06786,0.06429,0.06071,0.05714,0.05357,0.05,0.04643,0.04286,0.03929,0.03571,0.03214,0.02857,0.025,0.02143,0.01786,0.01429,0.01071,0.007143,0.003571,0dmnl/yearIF Normalized_efficiency_1 = 0
THEN
0
ELSE
LOOKUP(efficiency_to_repowering, Normalized_efficiency_1)dmnl/yearIF Normalized_efficiency_3 = 0
THEN
0
ELSE
LOOKUP(efficiency_to_repowering, Normalized_efficiency_3)dmnl/yearIF Normalized_efficiency_2 = 0
THEN
0
ELSE
LOOKUP(efficiency_to_repowering, Normalized_efficiency_2)dmnl/yearMAX(
MAX(
MAX(likelihood_to_repower_1),
MAX(likelihood_to_repower_2)),
MAX(likelihood_to_repower_3))dmnl/yearSUM(infant_and_constant_failure_1)+SUM(wear_out_1)Tons/YearsSUM(infant_and_constant_failure_2+wear_out_2)Tons/YearsSUM(infant_and_constant_failure_3+wear_out_3)Tons/YearsEoL_PVexportEoL_PVPV_collectionSWITCH
0 = lower goal scenario
1 = upper goal scenarion_type_shareannual_PV_installation_by_module_typep_type_shareannual_PV_installation_by_module_typep_type_sharemodule_type_control_variablen_type_sharemodule_type_control_variablealuminumother_materialsglassother_materialsother_materialsannual_PV_material_installedaluminumannual_PV_material_installedglassannual_PV_material_installedEoL_PV_materialmaterial_exportEoL_PV_materialmaterial_collectionN_type_share_of_c_Si_modulesn_type_shareN_type_share_of_c_Si_modulesp_type_shareThin_Film_sharep_type_shareThin_Film_sharen_type_shareThin_Film_shareannual_PV_installation_by_module_typeTandem_shareannual_PV_installation_by_module_typeTandem_sharemodule_type_control_variableThin_Film_sharemodule_type_control_variablecopperother_materialssiliconannual_PV_material_installedsiliconother_materialssilverannual_PV_material_installedsilverother_materialsSOREN_waste_stream_projectionaccounting_SORENtotal_PV_entering_EoLcontrol_variable_1control_variable_1total_PV_entering_EoLglass_sharetotal_PV_entering_EoLaluminum_sharetotal_PV_entering_EoLsilicon_sharetotal_PV_entering_EoLcopper_sharetotal_PV_entering_EoLsilver_sharetotal_PV_entering_EoLother_material_sharetotal_PV_entering_EoLN_Type_share_in_EoLtotal_PV_entering_EoLP_Type_share_in_EoLtotal_PV_entering_EoLThin_film_share_in_EoLcontrol_variable_1control_variable_summarycontrol_variable_summarycontrol_variable_summarycontrol_variable_summarycollection_success_rateexportcollection_success_ratePV_collectionmaterial_exportmaterial_collectionMw_wear_out_account_delayperceived_mw_wear_outaccounting_and_real_time_power_diffierenceperceived_total_MWPV_goal_gapPV_goal_gapannual_PV_installation_in_MWinstallation_timeannual_PV_installation_in_MWannual_PV_installation_in_MWaccounting_mw_installedannual_PV_installation_by_module_typeannual_PV_installation_in_tonsOutflow_3Inflow_3power_wear_outTotal_MW_in_useaccounting_and_real_time_power_diffierenceOutflow_PV_matPV_mat_conveyor_inflowannual_PV_installation_by_module_typepanel_to_power_ratioannual_PV_installation_in_tonsannual_PV_installation_in_tonsannual_PV_material_installedweibull_instantaneous_hazard_1wear_out_1constant_failureadditional_failure_rateinfant_failureadditional_failure_rateadditional_failure_rateinfant_and_constant_failure_1Tandem_sharep_type_shareTandem_sharen_type_shareadditional_power_failurePV_lifetime_1weibull_instantaneous_hazard_1shape_factor_Weibullweibull_instantaneous_hazard_1"lifetime_P_&_N_1"PV_lifetime_1lifetime_thinPV_lifetime_1lifetime_tandem_1PV_lifetime_1Goal_SWITCHPV_installation_scenarioFrance_installation_goals_lowPV_installation_scenarioFrance_installation_goals_highPV_installation_scenarioPV_installation_scenarioPV_goal_gapOutflow_PV_mat_2PV_mat_conveyor_inflow_2weibull_instantaneous_hazard_2wear_out_2PV_lifetime_2weibull_instantaneous_hazard_2"lifetime_P_&_N_2"PV_lifetime_2lifetime_thin_2PV_lifetime_2lifetime_tandem_2PV_lifetime_2copperannual_PV_material_installedannual_PV_material_installedcohort_1_installationstart_2nd_cohortcohort_1_installationcohort_1_installationPV_mat_conveyor_inflowannual_PV_material_installed"2nd_cohort_installation"start_2nd_cohort"2nd_cohort_installation"start_3rd_cohort"2nd_cohort_installation""2nd_cohort_installation"PV_mat_conveyor_inflow_2total_annual_waste_streamPV_entering_EoLtotal_annual_waste_streamPV_mat_entering_EoL"lifetime_P_&_N_1""lifetime_P_&_N_2"lifetime_thinlifetime_thin_2lifetime_tandem_1lifetime_tandem_2"2nd_cohort_lifetime_increase""lifetime_P_&_N_2""2nd_cohort_lifetime_increase"lifetime_thin_2Outflow_PV_mat_3PV_mat_conveyor_inflow_3weibull_instantaneous_hazard_3wear_out_3PV_lifetime_3weibull_instantaneous_hazard_3"lifetime_P_&_N_3"PV_lifetime_3lifetime_thin_3PV_lifetime_3lifetime_tandem_3PV_lifetime_3"lifetime_P_&_N_2""lifetime_P_&_N_3"lifetime_thin_2lifetime_thin_3lifetime_tandem_2lifetime_tandem_3"3rd_cohort_lifetime_increase""lifetime_P_&_N_3""3rd_cohort_lifetime_increase"lifetime_thin_3annual_PV_material_installed"3rd_cohort_installation"start_3rd_cohort"3rd_cohort_installation""3rd_cohort_installation"PV_mat_conveyor_inflow_3Outflow_4Inflow_4additional_power_failure_2Outflow_5Inflow_5additional_power_failure_3"1st_cohort_power"annual_PV_installation_in_MW"1st_cohort_power"annual_PV_installation_in_MW"2nd_cohort_power""2nd_cohort_power"annual_PV_installation_in_MW"3rd_gen_power""2nd_cohort_power""2nd_cohort_power"Inflow_4"1st_cohort_power"Inflow_3total_MW_outflowperceived_mw_wear_out"3rd_gen_power""3rd_gen_power"Inflow_5Cumulative_EoLCumulative_EoLCumulative_EoLHIS_PV_capacityPV_installation_scenariototal_annual_waste_streamsummary_annual_waste_streampower_wear_out_2power_wear_out_3infant_and_constnat_failurePercentage_infant_and_constant_failurePercentage_infant_and_constant_failurewaste_by_agePV_waste_under_15PV_waste_under_15percentage_of_waste_under_15percentage_of_waste_under_15Efficency_1Efficency_1system_efficiencytotal_tons_in_usesystem_efficiencyEfficency_1Normalized_efficiency_1system_efficiencyNormalized_efficiency_1efficiency_2efficiency_2efficiency_2Normalized_efficiency_2system_efficiencyNormalized_efficiency_2Efficiency_3Efficiency_3Efficiency_3Normalized_efficiency_3system_efficiencyNormalized_efficiency_3Normalized_efficiency_1efficiency_to_repoweringefficiency_to_repoweringlikelihood_to_repower_1Normalized_efficiency_1likelihood_to_repower_1efficiency_to_repoweringlikelihood_to_repower_3Normalized_efficiency_3likelihood_to_repower_3efficiency_to_repoweringlikelihood_to_repower_2Normalized_efficiency_2likelihood_to_repower_2infant_and_constant_failure_2infant_and_constant_failure_3weibull_instantaneous_hazard_2weibull_instantaneous_hazard_3likelihood_to_repower_2maximum_likelihood_to_repwerlikelihood_to_repower_1maximum_likelihood_to_repwerlikelihood_to_repower_3maximum_likelihood_to_repwerinfant_and_constant_failure_1PV_waste_outflow_1wear_out_1PV_waste_outflow_1infant_and_constant_failure_2PV_waste_outflow_2wear_out_2PV_waste_outflow_2infant_and_constant_failure_3PV_waste_outflow_3wear_out_3PV_waste_outflow_3