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c_supplymodel.gms
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*Setting the default slash
$setglobal ds \
*Change the default slash if in UNIX
$ifthen.unix %system.filesys% == UNIX
$setglobal ds /
$endif.unix
*========================================
* -- Supply Side Variable Declaration --
*========================================
positive variables
* load variable - set equal to load_exog to compute holistic marginal price
LOAD(r,allh,t) "--MW-- busbar load for each balancing region"
FLEX(flex_type,r,allh,t) "--MW-- flexible load shifted to each timeslice"
* PEAK_FLEX(r,ccseason,t) "--MW-- peak busbar load adjustment based on load flexibility"
DROPPED(r,allh,t) "--MW-- dropped load (only allowed before Sw_StartMarkets)"
EXCESS(r,allh,t) "--MW-- excess load (only allowed before Sw_StartMarkets)"
* capacity and investment variables
CAP_SDBIN(i,v,r,ccseason,sdbin,t) "--MW-- generation capacity by storage duration bin for relevant technologies"
CAP(i,v,r,t) "--MW-- total generation capacity in MWac (MWdc for PV); PV capacity of hybrid PV+battery; max native, flexible EV load for EVMC"
CAP_ABOVE_LIM(tg,r,t) "--MW-- amount of capacity that is deployed above the interconnection queue limits"
CAP_RSC(i,v,r,rscbin,t) "--MW-- total generation capacity in MWac (MWdc for PV) for wind-ons and upv"
GROWTH_BIN(gbin,i,st,t) "--MW-- total new (from INV) generation capacity in each growth bin by state and technology group"
INV(i,v,r,t) "--MW-- generation capacity add in year t"
EXTRA_PRESCRIP(pcat,r,t) "--MW-- builds beyond those prescribed once allowed in firstyear(pcat) - exceptions for gas-ct, wind-ons, and wind-ofs"
INV_CAP_UP(i,v,r,rscbin,t) "--MW-- upsized generation capacity addition in year t"
INV_ENER_UP(i,v,r,rscbin,t) "--MW-- upsized energy addition in year t using capacity factor to convert to capacity units"
INV_REFURB(i,v,r,t) "--MW-- investment in refurbishments of technologies that use a resource supply curve"
INV_RSC(i,v,r,rscbin,t) "--MW-- investment in technologies that use a resource supply curve"
UPGRADES(i,v,r,t) "--MW-- investments in upgraded capacity from ii to i"
UPGRADES_RETIRE(i,v,r,t) "--MW-- upgrades that have been retired - used as a free slack variable in eq_cap_upgrade"
* The units for all of the operational variables are average MW or MWh/time-slice hours
* generation and storage variables
GEN(i,v,r,allh,t) "--MW-- electricity generation (post-curtailment) in hour h"
GEN_PLANT(i,v,r,allh,t) "--MW-- average plant generation from hybrid generation/storage technologies in hour h"
GEN_STORAGE(i,v,r,allh,t) "--MW-- average generation from hybrid storage technologies in hour h"
STORAGE_IN_PLANT(i,v,r,allh,t) "--MW-- hybrid plant storage charging in hour h that is charging from a coupled technology"
STORAGE_IN_GRID(i,v,r,allh,t) "--MW-- hybrid plant storage charging in hour h that is charging from the grid"
AVAIL_SITE(x,allh,t) "--MW-- available generation from all resources at reV site x"
CURT(r,allh,t) "--MW-- curtailment from vre generators in hour h"
MINGEN(r,allszn,t) "--MW-- minimum generation level in each season"
STORAGE_IN(i,v,r,allh,t) "--MW-- storage charging in hour h that is charging from a given source technology; not used for CSP-TES"
STORAGE_LEVEL(i,v,r,allh,t) "--MWh-- storage level in hour h"
STORAGE_INTERDAY_LEVEL(i,v,r,allszn,t) "--MWh-- storage level at hour 0 of the partition"
DR_SHIFT(i,v,r,allh,allhh,t) "--MWh-- annual demand response load shifted to timeslice h from timeslice hh"
DR_SHED(i,v,r,allh,t) "--MWh-- annual demand response load shed from timeslice h"
RAMPUP(i,r,allh,allhh,t) "--MW-- upward change in generation from h to hh"
* flexible CCS variables
CCSFLEX_POW(i,v,r,allh,t) "--avg MW-- average power consumed for CCS system"
CCSFLEX_POWREQ(i,v,r,allh,t) "--avg MW-- average power requirement for CCS system"
CCSFLEX_STO_STORAGE_LEVEL(i,v,r,allh,t) "--varies-- level of process storage (e.g., chemical solvent) in the CCS system"
CCSFLEX_STO_STORAGE_CAP(i,v,r,t) "--varies-- capacity of process storage (e.g., chemical solvent) in the CCS system"
* trade variables
FLOW(r,rr,allh,t,trtype) "--MW-- electricity flow on transmission lines in hour h"
OPRES_FLOW(ortype,r,rr,allh,t) "--MW-- interregional trade of operating reserves by operating reserve type"
PRMTRADE(r,rr,trtype,ccseason,t) "--MW-- planning reserve margin capacity traded from r to rr"
* operating reserve variables
OPRES(ortype,i,v,r,allh,t) "--MW-- operating reserves by type"
* variable fuel amounts
GASUSED(cendiv,gb,allh,t) "--MMBtu/hour-- total gas used by gas bin",
VGASBINQ_NATIONAL(fuelbin,t) "--MMBtu-- National quantity of gas by bin"
VGASBINQ_REGIONAL(fuelbin,cendiv,t) "--MMBtu-- Regional (census divisions) quantity of gas by bin"
BIOUSED(bioclass,r,t) "--MMBtu-- total biomass used by biomass class"
* RECS variables
RECS(RPSCat,i,st,ast,t) "--MWh-- renewable energy credits from state st to state ast",
ACP_PURCHASES(RPSCat,st,t) "--MWh-- purchases of ACP credits to meet the RPS constraints",
* transmission variables
CAPTRAN_ENERGY(r,rr,trtype,t) "--MW-- capacity of transmission for energy trading"
CAPTRAN_PRM(r,rr,trtype,t) "--MW-- capacity of transmission for PRM trading"
CAPTRAN_GRP(transgrp,transgrpp,t) "--MW-- capacity of groups of transmission interfaces"
INVTRAN(r,rr,trtype,t) "--MW-- investment in transmission capacity"
CAP_CONVERTER(r,t) "--MW-- VSC AC/DC converter capacity"
INV_CONVERTER(r,t) "--MW-- investment in AC/DC converter capacity"
CONVERSION(r,allh,intype,outtype,t) "--MW-- conversion of AC->DC or DC->AC"
CONVERSION_PRM(r,ccseason,intype,outtype,t) "--MW-- planning reserve margin capacity sent through VSC AC/DC converters"
CAP_SPUR(x,t) "--MW-- capacity of spur lines"
INV_SPUR(x,t) "--MW-- investment in spur line capacity"
INV_POI(r,t) "--MW-- investment in new POI capacity (for network reinforcement costs)"
* production-, CO2-, and hydrogen-specific variables
PRODUCE(p,i,v,r,allh,t) "--metric tons per hour-- production of hydrogen or DAC capture"
CO2_CAPTURED(r,allh,t) "--metric tons per hour-- amount of CO2 captured from DAC and CCS technologies"
CO2_STORED(r,cs,allh,t) "--metric tons per hour-- amount of CO2 stored underground"
CO2_FLOW(r,rr,allh,t) "--metric tons per hour-- interregional flow of CO2"
CO2_TRANSPORT_INV(r,rr,t) "--metric tons per hour-- investment in interregional CO2 transport capacity"
CO2_SPURLINE_INV(r,cs,t) "--metric tons per hour-- spurline investment from r to carbon storage site (saline storage basin)"
H2_FLOW(r,rr,allh,t) "--metric tons per hour-- interregional flow of hydrogen"
H2_TRANSPORT_INV(r,rr,t) "--metric tons per hour-- investment in interregional hydrogen transmission capacity"
H2_STOR_INV(h2_stor,r,t) "--metric tons-- investment in hydrogen storage capacity"
H2_STOR_CAP(h2_stor,r,t) "--metric tons-- hydrogen storage capacity"
H2_STOR_IN(h2_stor,r,allh,t) "--metric tons per hour-- injection of H2 into storage in a given timeslice"
H2_STOR_OUT(h2_stor,r,allh,t) "--metric tons per hour-- widthdrawal of H2 from storage in a given timeslice"
H2_STOR_LEVEL(h2_stor,r,actualszn,allh,t) "--metric tons-- total storage level of H2 in a timeslice by storage type"
H2_STOR_LEVEL_SZN(h2_stor,r,actualszn,t) "--metric tons-- total storage level of H2 in a period by storage type"
CREDIT_H2PTC(i,v,r,allh,t) "--MW-- generation by resources which qualify for the hydrogen production tax credit, in hour h"
* water climate variables
WATCAP(i,v,r,t) "--million gallons/year; Mgal/yr-- total water access capacity available in terms of withdraw/consumption per year"
WAT(i,v,w,r,allh,t) "--Mgal-- quantity of water withdrawn or consumed in hour h"
WATER_CAPACITY_LIMIT_SLACK(wst,r,t) "--Mgal/yr-- insufficient water supply in region r, of water type wst, in year t "
;
Variables
* with negative emissions technologies (e.g. BECCS, DAC) - emissions
* can become negative thus not restricted to the positive domain
EMIT(e,r,t) "--metric tons-- total emissions in a region"
* inter-day storage variables
STORAGE_INTERDAY_DISPATCH(i,v,r,allh,t) "--MW-- net dispatch for storage in hour h"
STORAGE_INTERDAY_LEVEL_MAX_DAY(i,v,r,allszn,t) "--MWh-- maximum relative state of charge on a representative period compared to hour 0 of the rep period"
STORAGE_INTERDAY_LEVEL_MIN_DAY(i,v,r,allszn,t) "--MWh-- minimum relative state of charge on a representative period compared to hour 0 of the rep period"
;
*========================================
* -- Supply Side Equation Declaration --
*========================================
EQUATION
* load constraint to compute proper marginal value
eq_loadcon(r,allh,t) "--MW-- load constraint used for computing the marginal energy price"
* load flexibility constraints
eq_load_flex_day(flex_type,r,allszn,t) "--MWh-- total flexible load in each season is equal to the exogenously-specified flexible load"
eq_load_flex1(flex_type,r,allh,t) "--MWh-- exogenously-specified flexible demand (load_exog_flex) must be served by flexible load (FLEX)"
eq_load_flex2(flex_type,r,allh,t) "--MWh-- flexible load (FLEX) can't exceed exogenously-specified flexible demand (load_exog_flex)"
* eq_load_flex_peak(r,allh,ccseason,t) "--MWh-- adjust peak demand as needed based on the load flexibility (FLEX)"
* capital stock constraints
eq_cap_init_noret(i,v,r,t) "--MW-- Existing capacity that cannot be retired is equal to exogenously-specified amount"
eq_cap_init_retmo(i,v,r,t) "--MW-- Existing capacity that can be retired must be monotonically decreasing"
eq_cap_init_retub(i,v,r,t) "--MW-- Existing capacity that can be retired is less than or equal to exogenously-specified amount"
eq_cap_new_noret(i,v,r,t) "--MW-- New capacity that cannot be retired is equal to sum of all previous years investment"
eq_cap_new_retmo(i,v,r,t) "--MW-- New capacity that can be retired must be monotonically decreasing unless increased by investment"
eq_cap_new_retub(i,v,r,t) "--MW-- New capacity that can be retired is less than or equal to all previous years investment"
eq_cap_rsc(i,v,r,rscbin,t) "--MW-- Capacity accounting for techs with exogenous capacity tracked by rscbin"
eq_cap_up(i,v,r,rscbin,t) "--MW-- limit on capacity upsizing"
eq_cap_upgrade(i,v,r,t) "--MW-- All purchased upgrades are greater than or equal to the sum of upgraded capacity"
eq_ener_up(i,v,r,rscbin,t) "--MW-- limit on energy upsizing"
eq_forceprescription(pcat,r,t) "--MW-- total investment in prescribed capacity must equal amount from exogenous prescriptions"
eq_refurblim(i,r,t) "--MW-- total refurbishments cannot exceed the amount of capacity that has reached the end of its life"
* renewable supply curves
eq_rsc_inv_account(i,v,r,t) "--MW-- INV for rsc techs is the sum over all bins of INV_RSC"
eq_rsc_INVlim(r,i,rscbin,t) "--MW-- total investment from each rsc bin cannot exceed the available investment"
* capacity growth limits
eq_growthlimit_relative(i,st,t) "--MW-- relative growth limit on technologies"
eq_growthbin_limit(gbin,st,tg,t) "--MW-- capacity limit for each growth bin"
eq_growthlimit_absolute(tg,t) "--MW-- absolute growth limit on technologies"
eq_interconnection_queues(tg,r,t) "--MW-- capacity deployment limit based on interconnection queues"
* storage capacity credit supply curves
eq_cap_sdbin_balance(i,v,r,ccseason,t) "--MW-- total binned storage capacity must be equal to total storage capacity"
eq_sdbin_limit(ccreg,ccseason,sdbin,t) "--MW-- binned storage capacity cannot exceed storage duration bin size"
* operation and reliability
eq_site_cf(x,allh,t) "--MW-- generation at site x <= CF * capacity of constituent resources"
eq_spurclip(x,allh,t) "--MW-- generation at site x <= spurline capacity to x"
eq_spur_noclip(x,t) "--MW-- spurline capacity to x must equal total generation capacity at x"
eq_capacity_limit(i,v,r,allh,t) "--MW-- generation limited to available capacity"
eq_capacity_limit_hybrid(r,allh,t) "--MW-- generation from hybrid resources limited to available capacity"
eq_capacity_limit_nd(i,v,r,allh,t) "--MW-- generation limited to available capacity for non-dispatchable resources"
eq_curt_gen_balance(r,allh,t) "--MW-- net generation and curtailment must equal gross generation"
eq_dhyd_dispatch(i,v,r,allszn,t) "--MWh-- dispatchable hydro seasonal energy constraint (when not allowing seasonal enregy shifting)"
eq_min_cf(i,r,t) "--MWh-- minimum capacity factor constraint for each generator fleet, applied to (i,r)"
eq_mingen_fixed(i,v,r,allh,t) "--MW-- Generation in each timeslice must be greater than mingen_fixed * available capacity"
eq_mingen_lb(r,allh,allszn,t) "--MW-- lower bound on minimum generation level"
eq_mingen_ub(r,allh,allszn,t) "--MW-- upper bound on minimum generation level"
eq_minloading(i,v,r,allh,allhh,t) "--MW-- minimum loading across same-season hours"
eq_ramping(i,r,allh,allhh,t) "--MW-- definition of RAMPUP"
eq_reserve_margin(r,ccseason,t) "--MW-- planning reserve margin requirement"
eq_supply_demand_balance(r,allh,t) "--MW-- supply demand balance"
eq_vsc_flow(r,allh,t) "--MW-- DC power flow"
eq_transmission_limit(r,rr,allh,t,trtype) "--MW-- transmission flow limit"
* operating reserve constraints
eq_OpRes_requirement(ortype,r,allh,t) "--MW-- operating reserve constraint"
eq_ORCap_large_res_frac(ortype,i,v,r,allh,t) "--MW-- operating reserve capacity availability constraint for generators with reserve_frac > 0.5"
eq_ORCap_small_res_frac(ortype,i,v,r,allh,t) "--MW-- operating reserve capacity availability constraint for generators with reserve_frac <= 0.5"
* regional and national policies
eq_emit_accounting(e,r,t) "--metric tons-- accounting for total emissions in a region"
eq_emit_rate_limit(e,r,t) "--metric tons per MWh-- emission rate limit"
eq_annual_cap(e,t) "--metric tons-- annual (year-specific) emissions cap",
eq_bankborrowcap(e) "--weighted metric tons-- flexible banking and borrowing cap (to be used w/intertemporal solve only"
eq_RGGI_cap(t) "--metric tons CO2-- RGGI constraint -- Regions' emissions must be less than the RGGI cap"
eq_state_cap(st,t) "--metric tons CO2-- state-level CO2 cap constraint -- used to represent California cap and trade program"
eq_CSAPR_Budget(csapr_group,t) "--metric tons NOx-- CSAPR trading group emissions cannot exceed the budget cap"
eq_CSAPR_Assurance(st,t) "--metric tons NOx-- CSAPR state emissions cannot exceed the assurance cap"
eq_BatteryMandate(st,t) "--MW-- battery storage capacity must be greater than indicated level"
eq_cdr_cap(t) "--metric tons CO2-- CO2 removal (DAC and BECCS) can only offset emissions from fossil+CCS and methane leakage"
eq_caa_max_cf(i,v,r,t) "--MWh-- maximum capacity factors for new gas plants (CCs and CTs) under Clean Air Act Section 111 (BSER)"
eq_caa_rate_standard(st,t) "--metric tons CO2-- maximum coal emissions per state under Clean Air Act Section 111 (rate-based emissions standard)"
* RPS Policy equations
eq_REC_Generation(RPSCat,i,st,t) "--RECs-- Generation of RECs by state"
eq_REC_Requirement(RPSCat,st,t) "--RECs-- RECs generated plus trade must meet the state's requirement"
eq_REC_ooslim(RPSCat,st,t) "--RECs-- RECs imported cannot exceed a fraction of total requirement for certain states",
eq_REC_launder(RPSCat,st,t) "--RECs-- RECs laundering constraint"
eq_REC_BundleLimit(RPSCat,st,ast,t) "--RECS-- trade in bundle recs must be less than interstate electricity transmission"
eq_REC_unbundledLimit(RPScat,st,t) "--RECS-- unbundled RECS cannot exceed some percentage of total REC requirements"
eq_RPS_OFSWind(st,t) "--MW-- MW of offshore wind capacity must be greater than or equal to RPS amount"
eq_national_gen(t) "--MWh-- e.g. a national RPS or CES. require a certain amount of total generation to be from specified sources."
* fuel supply curve equations
eq_gasused(cendiv,allh,t) "--MMBtu-- gas used must be from the sum of gas bins"
eq_gasbinlimit(cendiv,gb,t) "--MMBtu-- limit on gas from each bin"
eq_gasbinlimit_nat(gb,t) "--MMBtu-- national limit on gas from each bin"
eq_bioused(r,t) "--MMBtu-- bio used must be from the sum of bio bins"
eq_biousedlimit(bioclass,usda_region,t) "--MMBtu-- limit on bio from each bin in each USDA region"
* regional natural gas supply curves
eq_gasaccounting_regional(cendiv,t) "--MMBtu-- regional gas consumption cannot exceed the amount used in bins"
eq_gasaccounting_national(t) "--MMBtu-- national gas consumption cannot exceed the amount used in bins"
eq_gasbinlimit_regional(fuelbin,cendiv,t) "--MMBtu-- regional binned gas usage cannot exceed bin capacity"
eq_gasbinlimit_national(fuelbin,t) "--MMBtu-- national binned gas usage cannot exceed bin capacity"
* hydrogen supply and demand
eq_prod_capacity_limit(i,v,r,allh,t) "--metric tons-- production cannot exceeds its capacity"
eq_h2_demand(p,t) "--metric tons-- production of hydrogen must meet exogenous demand plus H2-CT use"
eq_h2_demand_regional(r,allh,t) "--metric tons per hour-- regional hydrogen supply must equal demand net trade and storage"
eq_h2_transport_caplimit(r,rr,allh,t) "--metric tons per hour-- H2 flow cannot exceed cumulative pipeline investment"
eq_h2_storage_flowlimit(h2_stor,r,allh,t) "--metric tons per hour-- H2 storage injection or withdrawal cannot exceed cumulative storage investment"
eq_h2_storage_capacity(h2_stor,r,t) "--metric tons-- H2 storage capacity is sum of H2 storage investments"
eq_h2_min_storage_cap(r,t) "--metric tons-- H2 storage capacity must be ≥ Sw_H2_MinStorHours * H2 usage capacity"
eq_h2_ptc_region_balance(h2ptcreg,t) "--MWh-- clean generation for hydrogen production must be more than electricity required for electrolytic H2 production in that region and year"
eq_h2_ptc_region_hour_balance(h2ptcreg,allh,t) "--MWh-- clean generation for hydrogen production must be more than electricity required for electrolytic H2 production in that region, hour and year"
eq_h2_ptc_creditgen(i,v,r,allh,t) "--MWh-- total generation must be greater than clean generation for hydrogen production"
eq_h2_storage_caplimit(h2_stor,r,actualszn,allh,t) "--metric tons-- total H2 storage in a storage facility cannot exceed investment capacity"
eq_h2_storage_level(h2_stor,r,actualszn,allh,t) "--metric tons-- tracks H2 storage level by storage type and BA within and across periods"
eq_h2_storage_caplimit_szn(h2_stor,r,actualszn,t) "--metric tons-- total H2 storage in a storage facility cannot exceed investment capacity"
eq_h2_storage_level_szn(h2_stor,r,actualszn,t) "--metric tons-- tracks H2 storage level by storage type and BA within and across periods"
* CO2 capture and storage
eq_co2_capture(r,allh,t) "--metric tons-- accounting of CO2 captured from DAC and CCS technologies"
eq_co2_injection_limit(cs,allh,t) "--metric tons per hour-- limit on CO2 injection for each carbon site as a rate"
eq_co2_sink(r,allh,t) "--metric tons per hour-- co2 stored or used must exceed co2 captured plus net trade"
eq_co2_transport_caplimit(r,rr,allh,t) "--metric tons-- limit on interregional co2 trade"
eq_co2_spurline_caplimit(r,cs,allh,t) "--metric tons-- limit on transport of CO2 from BA to carbon storage site"
eq_co2_cumul_limit(cs,t) "--cumulative metric tons-- total stored in a reservor cannot exceed capacity"
* transmission equations
eq_CAPTRAN_ENERGY(r,rr,trtype,t) "--MW-- capacity accounting for transmission capacity for energy trading"
eq_CAPTRAN_PRM(r,rr,trtype,t) "--MW-- capacity accounting for transmission capacity for PRM trading"
eq_prescribed_transmission(r,rr,trtype,t) "--MW-- investment in transmission up to first year allowed must be less than the exogenous possible transmission",
eq_PRMTRADELimit(r,rr,trtype,ccseason,t) "--MW-- trading of PRM capacity cannot exceed the line's capacity"
eq_transmission_investment_max(t) "--MWmile-- investment in transmission must be <= Sw_TransInvMax"
eq_CAPTRAN_max(r,rr,trtype,t) "--MW-- upper limit for transmission capacity of each trtype across individual interfaces"
eq_CAPTRAN_max_total(r,rr,t) "--MW-- upper limit for transmission capacity of all trtypes across individual interfaces"
eq_CAP_CONVERTER(r,t) "--MW-- capacity accounting for VSC AC/DC converters"
eq_CAP_SPUR(x,t) "--MW-- capacity accounting for spur lines"
eq_converter_max(r,t) "--MW-- upper limit for VSC AC/DC converter capacity in individual BAs"
eq_CONVERSION_limit_energy(r,allh,t) "--MW-- AC/DC energy conversion is limited to converter capacity"
eq_CONVERSION_limit_prm(r,ccseason,t) "--MW-- AC/DC PRM conversion is limited to converter capacity"
eq_PRMTRADE_VSC(r,ccseason,t) "--MW-- PRM capacity can flow through VSC lines but doesn't directly contribute to PRM"
eq_POI_cap(r,t) "--MW-- POI capacity accounting (for network reinforcement costs)"
eq_CAPTRAN_GRP(transgrp,transgrpp,t) "--MW-- combined flow capacity between transmission groups"
eq_transgrp_limit_energy(transgrp,transgrpp,allh,t) "--MW-- limit on combined interface energy flows"
eq_transgrp_limit_prm(transgrp,transgrpp,ccseason,t) "--MW-- limit on combined interface PRM flows"
eq_firm_transfer_limit(nercr,allh,t) "--MW-- limit net firm capacity imports into NERC regions when using stress periods"
eq_firm_transfer_limit_cc(nercr,ccseason,t) "--MW-- limit net firm capacity imports into NERC regions when using capacity credit"
* storage-specific equations
eq_storage_capacity(i,v,r,allh,t) "--MW-- second storage capacity constraint in addition to eq_capacity_limit"
eq_storage_duration(i,v,r,allh,t) "--MWh-- limit STORAGE_LEVEL based on hours of storage available"
eq_storage_in_cap(i,v,r,allh,t) "--MW-- storage_in must be less than a given fraction of power output capacity"
eq_storage_in_minloading(i,v,r,allh,allhh,t) "--MW-- minimum level for storage_in across same-season hours"
eq_storage_level(i,v,r,allh,t) "--MWh-- storage level inventory balance from one time-slice to the next"
eq_storage_interday_level_max_day(i,v,r,allszn,allh,t) "--MWh-- define the maximum relative SOC on a representative period compared to hour 0 of the rep period"
eq_storage_interday_level_min_day(i,v,r,allszn,allh,t) "--MWh-- define the minimum relative SOC on a representative period compared to hour 0 of the rep period"
eq_storage_interday_min_level_start(i,v,r,allszn,t) "--MWh-- enforce minimun SOC at first period of each partition"
eq_storage_interday_min_level_end(i,v,r,allszn,t) "--MWh-- enforce minimun SOC at last period of each partition"
eq_storage_interday_level(i,v,r,allszn,t) "--MWh-- calculate SOC of each partition at its hour 0"
eq_storage_interday_max_level_start(i,v,r,allszn,t) "--MWh-- enforce maximum SOC at first period of each partition"
eq_storage_interday_max_level_end(i,v,r,allszn,t) "--MWh-- enforce maximum SOC at last period of each partition"
eq_storage_opres(i,v,r,allh,t) "--MWh-- there must be sufficient energy in the storage to be able to provide operating reserves"
eq_storage_thermalres(i,v,r,allh,t) "--MW-- thermal storage contribution to operating reserves is store_in only"
* demand-response specific equations
eq_dr_max_shed(i,v,r,allh,t) "--MW-- total shed allowed by demand response technologies from timeslice h"
eq_dr_max_shed_hrs(i,v,r,t) "--MW-- total hours shed is allowed to operate over the year"
eq_dr_max_shift(i,v,r,allh,allhh,t) "--MW-- total shifting allowed by demand response technologies to timeslice h from timeslice hh"
eq_dr_max_decrease(i,v,r,allh,t) "--MW-- maximum allowed decrease of load from demand response in timeslice h"
eq_dr_max_increase(i,v,r,allh,t) "--MW-- maximum allowed increase of load from demand response in timeslice h"
eq_dr_gen(i,v,r,allh,t) "--MW-- link demand response shifting to generation"
* hybrid plant equations
eq_plant_total_gen(i,v,r,allh,t) "--MW-- generation post curtailment = generation from pv (post curtailment) + generation from battery - charging from PV"
eq_hybrid_plant_energy_limit(i,v,r,allh,t) "--MW-- PV energy to storage (no curtailment recovery) + PV energy to inverter <= PV resource"
eq_plant_capacity_limit(i,v,r,allh,t) "--MW-- energy moving through the inverter cannot exceed the inverter capacity"
eq_pvb_itc_charge_reqt(i,v,r,t) "--MWh-- total energy charged from local PV >= ITC qualification fraction * total energy charged"
* Canadian imports balance
eq_Canadian_Imports(r,allszn,t) "--MWh-- Balance of Canadian imports by season"
* water usage accounting
eq_water_accounting(i,v,w,r,allh,t) "--Mgal-- water usage accounting"
eq_water_capacity_total(i,v,r,t) "--Mgal-- specify required water access based on generation capacity and water use rate"
eq_water_capacity_limit(wst,r,t) "--Mgal/yr-- total water access must not exceed supply by region and water type"
eq_water_use_limit(i,v,w,r,allszn,t) "--Mgal/yr-- water use must not exceed available access"
* flexible CCS constraints
eq_ccsflex_byp_ccsenergy_limit(i,v,r,allh,t) "--avg MW-- Limit the CCS power for a bypass system in each time-slice"
eq_ccsflex_sto_ccsenergy_limit_szn(i,v,r,allszn,t) "--MWh-- Limit the CCS power for a storage system across a characteristic day"
eq_ccsflex_sto_ccsenergy_balance(i,v,r,allszn,t) "--MWh-- Total CCS energy requirement can be distributed across a characteristic day"
eq_ccsflex_sto_storage_level(i,v,r,allh,t) "--varies-- Track the level of the CCS storage balance for each time-slice"
eq_ccsflex_sto_storage_level_max(i,v,r,allh,t) "--varies-- Limit the level of the CCS storage system"
;
*==========================
* --- LOAD CONSTRAINTS ---
*==========================
* ---------------------------------------------------------------------------
*the marginal off of this constraint allows you to
*determine the full price of electricity load
*i.e. the price of load with consideration to operating
*reserve and planning reserve margin considered
eq_loadcon(r,h,t)$tmodel(t)..
LOAD(r,h,t)
=e=
*[plus] the static, exogenous load
+ load_exog_static(r,h,t)
*[plus] exogenously defined exports to Canada
* note net canadian load (when Sw_Canada = 2) is included
* in eq_supply_demand since LOAD needs to stay positive
* while net_trade can be negative and cause infeasibilities
+ can_exports_h(r,h,t)$[Sw_Canada=1]
*[plus] load from EV charging (baseline/unmanaged)
+ evmc_baseline_load(r,h,t)$Sw_EVMC
*[plus] shifted load from adopted EVMC shape resources
+ sum{(i,v)$[evmc_shape(i)$valcap(i,v,r,t)], evmc_shape_load(i,r,h) * CAP(i,v,r,t)}
*[plus] load shifted from other timeslices
+ sum{flex_type, FLEX(flex_type,r,h,t) }$Sw_EFS_flex
*[plus] Load created by production activities - only tracked during representative hours
* [metric tons/hour] / [metric tons/MWh] = [MW]
+ sum{(p,i,v)$[consume(i)$valcap(i,v,r,t)$i_p(i,p)$(not sameas(i,"dac_gas"))],
PRODUCE(p,i,v,r,h,t) / prod_conversion_rate(i,v,r,t) }$[Sw_Prod$h_rep(h)]
*[plus] load for compressors associated with hydrogen storage injections or withdrawals
* metric tons/hour * MWh/metric tons = MW
+ sum{h2_stor$h2_stor_r(h2_stor,r),
h2_network_load(h2_stor,t)
* ( H2_STOR_IN(h2_stor,r,h,t) + H2_STOR_OUT(h2_stor,r,h,t) ) }$Sw_H2_CompressorLoad
* [plus] load for hydrogen pipeline compressors
* metric tons/hour * MWh/metric tons = MW
+ sum{rr$h2_routes(r,rr),
h2_network_load("h2_compressor",t)
* (( H2_FLOW(r,rr,h,t) + H2_FLOW(rr,r,h,t) ) / 2) }$Sw_H2_CompressorLoad
;
* ---------------------------------------------------------------------------
*======================================
* --- LOAD FLEXIBILITY CONSTRAINTS ---
*======================================
* ---------------------------------------------------------------------------
*The following 3 equations apply to the flexibility of load in ReEDS, originally developed
*as part of the EFS study in ReEDS heritage and adapted for ReEDS-2.0 here.
* Additional work has been done to represent flexible load as a generator + storage
* with boundaries on how many timeslices this generator may shift. See equations
* in the DR CONSTRAINTS section for that representation
* FLEX load in each season equals the total exogenously-specified flexible load in each season
eq_load_flex_day(flex_type,r,szn,t)$[tmodel(t)$Sw_EFS_flex]..
sum{h$h_szn(h,szn), FLEX(flex_type,r,h,t) * hours(h) } / numdays(szn)
=e=
sum{h$h_szn(h,szn), load_exog_flex(flex_type,r,h,t) * hours(h) } / numdays(szn)
;
* ---------------------------------------------------------------------------
* for the "previous" flex type: the amount of exogenously-specified load in timeslice "h"
* must be served by FLEX load either in the timeslice h or the timeslice PRECEEDING h
*
* for the "next" flex type: the amount of exogenously-specified load in timeslice "h"
* must be served by FLEX load either in the timeslice h or the timeslice FOLLOWING h
*
* for the "adjacent" flex type: the amount of exogenously-specified load in timeslice "h"
* must be served by FLEX load either in the timeslice h or a timeslice ADJACENT to h
eq_load_flex1(flex_type,r,h,t)$[tmodel(t)$Sw_EFS_flex]..
FLEX(flex_type,r,h,t) * hours(h)
+ sum{hh$flex_h_corr1(flex_type,h,hh), FLEX(flex_type,r,hh,t) * hours(hh) }
=g=
load_exog_flex(flex_type,r,h,t) * hours(h)
;
* ---------------------------------------------------------------------------
* for the "previous" flex type: FLEX load in timeslice "h" cannot exceed the sum of
* exogenously-specified load in timeslice h and the timeslice following h
*
* for the "next" flex type: FLEX load in timeslice "h" cannot exceed the sum of
* exogenously-specified load in timeslice h and the timeslice preceeding h
*
* for the "adjacent" flex type: FLEX load in timeslice "h" cannot exceed the sum of
* exogenously-specified load in timeslice h and the timeslices adjacent to h
eq_load_flex2(flex_type,r,h,t)$[tmodel(t)$Sw_EFS_flex]..
load_exog_flex(flex_type,r,h,t) * hours(h)
+ sum{hh$flex_h_corr2(flex_type,h,hh), load_exog_flex(flex_type,r,hh,t) * hours(hh) }
=g=
FLEX(flex_type,r,h,t) * hours(h)
;
* * ---------------------------------------------------------------------------
* This constraint and the associated PEAK_FLEX variable are not currently supported
* but are left in the model in case someone decides to revive them.
* eq_load_flex_peak(r,h,ccseason,t)$[tmodel(t)$Sw_EFS_flex]..
* * peak demand EFS flexibility adjustment is greater than
* PEAK_FLEX(r,ccseason,t)$h_ccseason(h,ccseason)
* =g=
* * the static peak in each timeslice
* peakdem_static_h(r,h,t)$h_ccseason(h,ccseason)
* * PLUS the flexibile load served in each timeslice
* + sum{flex_type, FLEX(flex_type,r,h,t) }$h_ccseason(h,ccseason)
* * MINUS the static peak demand in the season corresponding to each timeslice
* - peakdem_static_ccseason(r,ccseason,t)$h_ccseason(h,ccseason)
* ;
* ---------------------------------------------------------------------------
*=========================================================
* --- EQUATIONS RELATING CAPACITY ACROSS TIME PERIODS ---
*=========================================================
*====================================
* -- existing capacity equations --
*====================================
$ontext
The following six equations dictate how capacity is represented in the model.
The first three equations handle init-X vintages (those that existed pre-2010)
which are bounded by m_capacity_exog. With retirements (in the second and third
equations), the constraints imply that capacity must be less than or
equal to m_capacity_exog and monotonically decreasing over time -
implying that if endogenous capacity was reduced in the previous year,
it cannot be brought back online.
New capacity, handled in equations four through six, is the sum of previous
years' greenfield investments and refurbishments. The same logic is present
for retiring capacity, the only difference being that contemporaneous
investment can increase the present-period's capacity.
Upgraded capacity reduces the total amount of capacity available to the
upgraded-from technology. For example, the model starts with 100MW of
coaloldscr (m_capacity_exog = 100) capacity then upgrades 10MW of that to
coaloldscr_coal-ccs capacity. The remaining amount of available coaloldscr
is thus 90 and coaloldscr_coal-ccs capacity is 10 but both are still less
than the 100 available. As time progresses and exogenous capacity declines,
the model chooses which units to take offline.
$offtext
* ---------------------------------------------------------------------------
eq_cap_init_noret(i,v,r,t)$[valcap(i,v,r,t)$tmodel(t)$initv(v)$(not upgrade(i))
$(not retiretech(i,v,r,t))]..
m_capacity_exog(i,v,r,t)
* Account for capacity upsizing within init vintages
+ sum{(tt,rscbin)$[(tmodel(tt) or tfix(tt))$allow_cap_up(i,v,r,rscbin,tt)],
degrade(i,tt,t) * INV_CAP_UP(i,v,r,rscbin,tt) }
=e=
CAP(i,v,r,t)
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)],
CAP(ii,v,r,t) / (1 - upgrade_derate(ii,v,r,t))}$[Sw_Upgrades = 1]
* include contemporaneous upgrades when they are intended to
* persist as new bintages with sw_upgrades = 2
+ sum{(ii)$[upgrade_from(ii,i)$valcap(ii,v,r,t)$(not sameas(ii,'hydEND_hydED'))],
UPGRADES(ii,v,r,t) }$[Sw_Upgrades = 2]
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)$sameas(ii,'hydEND_hydED')],
CAP(ii,v,r,t) }$[Sw_Upgrades = 2]
;
* ---------------------------------------------------------------------------
eq_cap_init_retub(i,v,r,t)$[valcap(i,v,r,t)$tmodel(t)$initv(v)$(not upgrade(i))
$retiretech(i,v,r,t)]..
m_capacity_exog(i,v,r,t)
* Account for capacity upsizing within init vintages
+ sum{(tt,rscbin)$[(tmodel(tt) or tfix(tt))$allow_cap_up(i,v,r,rscbin,tt)],
degrade(i,tt,t) * INV_CAP_UP(i,v,r,rscbin,tt) }
=g=
CAP(i,v,r,t)
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)],
CAP(ii,v,r,t) / (1 - upgrade_derate(ii,v,r,t))}$[Sw_Upgrades = 1]
* include contemporaneous upgrades when they are intended to
* persist as new bintages with sw_upgrades = 2
+ sum{(ii)$[upgrade_from(ii,i)$valcap(ii,v,r,t)$(not sameas(ii,'hydEND_hydED'))],
UPGRADES(ii,v,r,t) }$[Sw_Upgrades = 2]
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)$sameas(ii,'hydEND_hydED')],
CAP(ii,v,r,t) }$[Sw_Upgrades = 2]
;
* ---------------------------------------------------------------------------
eq_cap_init_retmo(i,v,r,t)$[valcap(i,v,r,t)$tmodel(t)$initv(v)$(not upgrade(i))
$retiretech(i,v,r,t)]..
sum{tt$[tprev(t,tt)$valcap(i,v,r,tt)],
CAP(i,v,r,tt)
+ sum{ii$[valcap(ii,v,r,tt)$upgrade_from(ii,i)],
CAP(ii,v,r,tt) / (1 - upgrade_derate(ii,v,r,tt)) }$[Sw_Upgrades = 1]
+ sum{ii$[valcap(ii,v,r,tt)$upgrade_from(ii,i)$sameas(ii,'hydEND_hydED')],
CAP(ii,v,r,tt) }$[Sw_Upgrades = 2]
}
* Account for capacity upsizing within init vintages
+ sum{rscbin$allow_cap_up(i,v,r,rscbin,t), INV_CAP_UP(i,v,r,rscbin,t) }
=g=
CAP(i,v,r,t)
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)],
CAP(ii,v,r,t) / (1 - upgrade_derate(ii,v,r,t))}$[Sw_Upgrades = 1]
* include contemporaneous upgrades when they are intended to
* persist as new bintages with sw_upgrades = 2
+ sum{(ii)$[upgrade_from(ii,i)$valcap(ii,v,r,t)$(not sameas(ii,'hydEND_hydED'))],
UPGRADES(ii,v,r,t) }$[Sw_Upgrades = 2]
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)$sameas(ii,'hydEND_hydED')],
CAP(ii,v,r,t) }$[Sw_Upgrades = 2]
;
* ---------------------------------------------------------------------------
*==============================
* -- new capacity equations --
*==============================
* ---------------------------------------------------------------------------
eq_cap_new_noret(i,v,r,t)$[valcap(i,v,r,t)$tmodel(t)$newv(v)$(not upgrade(i))
$(not retiretech(i,v,r,t))]..
sum{tt$[inv_cond(i,v,r,t,tt)$(tmodel(tt) or tfix(tt))$valcap(i,v,r,tt)],
degrade(i,tt,t) * (INV(i,v,r,tt) + INV_REFURB(i,v,r,tt)$[refurbtech(i)$Sw_Refurb])
}
* Account for capacity upsizing within new vintages
+ sum{(tt,rscbin)$[(tmodel(tt) or tfix(tt))$allow_cap_up(i,v,r,rscbin,tt)],
degrade(i,tt,t) * INV_CAP_UP(i,v,r,rscbin,tt) }
=e=
CAP(i,v,r,t)
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)],
CAP(ii,v,r,t) / (1 - upgrade_derate(ii,v,r,t))}$[Sw_Upgrades = 1]
* include contemporaneous upgrades when they are intended to
* persist as new bintages with sw_upgrades = 2
+ sum{(ii)$[upgrade_from(ii,i)$valcap(ii,v,r,t)$(not sameas(ii,'hydEND_hydED'))],
UPGRADES(ii,v,r,t) }$[Sw_Upgrades = 2]
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)$sameas(ii,'hydEND_hydED')],
CAP(ii,v,r,t) }$[Sw_Upgrades = 2]
;
* ---------------------------------------------------------------------------
eq_cap_new_retub(i,v,r,t)$[valcap(i,v,r,t)$tmodel(t)$newv(v)$(not upgrade(i))
$retiretech(i,v,r,t)]..
sum{tt$[inv_cond(i,v,r,t,tt)$(tmodel(tt) or tfix(tt))$valcap(i,v,r,tt)],
degrade(i,tt,t) * (INV(i,v,r,tt) + INV_REFURB(i,v,r,tt)$[refurbtech(i)$Sw_Refurb])
}
* Account for capacity upsizing within new vintages
+ sum{(tt,rscbin)$[(tmodel(tt) or tfix(tt))$allow_cap_up(i,v,r,rscbin,tt)],
degrade(i,tt,t) * INV_CAP_UP(i,v,r,rscbin,tt) }
=g=
CAP(i,v,r,t)
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)],
CAP(ii,v,r,t) / (1 - upgrade_derate(ii,v,r,t))}$[Sw_Upgrades = 1]
* include contemporaneous upgrades when they are intended to
* persist as new bintages with sw_upgrades = 2
+ sum{(ii)$[upgrade_from(ii,i)$valcap(ii,v,r,t)$(not sameas(ii,'hydEND_hydED'))],
UPGRADES(ii,v,r,t) }$[Sw_Upgrades = 2]
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)$sameas(ii,'hydEND_hydED')],
CAP(ii,v,r,t) }$[Sw_Upgrades = 2]
;
* ---------------------------------------------------------------------------
eq_cap_new_retmo(i,v,r,t)$[valcap(i,v,r,t)$tmodel(t)$newv(v)$(not upgrade(i))
$retiretech(i,v,r,t)]..
sum{tt$[tprev(t,tt)$valcap(i,v,r,tt)],
degrade(i,tt,t) * CAP(i,v,r,tt)
+ sum{ii$[valcap(ii,v,r,tt)$upgrade_from(ii,i)],
CAP(ii,v,r,tt) / (1 - upgrade_derate(ii,v,r,tt)) }$[Sw_Upgrades = 1]
+ sum{ii$[valcap(ii,v,r,tt)$upgrade_from(ii,i)$sameas(ii,'hydEND_hydED')],
CAP(ii,v,r,tt) }$[Sw_Upgrades = 2]
}
+ INV(i,v,r,t)$valinv(i,v,r,t)
+ INV_REFURB(i,v,r,t)$[valinv(i,v,r,t)$refurbtech(i)$Sw_Refurb]
* Account for capacity upsizing within new vintages
+ sum{rscbin$allow_cap_up(i,v,r,rscbin,t), INV_CAP_UP(i,v,r,rscbin,t) }
=g=
CAP(i,v,r,t)
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)],
CAP(ii,v,r,t) / (1 - upgrade_derate(ii,v,r,t))}$[Sw_Upgrades = 1]
* include contemporaneous upgrades when they are intended to
* persist as new bintages with sw_upgrades = 2
+ sum{(ii)$[upgrade_from(ii,i)$valcap(ii,v,r,t)$(not sameas(ii,'hydEND_hydED'))],
UPGRADES(ii,v,r,t) }$[Sw_Upgrades = 2]
+ sum{ii$[valcap(ii,v,r,t)$upgrade_from(ii,i)$sameas(ii,'hydEND_hydED')],
CAP(ii,v,r,t) }$[Sw_Upgrades = 2]
;
* ---------------------------------------------------------------------------
* Capacity accounting for rsc techs
eq_cap_rsc(i,v,r,rscbin,t)
$[tmodel(t)
$rsc_i(i)$(not sccapcosttech(i))
$valcap(i,v,r,t)]..
sum{tt$[tfirst(tt)$exog_rsc(i)],
capacity_exog_rsc(i,v,r,rscbin,tt) }
+ sum{tt$[(yeart(tt) <= yeart(t))$(tmodel(tt) or tfix(tt))
$m_rscfeas(r,i,rscbin)
$valinv(i,v,r,tt)],
INV_RSC(i,v,r,rscbin,tt)
}
=e=
CAP_RSC(i,v,r,rscbin,t)
;
* ---------------------------------------------------------------------------
eq_cap_upgrade(i,v,r,t)$[valcap(i,v,r,t)$upgrade(i)$Sw_Upgrades$tmodel(t)]..
* without peristent upgrades, all upgrades correspond to their original bintage
+ sum{(tt)$[(tfix(tt) or tmodel(tt))
$(yeart(tt)<=yeart(t))
$(yeart(tt)>=Sw_Upgradeyear)
$valcap(i,v,r,tt)
$sum{ii$upgrade_from(i,ii), valcap(ii,v,r,tt) }],
UPGRADES(i,v,r,tt) * (1 - upgrade_derate(i,v,r,tt))
}$[(Sw_Upgrades = 1)$(not coal(i))]
* coal cannot upgrade after the retire year - ie no mothballing
+ sum{(tt)$[(tfix(tt) or tmodel(tt))
$(yeart(tt)<=yeart(t))
$(yeart(tt)>=Sw_Upgradeyear)
$valcap(i,v,r,tt)
$(yeart(tt)<=caa_coal_retire_year)],
UPGRADES(i,v,r,tt) * (1 - upgrade_derate(i,v,r,tt))
}$[(Sw_Upgrades = 1)$coal(i)]
* all previous years upgrades converted to new bintages of the present year
* NOTE: the 'v' in ivt(i,v,tt) here is an important distinction -
* although we're summing over 'vv' we still only want upgrades
* to be included for the upgrade tech's vintage combination
+ sum{(tt,vv)$[(tfix(tt) or tmodel(tt))$(initv(vv) or sameas(v,vv))
$(yeart(tt)<=yeart(t))$ivt(i,v,tt)
$(yeart(tt)>=Sw_Upgradeyear)
$valcap(i,v,r,tt)$(not sameas(i,'hydEND_hydED'))
$sum(ii$upgrade_from(i,ii),valcap(ii,vv,r,tt))],
UPGRADES(i,vv,r,tt) * (1 - upgrade_derate(i,vv,r,tt))
}$[Sw_Upgrades = 2]
+ sum{(tt)$[(tfix(tt) or tmodel(tt))$(yeart(tt)<=yeart(t))$(yeart(tt)>=Sw_Upgradeyear)
$valcap(i,v,r,tt)$sameas(i,'hydEND_hydED')],
UPGRADES(i,v,r,tt) * (1 - upgrade_derate(i,v,r,tt))
}$[Sw_Upgrades = 2]
=e=
CAP(i,v,r,t)
* note this is equivalent to the previous version that had a =g=
* sign in the corrolary equation
+ sum{tt$[(tfix(tt) or tmodel(tt))$valcap(i,v,r,tt)],
UPGRADES_RETIRE(i,v,r,tt)}$[not noret_upgrade_tech(i)]
;
* ---------------------------------------------------------------------------
* Capacity upsizing limit
* This uses rscbin to constrain hydropower upsizing using supply curve data.
eq_cap_up(i,v,r,rscbin,t)$[tmodel(t)$allow_cap_up(i,v,r,rscbin,t)]..
cap_cap_up(i,v,r,rscbin,t)
=g=
sum{tt$[(tmodel(tt) or tfix(tt))], INV_CAP_UP(i,v,r,rscbin,tt) }
;
* ---------------------------------------------------------------------------
*Energy upsizing limit
* This uses rscbin to constrain hydropower upsizing using supply curve data.
eq_ener_up(i,v,r,rscbin,t)$[tmodel(t)$allow_ener_up(i,v,r,rscbin,t)]..
cap_ener_up(i,v,r,rscbin,t)
=g=
sum{tt$[(tmodel(tt) or tfix(tt))], INV_ENER_UP(i,v,r,rscbin,tt) }
;
* ---------------------------------------------------------------------------
eq_forceprescription(pcat,r,t)$[tmodel(t)$force_pcat(pcat,t)$Sw_ForcePrescription
$sum{(i,newv)$[prescriptivelink(pcat,i)], valinv(i,newv,r,t) }]..
*capacity built in the current period or prior
sum{(i,newv,tt)$[valinv(i,newv,r,tt)$prescriptivelink(pcat,i)
$(yeart(tt)<=yeart(t))$(tmodel(tt) or tfix(tt))],
INV(i,newv,r,tt) + INV_REFURB(i,newv,r,tt)$[refurbtech(i)$Sw_Refurb]}
=e=
*must equal the cumulative prescribed amount
sum{tt$[(yeart(tt)<=yeart(t))
$(tmodel(tt) or tfix(tt))],
noncumulative_prescriptions(pcat,r,tt)}
* plus any extra buildouts (no penalty here - used as free slack)
* only on or after the first year the techs are available
+ EXTRA_PRESCRIP(pcat,r,t)$[yeart(t)>=firstyear_pcat(pcat)]
* or in regions where there is a offshore wind requirement
+ EXTRA_PRESCRIP(pcat,r,t)$[r_offshore(r,t)$sameas(pcat,'wind-ofs')
$(yeart(t)>=firstyear_RPS)
$sum{st$r_st(r,st), offshore_cap_req(st,t) }]
;
* ---------------------------------------------------------------------------
*limit the amount of refurbishments available in specific year
*this is the sum of all previous year's investment that is now beyond the age
*limit (i.e. it has exited service) plus the amount of retired exogenous capacity
*that we begin with
eq_refurblim(i,r,t)$[tmodel(t)$refurbtech(i)$Sw_Refurb]..
*investments that meet the refurbishment requirement (i.e. they've expired)
sum{(vv,tt)$[m_refurb_cond(i,vv,r,t,tt)$(tmodel(tt) or tfix(tt))$valinv(i,vv,r,tt)],
INV(i,vv,r,tt) }
*[plus] exogenous decay in capacity
*note here that the tfix or tmodel set does not apply
*since we'd want capital that expires in off-years to
*be included in this calculation as well
+ sum{(v,tt)$[yeart(tt)<=yeart(t)],
avail_retire_exog_rsc(i,v,r,tt) }
=g=
*must exceed the total sum of investments in refurbishments
*that have yet to expire - implying an investment can be refurbished more than once
*if the first refurbishment has exceed its age limit
sum{(vv,tt)$[inv_cond(i,vv,r,t,tt)$(tmodel(tt) or tfix(tt))$valinv(i,vv,r,tt)],
INV_REFURB(i,vv,r,tt)
}
;
* ---------------------------------------------------------------------------
eq_rsc_inv_account(i,v,r,t)$[tmodel(t)$valinv(i,v,r,t)$rsc_i(i)]..
sum{rscbin$m_rscfeas(r,i,rscbin), INV_RSC(i,v,r,rscbin,t) }
=e=
INV(i,v,r,t)
;
* ---------------------------------------------------------------------------
*note that the following equation only restricts inv_rsc and not inv_refurb
*therefore, the capacity indicated by the supply curve may be limiting
*but the plant can still be refurbished
*Also note the flag_eq_rsc_INVlim--its calculation needs to be updated if this equation
*is changed
eq_rsc_INVlim(r,i,rscbin,t)$[tmodel(t)
$rsc_i(i)
$m_rscfeas(r,i,rscbin)
$m_rsc_con(r,i)
$(not flag_eq_rsc_INVlim(r,i,rscbin,t))]..
*With water constraints, some RSC techs are expanded to include cooling technologies
*but the combination of m_rsc_con and rsc_agg allows for those investments
*to be limited by the numeraire techs' m_rsc_dat
*capacity indicated by the resource supply curve (with undiscovered geo available
*at the "discovered" amount and hydro upgrade availability adjusted over time)
m_rsc_dat(r,i,rscbin,"cap") * (
1$[not geo_hydro(i)] + geo_discovery(i,r,t)$geo_hydro(i))
* available hydro upgrade capacity
+ hyd_add_upg_cap(r,i,rscbin,t)$(Sw_HydroCapEnerUpgradeType=1)
* available DR capacity
+ rsc_dr(i,r,"cap",rscbin,t)
* available EVMC capacity
+ rsc_evmc(i,r,"cap",rscbin,t)
=g=
*must exceed the cumulative invested capacity in that region/class/bin...
sum{(ii,v,tt)$[valinv(ii,v,r,tt)$(yeart(tt) <= yeart(t))$rsc_agg(i,ii)$(not dr(i))],
INV_RSC(ii,v,r,rscbin,tt) * resourcescaler(ii) }
*plus exogenous (pre-start-year) capacity, using its level in the first year (tfirst)
+ sum{(ii,v,tt)$[tfirst(tt)$rsc_agg(i,ii)$(not dr(i))$exog_rsc(i)],
capacity_exog_rsc(ii,v,r,rscbin,tt) }
* in that year for DR (since DR investment is annual)
+ sum{(ii,v)$[valinv(ii,v,r,t)$rsc_agg(i,ii)$dr(i)],
INV_RSC(ii,v,r,rscbin,t) * resourcescaler(ii) }
;
* ---------------------------------------------------------------------------
eq_growthlimit_relative(i,st,t)$[sum{r$[r_st(r,st)], valinv_irt(i,r,t) }
$tmodel(t)
$stfeas(st)
$Sw_GrowthPenalties
$(yeart(t)<=Sw_GrowthPenLastYear)
$(yeart(t)>=model_builds_start_yr)]..
*the annual growth limit
(yeart(t) - sum{tt$[tprev(t,tt)], yeart(tt) })
* sum{gbin, GROWTH_BIN(gbin,i,st,t) }
=g=
* must exceed the current periods investment
sum{(v,r)$[valinv(i,v,r,t)$r_st(r,st)],
INV(i,v,r,t) }
;
eq_growthbin_limit(gbin,st,tg,t)$[valinv_tg(st,tg,t)
$tmodel(t)
$stfeas(st)
$Sw_GrowthPenalties
$(yeart(t)<=Sw_GrowthPenLastYear)
$(yeart(t)>=model_builds_start_yr)]..
*the growth bin limit
growth_bin_limit(gbin,st,tg,t)
=g=
* must exceed the value in the growth bin
sum{i$tg_i(tg,i), GROWTH_BIN(gbin,i,st,t) }
;
* ---------------------------------------------------------------------------
eq_growthlimit_absolute(tg,t)$[growth_limit_absolute(tg)$tmodel(t)
$Sw_GrowthAbsCon$(yeart(t)<=Sw_GrowthConLastYear)
$(yeart(t)>=model_builds_start_yr)]..
* the absolute limit of growth (in MW)
(sum{tt$[tprev(tt,t)], yeart(tt) } - yeart(t))
* growth_limit_absolute(tg)
=g=
* must exceed the total investment
sum{(i,v,r)$[valinv(i,v,r,t)$tg_i(tg,i)],
INV(i,v,r,t) }
;
* ---------------------------------------------------------------------------
* If using hybrid generators with endogenous spur lines, the available power from
* a reV site is limited by the CF and capacity of constituent resources at that site
eq_site_cf(x,h,t)
$[tmodel(t)
$Sw_SpurScen
$xfeas(x)]..
sum{(i,v,r)
$[spur_techs(i)
$x_r(x,r)
$valgen(i,v,r,t)],
* Capacity factor of techs with endogenously-modeled spur lines
m_cf(i,v,r,h,t)
* multiplied by total capacity of those techs
* sum{rscbin
$[valcap(i,v,r,t)
$m_rscfeas(r,i,rscbin)
$spurline_sitemap(i,r,rscbin,x)],
CAP_RSC(i,v,r,rscbin,t)
}
}
=g=
AVAIL_SITE(x,h,t)
;
* ---------------------------------------------------------------------------
* If using hybrid generators with endogenous spur lines, each wind and solar generator
* is associated with a specific reV site x. The available generation from all generators
* at site x is limited to the spur-line capacity built to site x.
eq_spurclip(x,h,t)
$[Sw_SpurScen
$xfeas(x)
$tmodel(t)]..
* Capacity of spur line to reV site limits the available generation at that site
CAP_SPUR(x,t)
=g=
AVAIL_SITE(x,h,t)
;
* ---------------------------------------------------------------------------
* If spur-line sharing is disabled, the capacity of the spur line for site x
* must be >= the capacity of the hybrid resources (wind and solar) installed at site x
eq_spur_noclip(x,t)
$[Sw_SpurScen