-
Alois Dirnaichner authoredAlois Dirnaichner authored
equations.gms 36.34 KiB
*** | (C) 2006-2019 Potsdam Institute for Climate Impact Research (PIK)
*** | authors, and contributors see CITATION.cff file. This file is part
*** | of REMIND and licensed under AGPL-3.0-or-later. Under Section 7 of
*** | AGPL-3.0, you are granted additional permissions described in the
*** | REMIND License Exception, version 1.0 (see LICENSE file).
*** | Contact: remind@pik-potsdam.de
*** SOF ./core/equations.gms
***---------------------------------------------------------------------------
***---------------------------------------------------------------------------
***---------------------------------------------------------------------------
*** DEFINITION OF MODEL EQUATIONS:
***---------------------------------------------------------------------------
***---------------------------------------------------------------------------
***---------------------------------------------------------------------------
*' Fuel costs are associated with the use of exhaustible primary energy (fossils, uranium) and biomass.
***---------------------------------------------------------------------------
q_costFu(t,regi)..
v_costFu(t,regi)
=e=
vm_costFuBio(t,regi) + sum(peEx(enty), vm_costFuEx(t,regi,enty))
;
***---------------------------------------------------------------------------
*' Specific investment costs of learning technologies are a model-endogenous variable;
*' those of non-learning technologies are fixed to constant values.
*' Total investment costs are the product of specific costs and capacity additions plus adjustment costs.
***---------------------------------------------------------------------------
q_costInv(t,regi)..
v_costInv(t,regi)
=e=
sum(en2en(enty,enty2,te),
v_costInvTeDir(t,regi,te) + v_costInvTeAdj(t,regi,te)$teAdj(te)
)
+
sum(teNoTransform,
v_costInvTeDir(t,regi,teNoTransform) + v_costInvTeAdj(t,regi,teNoTransform)$teAdj(teNoTransform)
)
;
*RP* 2010-05-10 adjustment costs
q_costInvTeDir(t,regi,te)..
v_costInvTeDir(t,regi,te)
=e=
vm_costTeCapital(t,regi,te) * sum(te2rlf(te,rlf), vm_deltaCap(t,regi,te,rlf) )
;
*RP* 2011-12-01 remove global adjustment costs to decrease runtime, only keep regional adjustment costs. Maybe change in the future.
v_adjFactorGlob.fx(t,regi,te) = 0;
q_costInvTeAdj(t,regi,teAdj)..
v_costInvTeAdj(t,regi,teAdj)
=e=
vm_costTeCapital(t,regi,teAdj) * ( (p_adj_coeff(t,regi,teAdj) * v_adjFactor(t,regi,teAdj)) + (p_adj_coeff_glob(teAdj) * v_adjFactorGlob(t,regi,teAdj) ) )
;
***---------------------------------------------------------------------------
*' Operation and maintenance resut form costs maintenance of existing facilities according to their capacity and
*' operation of energy transformations according to the amount of produced secondary and final energy.
***---------------------------------------------------------------------------
q_costOM(t,regi)..
v_costOM(t,regi)
=e=
sum(en2en(enty,enty2,te),
pm_data(regi,"omf",te)
* sum(te2rlf(te,rlf), vm_costTeCapital(t,regi,te) * vm_cap(t,regi,te,rlf) )
+
pm_data(regi,"omv",te)
* (vm_prodSe(t,regi,enty,enty2,te)$entySe(enty2)
+ vm_prodFe(t,regi,enty,enty2,te)$entyFe(enty2))
) +
sum(teNoTransform(te),
pm_data(regi,"omf",te)
* sum(te2rlf(te,rlf),
vm_costTeCapital(t,regi,te) * vm_cap(t,regi,te,rlf)
)
)
+ vm_omcosts_cdr(t,regi)
;
***---------------------------------------------------------------------------
*' Energy balance equations equate the production of and demand for each primary, secondary and final energy.
*' The balance equation for primary energy equals supply of primary energy demand on primary energy.
***---------------------------------------------------------------------------
q_balPe(t,regi,entyPe(enty))..
vm_prodPe(t,regi,enty) + p_macPE(t,regi,enty)
=e=
sum(pe2se(enty,enty2,te), vm_demPe(t,regi,enty,enty2,te))
*** through p_datacs one could correct for non-energetic use, e.g. bitumen for roads; set to 0 in current version, as the total oil value already contains the non-energy use part
+ p_datacs(regi,enty) / 0.95
;
***---------------------------------------------------------------------------
*' The secondary energy balance comprises the following terms (except power, defined on module):
*' 1. Secondary energy can be produced from primary or (another type of) secondary energy.
*' 2. Own consumption of secondary energy occurs from the production of secondary and final energy, and from CCS technologies.
*'Own consumption is calculated as the product of the respective production and a negative coefficient.
*'The mapping defines possible combinations: the first two enty types of the mapping define the underlying
*'transformation process, the 3rd argument the technology, and the 4th argument specifies the consumed energy type.
*' 3. Couple production is modeled as own consumption, but with a positive coefficient.
*' 4. Secondary energy can be demanded to produce final or (another type of) secondary energy.
***---------------------------------------------------------------------------
q_balSe(t,regi,enty2)$( entySE(enty2) AND (NOT (sameas(enty2,"seel"))) )..
sum(pe2se(enty,enty2,te), vm_prodSe(t,regi,enty,enty2,te))
+ sum(se2se(enty,enty2,te), vm_prodSe(t,regi,enty,enty2,te))
+ sum(pc2te(enty,entySE(enty3),te,enty2),
pm_prodCouple(regi,enty,enty3,te,enty2)
* vm_prodSe(t,regi,enty,enty3,te)
)
+ sum(pc2te(enty4,entyFE(enty5),te,enty2),
pm_prodCouple(regi,enty4,enty5,te,enty2)
* vm_prodFe(t,regi,enty4,enty5,te)
)
+ sum(pc2te(enty,enty3,te,enty2),
sum(teCCS2rlf(te,rlf),
pm_prodCouple(regi,enty,enty3,te,enty2)
* vm_co2CCS(t,regi,enty,enty3,te,rlf)
)
)
*** add (reused gas from waste landfills) to segas to not account for CO2
*** emissions - it comes from biomass
+ ( sm_MtCH4_2_TWa
* ( vm_macBase(t,regi,"ch4wstl")
- vm_emiMacSector(t,regi,"ch4wstl")
)
)$( sameas(enty2,"segabio") AND t.val gt 2005 )
+ sum(prodSeOth2te(enty2,te), vm_prodSeOth(t,regi,enty2,te) )
=e=
sum(se2fe(enty2,enty3,te), vm_demSe(t,regi,enty2,enty3,te))
+ sum(se2se(enty2,enty3,te), vm_demSe(t,regi,enty2,enty3,te))
+ sum(demSeOth2te(enty2,te), vm_demSeOth(t,regi,enty2,te) )
;
***---------------------------------------------------------------------------
*' Taking the technology-specific transformation eficiency into account,
*' the equations describe the transformation of an energy type to another type.
*' Depending on the detail of the technology representation, the transformation technology's eficiency
*' can depend either only on the current year or on the year when a specific technology was built.
*' Transformation from primary to secondary energy: ***---------------------------------------------------------------------------
*MLB 05/2008* correction factor included to avoid pre-triangular infeasibility
q_transPe2se(ttot,regi,pe2se(enty,enty2,te))$(ttot.val ge cm_startyear)..
vm_demPe(ttot,regi,enty,enty2,te)
=e=
(1 / pm_eta_conv(ttot,regi,te) * vm_prodSe(ttot,regi,enty,enty2,te))$teEtaConst(te)
+
***cb early retirement for some fossil technologies
(1 - vm_capEarlyReti(ttot,regi,te))
*
sum(teSe2rlf(teEtaIncr(te),rlf),
vm_capFac(ttot,regi,te)
* (
sum(opTimeYr2te(te,opTimeYr)$(tsu2opTimeYr(ttot,opTimeYr) AND (opTimeYr.val gt 1) ),
pm_ts(ttot-(pm_tsu2opTimeYr(ttot,opTimeYr)-1))
/ pm_dataeta(ttot-(pm_tsu2opTimeYr(ttot,opTimeYr)-1),regi,te)
* pm_omeg(regi,opTimeYr+1,te)
* vm_deltaCap(ttot-(pm_tsu2opTimeYr(ttot,opTimeYr)-1),regi,te,rlf)
)
*LB* add half of the last time step ttot
+ pm_dt(ttot)/2 / pm_dataeta(ttot,regi,te)
* pm_omeg(regi,"2",te)
* vm_deltaCap(ttot,regi,te,rlf)
$ifthen setglobal END2110
- (pm_ts(ttot) / pm_dataeta(ttot,regi,te) * pm_omeg(regi,"11",te)
* 0.5*vm_deltaCap(ttot,regi,te,rlf))$(ord(ttot) eq card(ttot))
$endif
)
);
***---------------------------------------------------------------------------
*' Transformation from secondary to final energy:
***---------------------------------------------------------------------------
q_transSe2fe(t,regi,se2fe(entySE,entyFE,te)) ..
pm_eta_conv(t,regi,te)
* vm_demSE(t,regi,entySE,entyFE,te)
=e=
vm_prodFE(t,regi,entySE,entyFE,te)
;
***---------------------------------------------------------------------------
*' Transformation between secondary energy types:
***---------------------------------------------------------------------------
q_transSe2se(t,regi,se2se(enty,enty2,te))..
pm_eta_conv(t,regi,te) * vm_demSe(t,regi,enty,enty2,te)
=e=
vm_prodSe(t,regi,enty,enty2,te);
***---------------------------------------------------------------------------
*' Final energy pathway I: Direct hand-over of FEs to CES.
***---------------------------------------------------------------------------
*MLB 5/2008* add correction for initial imbalance of fehes
qm_balFeForCesAndEs(t,regi,entyFe)$(feForCes(entyFe) OR feForEs(entyFe)) ..
sum(se2fe(entySe,entyFe,te), vm_prodFE(t,regi,entySe,entyFe,te))
=e=
*** FE Pathway I: Direct hand-over of FEs to CES
sum(fe2ppfEn(entyFe,ppfEn),
vm_cesIO(t,regi,ppfEn)
+ pm_cesdata(t,regi,ppfEn,"offset_quantity")
)
*** FE Pathway III: Energy service layer (prodFe -> demFeForEs -> prodEs)
+ sum(fe2es(entyFe,esty,teEs), vm_demFeForEs(t,regi,entyFe,esty,teEs) )
*** Other demand which is not Pathway II
+ vm_otherFEdemand(t,regi,entyFe)
;
***---------------------------------------------------------------------------
*' Final energy pathway II: Useful energy layer (prodFe -> demFe -> prodUe), with capacaity tracking.
***---------------------------------------------------------------------------
*' Final energy balance
q_balFe(t,regi,entyFe)$feForUe(entyFe)..
sum(se2fe(enty,entyFe,te), vm_prodFe(t,regi,enty,entyFe,te) )
*** couple production from FE to ES for heavy duty vehicles
+ sum(pc2te(entyFE2,entyUe,te,entyFE),
pm_prodCouple(regi,entyFE2,entyUe,te,entyFE) * vm_prodUe(t,regi,entyFE2,entyUe,te) )
=e=
sum(fe2ue(entyFe,entyUe,te), v_demFe(t,regi,entyFe,entyUe,te) )
+ vm_otherFEdemand(t,regi,entyFe)
;
*' Transformation from final energy to useful energy:
q_transFe2Ue(t,regi,fe2ue(entyFe,entyUe,te))..
pm_eta_conv(t,regi,te) * v_demFe(t,regi,entyFe,entyUe,te)
=e=
vm_prodUe(t,regi,entyFe,entyUe,te);
*' Hand-over to CES:
q_esm2macro(t,regi,in)$ppfenFromUe(in)..
vm_cesIO(t,regi,in) + pm_cesdata(t,regi,in,"offset_quantity")
=e=
*** all entyFe that are first transformed into entyUe and then fed into the CES production function
sum(fe2ue(entyFe,entyUe,te)$ue2ppfen(entyUe,in), vm_prodUe(t,regi,entyFe,entyUe,te))
;
*' Definition of capacity constraints for FE to ES transformation:
q_limitCapUe(t,regi,fe2ue(entyFe,entyUe,te))..
vm_prodUe(t,regi,entyFe,entyUe,te)
=l=
sum(teue2rlf(te,rlf),
vm_capFac(t,regi,te) * vm_cap(t,regi,te,rlf)
)
;
***---------------------------------------------------------------------------
*' FE Pathway III: Energy service layer (prodFe -> demFeForEs -> prodEs), no capacity tracking.
***---------------------------------------------------------------------------
*' Transformation from final energy to useful energy:
q_transFe2Es(t,regi,fe2es(entyFe,esty,teEs))..
pm_fe2es(t,regi,teEs) * vm_demFeForEs(t,regi,entyFe,esty,teEs)
=e=
v_prodEs(t,regi,entyFe,esty,teEs);
*' Hand-over to CES:
q_es2ppfen(t,regi,in)$ppfenFromEs(in)..
vm_cesIO(t,regi,in) + pm_cesdata(t,regi,in,"offset_quantity")
=e=
sum(fe2es(entyFe,esty,teEs)$es2ppfen(esty,in), v_prodEs(t,regi,entyFe,esty,teEs))
;
*' Shares of FE carriers w.r.t. a CES node:
q_shFeCes(t,regi,entyFe,in,teEs)$feViaEs2ppfen(entyFe,in,teEs)..
sum(fe2es(entyFe2,esty,teEs2)$es2ppfen(esty,in), vm_demFeForEs(t,regi,entyFe2,esty,teEs2))
* pm_shFeCes(t,regi,entyFe,in,teEs)
=e=
sum(fe2es(entyFe,esty,teEs)$es2ppfen(esty,in), vm_demFeForEs(t,regi,entyFe,esty,teEs))
;
***---------------------------------------------------------------------------
*' Definition of capacity constraints for primary energy to secondary energy transformation:
***--------------------------------------------------------------------------
q_limitCapSe(t,regi,pe2se(enty,enty2,te))..
vm_prodSe(t,regi,enty,enty2,te)
=e=
sum(teSe2rlf(te,rlf), vm_capFac(t,regi,te) * pm_dataren(regi,"nur",rlf,te)
* vm_cap(t,regi,te,rlf)
)$(NOT teReNoBio(te))
+
sum(teRe2rlfDetail(te,rlf),
( 1$teRLDCDisp(te) + pm_dataren(regi,"nur",rlf,te)$(NOT teRLDCDisp(te)) ) * vm_capFac(t,regi,te)
* vm_capDistr(t,regi,te,rlf)
)$(teReNoBio(te))
;
***----------------------------------------------------------------------------
*' Definition of capacity constraints for secondary energy to secondary energy transformation:
***---------------------------------------------------------------------------
q_limitCapSe2se(t,regi,se2se(enty,enty2,te))..
vm_prodSe(t,regi,enty,enty2,te)
=e=
sum(teSe2rlf(te,rlf),
vm_capFac(t,regi,te) * pm_dataren(regi,"nur",rlf,te)
* vm_cap(t,regi,te,rlf)
);
***---------------------------------------------------------------------------
*' Definition of capacity constraints for secondary energy to final energy transformation:
***---------------------------------------------------------------------------
q_limitCapFe(t,regi,te)..
sum((entySe,entyFe)$(se2fe(entySe,entyFe,te)), vm_prodFe(t,regi,entySe,entyFe,te))
=l=
sum(teFe2rlf(te,rlf), vm_capFac(t,regi,te) * vm_cap(t,regi,te,rlf));
***---------------------------------------------------------------------------
*' Definition of capacity constraints for CCS technologies:
***---------------------------------------------------------------------------
q_limitCapCCS(t,regi,ccs2te(enty,enty2,te),rlf)$teCCS2rlf(te,rlf)..
vm_co2CCS(t,regi,enty,enty2,te,rlf)
=e=
sum(teCCS2rlf(te,rlf), vm_capFac(t,regi,te) * vm_cap(t,regi,te,rlf));
***-----------------------------------------------------------------------------
*' The capacities of vintaged technologies depreciate according to a vintage depreciation scheme,
*' with generally low depreciation at the beginning of the lifetime, and fast depreciation around the average lifetime.
*' Depreciation can generally be tracked for each grade separately.
*' By implementation, however, only grades of level 1 are affected. The depreciation of any fossil
*' technology can be accelerated by early retirement, which is a crucial way to quickly phase out emissions
*' after the implementation of stringent climate policies.
*' Calculation of actual capacities (exponential and vintage growth TE):
***-----------------------------------------------------------------------------
q_cap(ttot,regi,te2rlf(te,rlf))$(ttot.val ge cm_startyear)..
vm_cap(ttot,regi,te,rlf)
=e=
***cb early retirement for some fossil technologies
(1 - vm_capEarlyReti(ttot,regi,te))
*
(sum(opTimeYr2te(te,opTimeYr)$(tsu2opTimeYr(ttot,opTimeYr) AND (opTimeYr.val gt 1) ),
pm_ts(ttot-(pm_tsu2opTimeYr(ttot,opTimeYr)-1))
* pm_omeg(regi,opTimeYr+1,te)
* vm_deltaCap(ttot-(pm_tsu2opTimeYr(ttot,opTimeYr)-1),regi,te,rlf)
)
*LB* half of the last time step ttot
+ pm_dt(ttot)/2
* pm_omeg(regi,"2",te)
* vm_deltaCap(ttot,regi,te,rlf)
$ifthen setGlobal END2110
- (pm_ts(ttot)* pm_omeg(regi,"11",te)
* 0.5 * vm_deltaCap(ttot,regi,te,rlf))$(ord(ttot) eq card(ttot))
$endif
);
q_capDistr(t,regi,teReNoBio(te))..
sum(teRe2rlfDetail(te,rlf), vm_capDistr(t,regi,te,rlf) ) =e=
vm_cap(t,regi,te,"1")
;
***---------------------------------------------------------------------------
*' Technological change is an important driver of the evolution of energy systems.
*' For mature technologies, such as coal-fired power plants, the evolution
*' of techno-economic parameters is prescribed exogenously. For less mature
*' technologies with substantial potential for cost decreases via learning-bydoing,
*' investment costs are determined via an endogenous one-factor learning
*' curve approach that assumes floor costs.
***---------------------------------------------------------------------------
***---------------------------------------------------------------------------
*' Calculation of cumulated capacities (learning technologies only):
***---------------------------------------------------------------------------
qm_deltaCapCumNet(ttot,regi,teLearn)$(ord(ttot) lt card(ttot) AND pm_ttot_val(ttot+1) ge max(2010, cm_startyear))..
vm_capCum(ttot+1,regi,teLearn)
=e=
sum(te2rlf(teLearn,rlf),
(pm_ts(ttot) / 2 * vm_deltaCap(ttot,regi,teLearn,rlf)) + (pm_ts(ttot+1) / 2 * vm_deltaCap(ttot+1,regi,teLearn,rlf))
)
+
vm_capCum(ttot,regi,teLearn);
***---------------------------------------------------------------------------
*' Initial values for cumulated capacities (learning technologies only):
***---------------------------------------------------------------------------
q_capCumNet(t0,regi,teLearn)..
vm_capCum(t0,regi,teLearn)
=e=
pm_data(regi,"ccap0",teLearn);
***---------------------------------------------------------------------------
*' Additional equation for fuel shadow price calulation:
***---------------------------------------------------------------------------
*ml* reasonable results only for members of peExGrade and peren2rlf30
*NB*110625 changes for transition towards grades
qm_fuel2pe(t,regi,peRicardian(enty))..
vm_prodPe(t,regi,enty)
=e=
sum(pe2rlf(enty,rlf2),vm_fuExtr(t,regi,enty,rlf2))-(vm_Xport(t,regi,enty)-(1-pm_costsPEtradeMp(regi,enty))*vm_Mport(t,regi,enty))$(tradePe(enty)) -
sum(pe2rlf(enty2,rlf2), (pm_fuExtrOwnCons(regi, enty, enty2) * vm_fuExtr(t,regi,enty2,rlf2))$(pm_fuExtrOwnCons(regi, enty, enty2) gt 0));
***---------------------------------------------------------------------------
*' Definition of resource constraints for renewable energy types:
***---------------------------------------------------------------------------
*ml* assuming maxprod to be technical potential
q_limitProd(t,regi,teRe2rlfDetail(teReNoBio(te),rlf))..
pm_dataren(regi,"maxprod",rlf,te)
=g=
( 1$teRLDCDisp(te) + pm_dataren(regi,"nur",rlf,te)$(NOT teRLDCDisp(te)) ) * vm_capFac(t,regi,te) * vm_capDistr(t,regi,te,rlf);
***-----------------------------------------------------------------------------
*' Definition of competition for geographical potential for renewable energy types:
***-----------------------------------------------------------------------------
*RP* assuming q_limitGeopot to be geographical potential, whith luse equivalent to the land use parameter
q_limitGeopot(t,regi,peReComp(enty),rlf)..
p_datapot(regi,"limitGeopot",rlf,enty)
=g=
sum(te$teReComp2pe(enty,te,rlf), (vm_capDistr(t,regi,te,rlf) / (pm_data(regi,"luse",te)/1000)));
*** learning curve for investment costs
q_costTeCapital(t,regi,teLearn) ..
vm_costTeCapital(t,regi,teLearn)
=e=
*** special treatment for first time steps: using global estimates better
*** matches historic values
( fm_dataglob("learnMult_wFC",teLearn)
* ( ( sum(regi2, vm_capCum(t,regi2,teLearn))
+ pm_capCumForeign(t,regi,teLearn) )
** fm_dataglob("learnExp_wFC",teLearn)
)
)$( t.val le 2005 )
*** special treatment for 2010, 2015: start divergence of regional values by using a
*** t-split of global 2005 to regional 2020 in order to phase-in the observed 2020 regional
*** variation from input-data
+ ( (2020 - t.val)/15 * fm_dataglob("learnMult_wFC",teLearn)
* ( sum(regi2, vm_capCum(t,regi2,teLearn))
+ pm_capCumForeign(t,regi,teLearn)
)
** fm_dataglob("learnExp_wFC",teLearn)
+ (t.val - 2005)/15 * pm_data(regi,"learnMult_wFC",teLearn)
* ( sum(regi2, vm_capCum(t,regi2,teLearn))
+ pm_capCumForeign(t,regi,teLearn)
)
** pm_data(regi,"learnExp_wFC",teLearn)
)$( (t.val gt 2005) AND (t.val lt 2020) )
*** assuming linear convergence of regional learning curves to global values until 2050
+ ( (pm_ttot_val(t) - 2020) / 30 * fm_dataglob("learnMult_wFC",teLearn)
* ( sum(regi2, vm_capCum(t,regi2,teLearn))
+ pm_capCumForeign(t,regi,teLearn)
)
** fm_dataglob("learnExp_wFC",teLearn)
+ (2050 - pm_ttot_val(t)) / 30 * pm_data(regi,"learnMult_wFC",teLearn)
* ( sum(regi2, vm_capCum(t,regi2,teLearn))
+ pm_capCumForeign(t,regi,teLearn)
)
** pm_data(regi,"learnExp_wFC",teLearn)
)$( t.val ge 2020 AND t.val le 2050 )
*** globally harmonized costs after 2050
+ ( fm_dataglob("learnMult_wFC",teLearn)
* (sum(regi2, vm_capCum(t,regi2,teLearn)) + pm_capCumForeign(t,regi,teLearn) )
**(fm_dataglob("learnExp_wFC",teLearn))
)$(t.val gt 2050)
*** floor costs - calculated such that they coincide for all regions
+ pm_data(regi,"floorcost",teLearn)
;
***---------------------------------------------------------------------------
*' EMF27 limits on fluctuating renewables, only turned on for special EMF27 and AWP 2 scenarios, not for SSP
***---------------------------------------------------------------------------
*** this is to prevent that in the long term, all solids are supplied by biomass. Residential solids can be fully supplied by biomass (-> wood pellets), so the FE residential demand is subtracted
*** vm_cesIO(t,regi,"fesob") will be 0 in the stationary realization
q_limitBiotrmod(t,regi)$(t.val > 2020)..
vm_prodSe(t,regi,"pebiolc","sesobio","biotrmod")
- sum (in$sameAs("fesob",in), vm_cesIO(t,regi,in))
- sum (fe2es(entyFe,esty,teEs)$buildMoBio(esty), vm_demFeForEs(t,regi,entyFe,esty,teEs) )
=l=
(2 + max(0,min(1,( 2100 - pm_ttot_val(t)) / ( 2100 - 2020 ))) * 3) !! 5 in 2020 and 2 in 2100
* vm_prodSe(t,regi,"pecoal","sesofos","coaltr")
;
***-----------------------------------------------------------------------------
*' Emissions result from primary to secondary energy transformation,
*' from secondary to final energy transformation (some air pollutants), or
*' transformations within the chain of CCS steps (Leakage).
***-----------------------------------------------------------------------------
q_emiTeDetail(t,regi,enty,enty2,te,enty3)$( emi2te(enty,enty2,te,enty3)
OR ( pe2se(enty,enty2,te)
AND sameas(enty3,"cco2")) ) ..
vm_emiTeDetail(t,regi,enty,enty2,te,enty3)
=e=
sum(emi2te(enty,enty2,te,enty3), sum(pe2se(enty,enty2,te),
pm_emifac(t,regi,enty,enty2,te,enty3)
* vm_demPE(t,regi,enty,enty2,te)
)
+ sum(se2fe(enty,enty2,te),
pm_emifac(t,regi,enty,enty2,te,enty3)
* vm_prodFE(t,regi,enty,enty2,te)
)
+ sum((ccs2Leak(enty,enty2,te,enty3),teCCS2rlf(te,rlf)),
pm_emifac(t,regi,enty,enty2,te,enty3)
* vm_co2CCS(t,regi,enty,enty2,te,rlf)
)
)
;
***--------------------------------------------------
*' Total energy-emissions:
***--------------------------------------------------
*mh calculate total energy system emissions for each region and timestep:
q_emiTe(t,regi,emiTe(enty)) ..
vm_emiTe(t,regi,enty)
=e=
!! emissions from fuel combustion
sum(emi2te(enty2,enty3,te,enty),
vm_emiTeDetail(t,regi,enty2,enty3,te,enty)
)
!! emissions from non-conventional fuel extraction
+ sum(emi2fuelMine(enty,enty2,rlf),
p_cint(regi,enty,enty2,rlf)
* vm_fuExtr(t,regi,enty2,rlf)
)$( c_cint_scen eq 1 )
!! emissions from conventional fuel extraction
+ sum((pe2rlf(enty3,rlf2),enty2)$( pm_fuExtrOwnCons(regi,enty,enty2) gt 0 ),
p_cintraw(enty2)
* pm_fuExtrOwnCons(regi,enty2,enty3)
* vm_fuExtr(t,regi,enty3,rlf2)
)
!! Industry CCS emissions
- sum(emiMac2mac(emiInd37_fuel,enty2),
vm_emiIndCCS(t,regi,emiInd37_fuel)
)$( sameas(enty,"co2") )
!! Valve from cco2 capture step, to mangage if capture capacity and CCU/CCS
!! capacity don't have the same lifetime
+ v_co2capturevalve(t,regi)$( sameas(enty,"co2") )
!! CO2 from short-term CCU
+ sum(teCCU2rlf(te2,rlf),
vm_co2CCUshort(t,regi,"cco2","ccuco2short",te2,rlf)
)
;
***------------------------------------------------------
*' Mitigation options that are independent of energy consumption are represented
*' using marginal abatement cost (MAC) curves, which describe the
*' percentage of abated emissions as a function of the costs.
*' Baseline emissions are obtained by three different methods: by source (via emission factors),
*' by econometric estimate, and exogenous. Emissions are calculated as
*' baseline emissions times (1 - relative emission reduction).
*' In case of CO2 from landuse (co2luc), emissions can be negative.
*' To treat these emissions in the same framework, we subtract the minimal emission level from
*' baseline emissions. This shift factor is then added again when calculating total emissions.
*' The ndogenous baselines of non-energy emissions are calculated in the following equation:
***------------------------------------------------------
q_macBase(t,regi,enty)$( emiFuEx(enty) OR sameas(enty,"n2ofertin") ) ..
vm_macBase(t,regi,enty)
=e=
sum(emi2fuel(enty2,enty),
p_efFossilFuelExtr(regi,enty2,enty)
* sum(pe2rlf(enty2,rlf), vm_fuExtr(t,regi,enty2,rlf))
)$( emiFuEx(enty) )
+ ( p_macBaseMagpie(t,regi,enty) + p_efFossilFuelExtr(regi,"pebiolc","n2obio")
* vm_fuExtr(t,regi,"pebiolc","1")
)$( sameas(enty,"n2ofertin") )
;
***------------------------------------------------------
*' Total non-energy emissions:
***------------------------------------------------------
q_emiMacSector(t,regi,emiMacSector(enty))..
vm_emiMacSector(t,regi,enty)
=e=
( vm_macBase(t,regi,enty)
* sum(emiMac2mac(enty,enty2),
1 - (pm_macSwitch(enty) * pm_macAbatLev(t,regi,enty2))
)
)$( NOT sameas(enty,"co2cement_process") )
*** cement process emissions are accounted for in the industry module
+ ( vm_macBaseInd(t,regi,enty,"cement")
- vm_emiIndCCS(t,regi,enty)
)$( sameas(enty,"co2cement_process") )
+ p_macPolCO2luc(t,regi)$( sameas(enty,"co2luc") )
;
q_emiMac(t,regi,emiMac) ..
vm_emiMac(t,regi,emiMac)
=e=
sum(emiMacSector2emiMac(emiMacSector,emiMac),
vm_emiMacSector(t,regi,emiMacSector)
)
;
***------------------------------------------------------
*' Total regional emissions are the sum of emissions from technologies, MAC-curves, CDR-technologies and emissions that are exogenously given for REMIND.
***------------------------------------------------------
*LB* calculate total emissions for each region at each time step
q_emiAll(t,regi,emi(enty))..
vm_emiAll(t,regi,enty)
=e=
vm_emiTe(t,regi,enty)
+ vm_emiMac(t,regi,enty)
+ vm_emiCdr(t,regi,enty)
+ pm_emiExog(t,regi,enty)
;
***------------------------------------------------------
*' Total global emissions are calculated for each GHG emission type and links the energy system to the climate module.
***------------------------------------------------------
*LB* calculate total global emissions for each timestep - link to the climate module
q_emiAllGlob(t,emi(enty))..
vm_emiAllGlob(t,enty)
=e=
sum(regi,
vm_emiAll(t,regi,enty)
+ pm_emissionsForeign(t,regi,enty)
)
;
***------------------------------------------------------
*' Total regional emissions in CO2 equivalents that are part of the climate policy are computed based on regional GHG
*' emissions from different sectors(energy system, non-energy system, exogenous, CDR technologies).
***------------------------------------------------------
*mlb 8/2010* extension for multigas accounting/trading
*cb only "static" equation to be active before cm_startyear, as multigasscen could be different from a scenario to another that is fixed on the first
q_co2eq(ttot,regi)$(ttot.val ge cm_startyear)..
vm_co2eq(ttot,regi)
=e=
vm_emiAll(ttot,regi,"co2")
+ (s_tgn_2_pgc * vm_emiAll(ttot,regi,"n2o") + s_tgch4_2_pgc * vm_emiAll(ttot,regi,"ch4")) $(cm_multigasscen eq 2 or cm_multigasscen eq 3) - vm_emiMacSector(ttot,regi,"co2luc") $(cm_multigasscen eq 3);
***------------------------------------------------------
*' Total global emissions in CO2 equivalents that are part of the climate policy also take into account foreign emissions.
***------------------------------------------------------
*mlb 20140108* computation of global emissions (related to cap)
q_co2eqGlob(t) $(t.val > 2010)..
vm_co2eqGlob(t) =e= sum(regi, vm_co2eq(t,regi) + pm_co2eqForeign(t,regi));
***------------------------------------
*' Linking GHG emissions to tradable emission permits.
***------------------------------------
*mh for each region and time step: emissions + permit trade balance < emission cap
q_emiCap(t,regi) ..
vm_co2eq(t,regi) + vm_Xport(t,regi,"perm") - vm_Mport(t,regi,"perm")
+ vm_banking(t,regi)
=l= vm_perm(t,regi);
***-----------------------------------------------------------------
*** Budgets on GHG emissions (single or two subsequent time periods)
***-----------------------------------------------------------------
qm_co2eqCum(regi)..
v_co2eqCum(regi)
=e=
sum(ttot$(ttot.val lt sm_endBudgetCO2eq and ttot.val gt s_t_start),
pm_ts(ttot)
* vm_co2eq(ttot,regi)
)
+ sum(ttot$(ttot.val eq sm_endBudgetCO2eq or ttot.val eq s_t_start),
pm_ts(ttot)
/ 2
* vm_co2eq(ttot,regi)
)
;
q_budgetCO2eqGlob$(cm_emiscen=6)..
sum(regi, v_co2eqCum(regi))
=l=
sum(regi, pm_budgetCO2eq(regi));
***---------------------------------------------------------------------------
*' Definition of carbon capture :
***---------------------------------------------------------------------------
q_balcapture(t,regi,ccs2te(ccsCO2(enty),enty2,te)) ..
sum(teCCS2rlf(te,rlf),vm_co2capture(t,regi,enty,enty2,te,rlf))
=e=
sum(emi2te(enty3,enty4,te2,enty),
vm_emiTeDetail(t,regi,enty3,enty4,te2,enty)
)
+ sum(teCCS2rlf(te,rlf),
vm_ccs_cdr(t,regi,enty,enty2,te,rlf)
)
*** CCS from industry
+ sum(emiInd37,
vm_emiIndCCS(t,regi,emiInd37)
)
;
***---------------------------------------------------------------------------
*' Definition of splitting of captured CO2 to CCS, CCU and a valve (the valve
*' accounts for different lifetimes of capture, CCS and CCU technologies s.t.
*' extra capture capacities of CO2 capture can release CO2 directly to the
*' atmosphere)
***---------------------------------------------------------------------------
q_balCCUvsCCS(t,regi) ..
sum(teCCS2rlf(te,rlf), vm_co2capture(t,regi,"cco2","ico2",te,rlf))
=e=
sum(teCCS2rlf(te,rlf), vm_co2CCS(t,regi,"cco2","ico2",te,rlf))
+ sum(teCCU2rlf(te,rlf), vm_co2CCUshort(t,regi,"cco2","ccuco2short",te,rlf)) + v_co2capturevalve(t,regi)
;
***---------------------------------------------------------------------------
*' Definition of the CCS transformation chain:
***---------------------------------------------------------------------------
*** no effect while CCS chain is limited to just one step (ccsinje)
q_transCCS(t,regi,ccs2te(enty,enty2,te),ccs2te2(enty2,enty3,te2),rlf)$teCCS2rlf(te2,rlf)..
(1-pm_emifac(t,regi,enty,enty2,te,"co2")) * vm_co2CCS(t,regi,enty,enty2,te,rlf)
=e=
vm_co2CCS(t,regi,enty2,enty3,te2,rlf);
q_limitCCS(regi,ccs2te2(enty,"ico2",te),rlf)$teCCS2rlf(te,rlf)..
sum(ttot $(ttot.val ge 2005), pm_ts(ttot) * vm_co2CCS(ttot,regi,enty,"ico2",te,rlf))
=l=
pm_dataccs(regi,"quan",rlf);
***---------------------------------------------------------------------------
*' Emission constraint on SO2 after 2050:
***---------------------------------------------------------------------------
q_limitSo2(ttot+1,regi) $((pm_ttot_val(ttot+1) ge max(cm_startyear,2055)) AND (cm_emiscen gt 1) AND (ord(ttot) lt card(ttot))) ..
vm_emiTe(ttot+1,regi,"so2")
=l=
vm_emiTe(ttot,regi,"so2");
q_limitCO2(ttot+1,regi) $((pm_ttot_val(ttot+1) ge max(cm_startyear,2055)) AND (ttot.val le 2100) AND (cm_emiscen eq 8)) ..
vm_emiTe(ttot+1,regi,"co2")
=l=
vm_emiTe(ttot,regi,"co2");
q_eqadj(regi,ttot,teAdj(te))$(ttot.val ge max(2010, cm_startyear)) ..
v_adjFactor(ttot,regi,te)
=e=
power(
(sum(te2rlf(te,rlf),vm_deltaCap(ttot,regi,te,rlf)) - sum(te2rlf(te,rlf),vm_deltaCap(ttot-1,regi,te,rlf)))/(pm_ttot_val(ttot)-pm_ttot_val(ttot-1))
,2)
/( sum(te2rlf(te,rlf),vm_deltaCap(ttot-1,regi,te,rlf)) + p_adj_seed_reg(ttot,regi) * p_adj_seed_te(ttot,regi,te)
+ p_adj_deltacapoffset("2010",regi,te)$(ttot.val eq 2010) + p_adj_deltacapoffset("2015",regi,te)$(ttot.val eq 2015)
);
***---------------------------------------------------------------------------
*' The use of early retirement is restricted by the following equations:
***---------------------------------------------------------------------------
q_limitCapEarlyReti(ttot,regi,te)$(ttot.val lt 2109 AND pm_ttot_val(ttot+1) ge max(2010, cm_startyear))..
vm_capEarlyReti(ttot+1,regi,te)
=g=
vm_capEarlyReti(ttot,regi,te);
q_smoothphaseoutCapEarlyReti(ttot,regi,te)$(ttot.val lt 2120 AND pm_ttot_val(ttot+1) ge max(2010, cm_startyear))..
vm_capEarlyReti(ttot+1,regi,te)
=l=
vm_capEarlyReti(ttot,regi,te) + (pm_ttot_val(ttot+1)-pm_ttot_val(ttot)) * (cm_earlyreti_rate
*** more retirement possible for coal power plants in early time steps for Europe and USA, to account for relatively old fleet
+ p_earlyreti_adjRate(regi,te)$(ttot.val lt 2035)
*** more retirement possible for first generation biofuels
+ 0.05$(sameas(te,"biodiesel") or sameas(te, "bioeths")));
*JK* Result of split of budget equation. Sum of all energy related costs.
q_costEnergySys(ttot,regi)$( ttot.val ge cm_startyear ) ..
vm_costEnergySys(ttot,regi)
=e=
( v_costFu(ttot,regi)
+ v_costOM(ttot,regi)
+ v_costInv(ttot,regi)
)
+ sum(emiInd37, vm_IndCCSCost(ttot,regi,emiInd37))
+ pm_CementDemandReductionCost(ttot,regi)
;
***---------------------------------------------------------------------------
*' Investment equation for end-use capital investments (energy service layer):
***---------------------------------------------------------------------------
q_esCapInv(ttot,regi,teEs)$pm_esCapCost(ttot,regi,teEs) ..
vm_esCapInv(ttot,regi,teEs)
=e=
sum (fe2es(entyFe,esty,teEs),
pm_esCapCost(ttot,regi,teEs) * v_prodEs(ttot,regi,entyFe,esty,teEs)
);
;
*' Limit electricity use for fehes to 1/4th of total electricity use:
q_limitSeel2fehes(t,regi)..
1/4 * vm_usableSe(t,regi,"seel")
=g=
- vm_prodSe(t,regi,"pegeo","sehe","geohe") * pm_prodCouple(regi,"pegeo","sehe","geohe","seel")
;
*' Requires minimum share of liquids from oil in total liquids of 5%:
q_limitShOil(t,regi)..
sum(pe2se("peoil",enty2,te)$(sameas(te,"refliq") ),
vm_prodSe(t,regi,"peoil",enty2,te)
)
=g=
0.05 *
sum(se2fe(enty,enty2,te)$(sameas(te,"tdfoshos") OR sameas(te,"tdfospet") OR sameas(te,"tdfosdie") ),
vm_demSe(t,regi,enty,enty2,te)
)
;
***---------------------------------------------------------------------------
*' PE Historical Capacity:
*** set the bound at 0.9*historic capacities so that the model still needs to build additional capacity beyond the bound in order to fulfill FE demand, otherwise the calibration routine has problems
***---------------------------------------------------------------------------
q_PE_histCap(t,regi,entyPe,entySe)$(p_PE_histCap(t,regi,entyPe,entySe))..
sum(te$pe2se(entyPe,entySe,te),
sum(te2rlf(te,rlf), vm_cap(t,regi,te,rlf))
)
=g=
0.9 * p_PE_histCap(t,regi,entyPe,entySe)
;
***---------------------------------------------------------------------------
*' Share of green hydrogen in all hydrogen.
***---------------------------------------------------------------------------
q_shGreenH2(t,regi)..
sum(te, vm_prodSe(t,regi,"seel","seh2",te))
=e=
(
sum(pe2se(entyPe,"seh2",te), vm_prodSe(t,regi,entyPe,"seh2",te))
+ sum(se2se(entySe,"seh2",te), vm_prodSe(t,regi,entySe,"seh2",te))
) * v_shGreenH2(t,regi)
;
*** EOF ./core/equations.gms