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eqobjinv.mod
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eqobjinv.mod
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*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
* Copyright (C) 2000-2023 Energy Technology Systems Analysis Programme (ETSAP)
* This file is part of the IEA-ETSAP TIMES model generator, licensed
* under the GNU General Public License v3.0 (see file NOTICE-GPLv3.txt).
*=============================================================================*
* EQOBJINV the objective functions on investments
* - Investment Costs
* - Investmnet Tax/Subsidies
* - Decommissioning
*=============================================================================*
*GaG Questions/Comments:
* - Note that V=T in OBJ.DOC, but in the code V is assocated with the vintage year,
* that is the year of investment as distinguished from T = the current MILESTONYR
* - COEF_RPTI calculated in PPMAIN.MOD
* - combining all the INVs into a single equation at the moment
*-----------------------------------------------------------------------------
*$ONLISTING
* Discounting shift is zero unless the user says otherwise:
$IF NOT SET DISCSHIFT $SETGLOBAL DISCSHIFT 0
* If annual cost should be reported for TLIFE years and not just ELIFE,
* change INVLIF and DECLIF to TLIFE and DLIFE instead of ELIFE and DELIF
$SETGLOBAL INVLIF ELIFE
$SETGLOBAL DECLIF DELIF
* For loop controls
ALIAS(AGE,JOT);
SCALARS OBJ_C /0/, OBJ_D /0/;
* OBJ coefficient SUM control set with the ALLYEAR indexes in sequence =
* V - investment vintage year, K - commissioning index, Y - decommissioning index
SET OBJ_SUMII(R,ALLYEAR,P,AGE,ALLYEAR,AGE) //;
SET OBJ_SUMIII(R,ALLYEAR,P,ALLYEAR,YEAR,ALLYEAR)//;
SET OBJ_YES(REG,ALLYEAR,P) //;
SET OBJ_I2(REG,ALLYEAR,P) //;
SET YKAGE(ALLYEAR,ALLYEAR,AGE) //;
SET KAGE(ALLYEAR,AGE) //;
SET OBJ_SPRED(R,ALLYEAR,P,AGE) //;
SET INVSTEP(ALLYEAR,AGE,ALLYEAR,AGE) //;
SET INVSPRED(ALLYEAR,AGE,ALLYEAR,ALLYEAR) //;
PARAMETER OBJ_PASTI(REG,ALLYEAR,P,CUR) //;
PARAMETER SALV_INV(REG,ALLYEAR,PRC,ALLYEAR) //;
PARAMETER COR_SALVI(REG,ALLYEAR,PRC,CUR) //;
PARAMETER COR_SALVD(REG,ALLYEAR,PRC,CUR) //;
PARAMETER OBJ_DIVI(REG,ALLYEAR,PRC) //;
PARAMETER OBJ_DIVIII(REG,ALLYEAR,PRC) //;
SET OBJ_IDC(R,ALLYEAR,P,LIFE,ALLYEAR,AGE);
PARAMETER OBJ_IAD(R,CUR);
*===============================================================================
* Hold on to those RTPs for which some investment related cost is provided
*===============================================================================
* Investment
RTP(R,PASTMILE,P)$(NCAP_PASTI(R,PASTMILE,P)=0) = NO;
OBJ_ICUR(RTP(R,V,P),CUR)$(OBJ_ICOST(R,V,P,CUR) + OBJ_ISUB(R,V,P,CUR) + OBJ_ITAX(R,V,P,CUR)) = YES;
* if ETL technology then going to do it as well
$IF '%ETL%'==YES OBJ_ICUR(RTP(R,V,TEG),CUR)$G_RCUR(R,CUR) = YES;
* Decommissioning
OBJ_ICUR(RTP(R,V,P),CUR)$OBJ_DCOST(R,V,P,CUR) = YES;
LOOP(CUR,OBJ_SUMS3(RTP(R,V,P))$OBJ_DCOST(R,V,P,CUR) = YES);
LOOP((RTP,COM)$NCAP_OCOM(RTP,COM),OBJ_SUMS3(RTP) = YES);
* Currency independent OBJ_YES
OBJ_ICUR(RTP_OFF,CUR)$(NOT NCAP_PASTI(RTP_OFF)) = NO;
OBJ_ICUR(R,LL,P,CUR)$(NOT RDCUR(R,CUR)) = NO;
OPTION OBJ_YES < OBJ_ICUR; OBJ_YES(OBJ_SUMS3) = YES;
* Correct small TLIFE and DLIFE values, because rounded values are used as divisors
NCAP_TLIFE(OBJ_YES(R,V,P))$(ROUND(NCAP_TLIFE(R,V,P)) LE 0) = 1;
NCAP_ELIFE(OBJ_YES(R,V,P))$(ROUND(NCAP_ELIFE(R,V,P)) LE 0) = 1;
NCAP_DLIFE(OBJ_SUMS3(R,V,P))$(ROUND(NCAP_DLIFE(R,V,P)) LE 0) = 1;
NCAP_DELIF(OBJ_SUMS3(R,V,P)) = MAX(1,NCAP_DELIF(R,V,P));
* Classify processes into I1 / I2 Cases
OBJ_I2(RTP)$NCAP_ILED(RTP) = YES;
LOOP(SAMEAS(LIFE,'1'),OBJ_SPRED(OBJ_YES(R,V,P),LIFE+MAX(0,MIN(CARD(AGE),NCAP_%INVLIF%(R,V,P))-1))=YES);
*------------------------------------------------------------------------------
* COR_SALVI can be used to take into account technology-specific discount rate
* Take also into account a user-defined discounting shift (0/0.5/1 years):
COR_SALVI(OBJ_ICUR(R,V,P,CUR))=(((((1+NCAP_DRATE(R,V,P))/(1+OBJ_RFR(R,V,CUR)))**%DISCSHIFT%)*
((1-1/(1+NCAP_DRATE(R,V,P)))*(1-(1+OBJ_RFR(R,V,CUR))**(-NCAP_ELIFE(R,V,P))))/
((1-1/(1+OBJ_RFR(R,V,CUR)))*(1-(1+NCAP_DRATE(R,V,P))**(-NCAP_ELIFE(R,V,P))))
-1)$(NCAP_DRATE(R,V,P) GT 0) + 1)*(1+G_DRATE(R,V,CUR))**%DISCSHIFT%;
COR_SALVI(OBJ_ICUR(OBJ_I2(R,V,P),CUR)) = COR_SALVI(R,V,P,CUR) / ((1+G_DRATE(R,V,CUR))**%DISCSHIFT%);
* OBJ_CRF/OBJ_CRFD must now be based on G_DRATE because we use COR_SALVI and COR_SALVD for the correction
OBJ_CRF(OBJ_ICUR(R,V,P,CUR)) = COR_SALVI(R,V,P,CUR) * (1-(1/(1+G_DRATE(R,V,CUR)))) / (1-(1+G_DRATE(R,V,CUR))**(-ROUND(NCAP_%INVLIF%(R,V,P))));
*------------------------------------------------------------------------------
* OBJ_PASTI is the correction for past investments (similar to SALV_INV fraction)
OBJ_PASTI(OBJ_ICUR(RTP(R,PASTYEAR(V),P),CUR)) = NCAP_PASTI(R,V,P) *
MAX(0,MIN(1,(((1+G_DRATE(R,V,CUR))**(YEARVAL(V)+ROUND(NCAP_ILED(R,V,P))-MINYR+NCAP_%INVLIF%(R,V,P))-1) /
((1+G_DRATE(R,V,CUR))**NCAP_%INVLIF%(R,V,P)-1))));
*------------------------------------------------------------------------------
* Operating years for all technical lifetimes
Z=SMAX((RTP(R,PYR_S(V),P),T)$PRC_RESID(R,T,P),E(T))-MIYR_V1+2;
MAXLIFE = MAX(SMAX(T,2*D(T)),Z,CEIL(MAXLIFE));
OPYEAR(LIFE,AGE)$((ORD(AGE) LE ORD(LIFE))$(ORD(LIFE) LE MAXLIFE)) = YES;
*--------------------------------------------------------------------------------------
$ SET ZHALF "CEIL(Z/2-.5)" SET ISTEP IPD(T)
$ IF NOT '%CTST%'=='' $SET ZHALF "FLOOR(ROUND(Z)/2)" SET ISTEP MIN(IPD(T),ROUND(Z))
*===============================================================================
* Case 1.a: ILEDt <= ILEDmin,t and TLIFEt + ILEDt >= D(t)
*===============================================================================
OBJ_1A(RTP(R,V,P))$((NOT OBJ_I2(R,V,P))$(COEF_RPTI(R,V,P) LT 1.01)) = YES;
*------------------------------------------------------------------------------
* build trapazoid covering year and number of payment blocks for a process
*------------------------------------------------------------------------------
* - K is EACHYEAR
* beginning from the
* MAX(period length before the middle year of the current (investment)
* period, or the current year - the economic lifetime + 1)
* until the
* MIN(middle year of the current (investment) period - 1, or the year
* calculating)
*===============================================================================
* Case I/II.1.a: Investment/Tax&Sub ILEDt <= ILEDmin,t and TLIFEt + ILEDt >= D(t)
*===============================================================================
* there is a relevant cost
*V1.3a speed up code a bit
$IF '%VALIDATE%' == 'YES' $GOTO M2T
* Set period parameters for Case 1a:
FIL2(V) = (IPD(V)-1)$T(V);
MY_ARRAY(V) = B(V)-YEARVAL(V) + (M(V)-B(V)-FIL2(V))$T(V);
LOOP(SAMEAS(AGE,'1'),
* K is both investment year and cost/commissioning year
OBJ_SUMII(OBJ_SPRED(OBJ_1A(R,V(LL),P),LIFE),K(LL+MY_ARRAY(LL)),AGE+FIL2(V)) = YES;
);
$GOTO CONT
* create square for investment costing if validating MARKAL
$LABEL M2T
* Y is investment year, V is cost basis year
OBJ_SUMII(OBJ_SPRED(OBJ_1A(R,V,P),LIFE),Y,'1')$(YEARVAL(Y) = B(V)) = YES;
$LABEL CONT
*===============================================================================
* Case 1.b: ILEDt <= ILEDmin,t and TLIFEt + ILEDt < D(t)
* Note - no PASTINV as TLIFE always >= D(t) which = 1
*===============================================================================
OBJ_1B(RTP(R,T,P))$((NOT OBJ_I2(R,T,P))$(NOT OBJ_1A(R,T,P))) = YES;
*===============================================================================
* Case I/II.1.b: Investment/Tax&Sub ILEDt <= ILEDmin,t and TLIFEt + ILEDt < D(t)
* Note - no PASTINV as TLIFE always >= D(t) which = 1
*===============================================================================
*------------------------------------------------------------------------------
* build repeated investment blocks until end of lifetime
*------------------------------------------------------------------------------
* calculate the contribution in each year, if there is a cost
$IF '%VALIDATE%' == 'YES' $GOTO M2T_2
LOOP(SAMEAS(AGE,'1'),
LOOP(OBJ_SPRED(OBJ_1B(R,T(LL),P),LIFE),
Z = NCAP_TLIFE(R,T,P);
* Slightly different handling according to objective formulation
IF((ROUND(Z)-IPD(T)%CTST%) LE 0,
F = B(T) - %ZHALF% - YEARVAL(T);
Z = ROUND(COEF_RPTI(R,T,P)*Z)-1;
* LL+F is both first investment year and first cost/commissioning year
OBJ_SUMII(R,T,P,LIFE,K(LL+F),AGE+Z) = YES;
ELSE CNT = %ISTEP%; F = B(T)-YEARVAL(T)-FLOOR(CNT/2); CNT = CNT-1;
FOR(OBJ_C = 1 TO COEF_RPTI(R,T,P),
OBJ_SUMII(R,T,P,LIFE,K(LL+F),AGE+CNT) = YES; F = F+Z));
);
);
$GOTO CONT_2
* create square for investment costing if validating MARKAL
$LABEL M2T_2
LOOP(OBJ_SPRED(OBJ_1B(R,T(LL),P),LIFE),
Z = NCAP_TLIFE(R,T,P);
FOR(OBJ_C = 1 TO COEF_RPTI(R,T,P),
F = B(T) + ROUND((OBJ_C-1)*Z) - YEARVAL(T);
* Y is investment year, T is cost basis year
OBJ_SUMII(R,T,P,LIFE,Y(LL+F),'1') = YES);
);
$LABEL CONT_2
*===============================================================================
* Case 2.a: ILEDt > ILEDmin,t and TLIFEt + ILEDt >= D(t)
*===============================================================================
OBJ_2A(OBJ_I2(R,V,P))$(COEF_RPTI(R,V,P) LE 1) = YES;
*===============================================================================
* Case I/II.2.a: Investment/Tax&Sub ILEDt > ILEDmin,t and TLIFEt + ILEDt >= D(t)
*===============================================================================
*------------------------------------------------------------------------------
* build trapazoid covering year and number of payment blocks for a process
* - K is EACHYEAR
* for MILESTONYR or PASTYEAR
* beginning from the
* MAX(beginning of the period, or the current year - the economic lifetime + 1)
* until the
* MIN(beginning of the period + leadtime - 1, or the year calculating)
*------------------------------------------------------------------------------
* there is a relevant cost
LOOP(SAMEAS(AGE,'1'),
LOOP(OBJ_SPRED(OBJ_2A(R,V(LL),P),LIFE),
Z = NCAP_ILED(R,V,P); MY_F = B(V)-YEARVAL(V)+Z;
* LL+F is investment year; LL+MY_F is commissioning year (cost basis)
OBJ_IDC(R,V,P,LIFE,LL+MY_F,AGE+MAX(0,Z-1)) = YES;
));
*===============================================================================
* Case 2.b: ILEDt > ILEDmin,t and TLIFEt + ILEDt < D(t)
* Note - no PASTINV as TLIFE always >= D(t) which = 1
*===============================================================================
OBJ_2B(OBJ_I2(R,T,P))$(NOT OBJ_2A(R,T,P)) = YES;
*===============================================================================
* Case I/II.2.b: Investment/Tax&Sub ILEDt > ILEDmin,t and TLIFEt + ILEDt < D(t)
* Note - no PASTINV as TLIFE always >= D(t) which = 1
*===============================================================================
*------------------------------------------------------------------------------
* build repeated investment blocks until end of lifetime
*------------------------------------------------------------------------------
* calculate the contribution in each year, if there is a cost
LOOP(SAMEAS(AGE,'1'),
LOOP(OBJ_SPRED(OBJ_2B(R,T(LL),P),LIFE),
FOR(OBJ_C = 1 TO COEF_RPTI(R,T,P),
Z = NCAP_ILED(R,T,P);
MY_F = ROUND(B(T)+(OBJ_C-1)*NCAP_TLIFE(R,T,P))-YEARVAL(T)+Z;
* LL+F is investment year; LL+MY_F is commissioning year (cost basis)
OBJ_IDC(R,T,P,LIFE,LL+MY_F,AGE+MAX(0,Z-1)) = YES);
));
*===============================================================================
* Calculate Interest During Construction (IDC) for any fractional ILED
* Note: Zero ILED represents half year's interest, consistently
LOOP(OBJ_ICUR(OBJ_I2(R,V,P),CUR), Z = COEF_ILED(R,V,P);
IF(Z, OBJ_C=1+G_DRATE(R,V,CUR); MY_F=0; F=0;
*..Interest according to rounded spreads using actual discount rates
LOOP(OBJ_IDC(R,V,P,LIFE,LL,JOT), CNT=ORD(JOT);
MY_F=MY_F+SUM((OPYEAR(JOT,AGE),YEAR(LL-ORD(AGE))),OBJ_DISC(R,YEAR,CUR)); F=F+OBJ_DISC(R,LL,CUR));
MY_F = MY_F/F/CNT-1;
*..Interest according to rounded and accurate spreads using constant discount rate
F = ((OBJ_C**CNT)-1)/(1-1/OBJ_C)/CNT-1;
CNT = MAX(0.001,Z);
Z = ((OBJ_C**CNT)-1)/(1-1/OBJ_C)/CNT-1;
ELSE F=1); OBJ_DIVI(R,V,P) = 1/(1+Z*MY_F/F));
* Add spread header tuples
OBJ_SUMII(R,V,P,LIFE,LL,JOT+(1-ORD(JOT)))$OBJ_IDC(R,V,P,LIFE,LL,JOT) = YES;
OPTION CLEAR=OBJ_IDC;
*===============================================================================
* Generate the Investment spreads
*===============================================================================
OPTION KAGE < OBJ_SUMII;
INVSTEP(KAGE(LL,JOT),LL+(ORD(AGE)-1),AGE+(ORD(JOT)-ORD(AGE)))$OPYEAR(JOT,AGE) = YES;
$IF NOT '%CTST%'=='' $BATINCLUDE coef_alt.lin INV
INVSPRED(LL,JOT,K,K)$INVSTEP(LL,JOT,K,JOT) = YES;
*===============================================================================
* Case III.1.a-b, III.2.a-b: Decommissioning
*===============================================================================
OPTION CLEAR=UNCD7;
* Collect header tuples for decommissioning spreads
UNCD7(OBJ_SUMS3(R,V,P),LIFE+(NCAP_DLIFE(R,V,P)-ORD(LIFE)),LL--(ORD(LL)$OBJ_I2(R,V,P)),LL,JOT)$OBJ_SUMII(R,V,P,LIFE,LL,JOT) = YES;
* Generate the Decommissioning spreads
OPTION CLEAR = YKAGE;
LOOP(UNCD7(R,V,P,LIFE,LASTLL(LL),K,JOT),YKAGE(LL,K,LIFE) = YES);
LOOP(YKAGE(YEAR,K(LL),JOT),INVSPRED(YEAR,AGE+(ORD(JOT)-ORD(AGE)),LL+(ORD(AGE)-1),K)$OPYEAR(JOT,AGE) = YES);
LOOP(UNCD7(R,V,P,LIFE,YEAR,K_EOH,JOT), F = CEIL(NCAP_TLIFE(R,V,P)+NCAP_DLAG(R,V,P));
* K is commissioning year (cost basis), LL+F is decommissioning year
IF(LASTLL(YEAR),
OBJ_SUMIII(R,V,P,K(K_EOH),K,LL+F)$INVSPRED(YEAR,LIFE,LL,K_EOH) = YES;
ELSE OBJ_SUMIII(R,V,P,LL, K,LL+F)$INVSPRED(K_EOH,JOT,LL,K) = YES));
INVSPRED('0',JOT,YEAR,K) = NO;
*------------------------------------------------------------------------------
* The equation divisors for investments:
$IF NOT '%CTST%'=='' $GOTO CLRS
OBJ_DIVI(OBJ_YES(OBJ_1A(R,V,P))) = 1+(IPD(V)-1)$MILESTONYR(V);
OBJ_DIVI(OBJ_YES(OBJ_1B(R,T,P))) = NCAP_TLIFE(R,T,P);
IF(ALTOBJ,OBJ_DIVI(OBJ_YES(OBJ_1B(R,T,P)))$((ROUND(NCAP_TLIFE(R,T,P))-IPD(T)%CTST%) GT 0) = IPD(T)*MIN(1,NCAP_TLIFE(R,T,P)));
$IF '%VALIDATE%'== YES OBJ_DIVI(OBJ_YES(R,T,P))$(NOT OBJ_I2(R,T,P)) = 1;
* The equation divisors for decommissioning :
OBJ_DIVIII(OBJ_SUMS3(R,V,P)) = OBJ_DIVI(R,V,P);
OBJ_DIVIII(OBJ_SUMS3(OBJ_I2(R,V,P))) = ROUND(NCAP_DLIFE(R,V,P));
$IF '%VALIDATE%' == YES OPTION CLEAR=OBJ_PASTI;
*------------------------------------------------------------------------------
$LABEL CLRS
OPTION CLEAR = OBJ_YES, CLEAR = OBJ_SUMS3, CLEAR = YKAGE;
OPTION CLEAR = INVSTEP, CLEAR = OBJ_SPRED, CLEAR = OBJ_I2;
$LABEL EQUA %2
*===============================================================================
* Generate Investment equation summing over all active indexes by region and currency
*===============================================================================
%EQ%_OBJINV(RDCUR(R,CUR) %SOW%) ..
*------------------------------------------------------------------------------
* Cases I - Investment Cost and II - Taxes/Subsidies
*------------------------------------------------------------------------------
SUM(OBJ_SUMII(R,T,P,LIFE,K_EOH,JOT)$OBJ_ICUR(R,T,P,CUR), %CAPJD%
SUM(INVSPRED(K_EOH,JOT,Y,K), OBJ_DISC(R,K,CUR) *
(OBJ_ICOST(R,K,P,CUR) + OBJ_ITAX(R,K,P,CUR) - OBJ_ISUB(R,K,P,CUR))) *
COR_SALVI(R,T,P,CUR) / OBJ_DIVI(R,T,P) * %VART%_NCAP(R,T,P %SWS%)
* handle ETL
$IF '%ETL%'==YES + SUM(G_RCUR(R,CUR),%VART%_IC(R,T,P %SWS%)*SUM(INVSPRED(K_EOH,JOT,Y,K),OBJ_DISC(R,K,CUR))*COR_SALVI(R,T,P,CUR)/OBJ_DIVI(R,T,P))$SEG(R,P)
)
+
$IFI NOT %STAGES%==YES $GOTO PASTI
SUM((OBJ_SUMII(R,T,P,LIFE,K_EOH,JOT),SW_TSW(SOW,T,WW))$OBJ_SIC(R,T,P,WW), %CAPJD%
SUM(INVSPRED(K_EOH,JOT,Y,K), OBJ_DISC(R,K,CUR) * OBJ_ICOST(R,K,P,CUR) * (1-SALV_INV(R,T,P,Y))) *
OBJ_SIC(R,T,P,WW) * COR_SALVI(R,T,P,CUR) / OBJ_DIVI(R,T,P) * %VAR%_NCAP(R,T,P %SWD%)) +
$LABEL PASTI
* PASTI charge
SUM(OBJ_SUMII(R,PASTYEAR(V),P,LIFE,K_EOH,JOT)$OBJ_PASTI(R,V,P,CUR), %CAPJD%
SUM(INVSPRED(K_EOH,JOT,LL,K), OBJ_DISC(R,K,CUR) *
(OBJ_ICOST(R,K,P,CUR) + OBJ_ITAX(R,K,P,CUR) - OBJ_ISUB(R,K,P,CUR))) *
OBJ_PASTI(R,V,P,CUR) * COR_SALVI(R,V,P,CUR) / OBJ_DIVI(R,V,P))
+ OBJ_IAD(R,CUR) +
*------------------------------------------------------------------------------
* Cases III - Decommissioning
*------------------------------------------------------------------------------
SUM(OBJ_SUMIII(R,V,P,LL,K,Y)$OBJ_DCOST(R,V,P,CUR),
OBJ_DISC(R,Y,CUR) * COR_SALVD(R,V,P,CUR) * OBJ_DCOST(R,K,P,CUR) *
(%VARV%_NCAP(R,V,P %SWS%)$MILESTONYR(V) + OBJ_PASTI(R,V,P,CUR)$PASTYEAR(V)) / OBJ_DIVIII(R,V,P))
=E=
SUM(OBV,SUM_OBJ('OBJINV',OBV)*%VAR%_OBJ(R,OBV,CUR %SOW%));
*$OFFLISTING