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Made MIP hydrogen variables an option and made LP problem choice defa…
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…ult, to enhance clarity
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Mathias157 committed Jul 1, 2024
1 parent d1b5297 commit 91311a7
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Showing 5 changed files with 1,189 additions and 1,187 deletions.
80 changes: 40 additions & 40 deletions base/addons/hydrogen/bb4/hydrogen_balbase4.inc
Original file line number Diff line number Diff line change
@@ -1,40 +1,40 @@


QHYDROGEN_HGEHTOH2
QHYDROGEN_HGETOHH2
QHYDROGEN_H2TOEH
QHYDROGEN_EQ
QHYDROGEN_EQ_AREA
QHYDROGEN_STOMAXCON
QHYDROGEN_STOMAXLOAD
QHYDROGEN_STOMAXUNLD
QHYDROGEN_STOVOL
QHYDROGEN_GCH4KT_UP
$ifi %COMBTECH%==yes QHYDROGENGKE_UP_ADD
QBIOMETHANE_EQ
QBIOMETHANE_STOVOLTS
QGKBIOMETHANE_UP
QGKBIOGASUPGRADING_UP
QGKBIOGASMETHANATION_UP



QXH2K_UP
$ifi %H2TransInvest%==yes QXH2KNACCUMNET
$ifi %H2TransInvest%==yes QXH2KNACCUMNET_NGTOH2
$ifi %H2TransInvest%==yes QXH2INVSYMMETRY
$ifi %H2TransInvest%==yes QXH2INVSYMMETRY_NGTOH2
$ifi %H2TransInvest%==yes QXH2KMAX_NGTOH2
$ifi %H2TransInvest%==yes QVXH2KN_ES
$ifi %H2TransInvest%==yes QXH2LAMBDA_ES

* Flexible hydrogen demand in space by Ioannis
$ifi not %flexible_h2_space%==yes $goto no_flexible_h2_space
QSYNTHETIC_EQ_PRODUCTION
QSYNTHETIC_EQ_SHIFT
QSYNTHETIC_EQ_SHIFT_UP
QSYNTHETIC_EQ_SHIFT_DOWN
QSYNTHETIC_EQ_SHIFT_BALANCE_MOVE
QSYNTHETIC_EQ_SHIFT_BALANCE_OVERALL
$label no_flexible_h2_space

QHYDROGEN_HGEHTOH2
QHYDROGEN_HGETOHH2
QHYDROGEN_H2TOEH
QHYDROGEN_EQ
QHYDROGEN_EQ_AREA
QHYDROGEN_STOMAXCON
QHYDROGEN_STOMAXLOAD
QHYDROGEN_STOMAXUNLD
QHYDROGEN_STOVOL
QHYDROGEN_GCH4KT_UP
$ifi %COMBTECH%==yes QHYDROGENGKE_UP_ADD
QBIOMETHANE_EQ
QBIOMETHANE_STOVOLTS
QGKBIOMETHANE_UP
QGKBIOGASUPGRADING_UP
QGKBIOGASMETHANATION_UP
QXH2K_UP
$ifi %H2TransInvest%==yes QXH2KNACCUMNET
$ifi %H2TransInvest%==yes QXH2KNACCUMNET_NGTOH2
$ifi %H2TransInvest%==yes QXH2INVSYMMETRY
$ifi %H2TransInvest%==yes QXH2INVSYMMETRY_NGTOH2
$ifi %H2TransInvest%==yes QXH2KMAX_NGTOH2
$ifi %H2TransInvest%==yes $ifi %ES_H2TRANS%==yes QVXH2KN_ES
$ifi %H2TransInvest%==yes $ifi %ES_H2TRANS%==yes QXH2LAMBDA_ES
* Flexible hydrogen demand in space by Ioannis
$ifi not %flexible_h2_space%==yes $goto no_flexible_h2_space
QSYNTHETIC_EQ_PRODUCTION
QSYNTHETIC_EQ_SHIFT
QSYNTHETIC_EQ_SHIFT_UP
QSYNTHETIC_EQ_SHIFT_DOWN
QSYNTHETIC_EQ_SHIFT_BALANCE_MOVE
QSYNTHETIC_EQ_SHIFT_BALANCE_OVERALL
$label no_flexible_h2_space
177 changes: 89 additions & 88 deletions base/addons/hydrogen/bb4/hydrogen_qobj.inc
Original file line number Diff line number Diff line change
@@ -1,88 +1,89 @@
* -------- HYDROGEN COSTS -------- *

* Change in revenue when deviating from producing the fixed hydrogen demand
* in the transport sector specified by DH2_T_Y(AAA,S,T). Introduced to make
* it possible to specify more advanced hydrogen supply functions.
* SHOULD THE SUPPLY FUNCTION BE YEAR DEPENDANT?
*No steam reforming plants considered
$ontext
+ SUM(IA,
SUM((IS3,T), IHOURSINST(IS3,T)
* (SUM(DH2F_D,VDH2F_T(IA,IS3,T,DH2F_D)* IDEFP_T(IR,IS3,T,DEF_D1) )


)

)
)

- SUM(IR,
SUM((IS3,T), IHOURSINST(IS3,T)
* (SUM(DEF_U1, VDEF_T(IR,IS3,T,DEF_U1)* IDEFP_T(IR,IS3,T,DEF_U1) )
+ SUM(DEF_U2, VDEF_T(IR,IS3,T,DEF_U2)* IDEFP_T(IR,IS3,T,DEF_U2) ))
)
)

revenue sale of hydrogen to the transport sector
+ SUM(DH2F_U,VDH2F_T(IA,IS3,T,DH2F_U) )
* - SUM(DH2F_D,VDH2F_T(IA,IS3,T,DH2F_D) )
*
$offtext

* Variable Operation and maintainance cost of steam reforming:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GCH4TOH2), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GCH4TOH2) * SUM((IS3,T), IHOURSINST(IS3,T)*VHYDROGEN_GH2_T(Y,IA,IHYDROGEN_GCH4TOH2,IS3,T)))

* Variable Operation and maintainance cost of hydrogen storage:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GH2STO), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GH2STO) * SUM((IS3,T), IHOURSINST(IS3,T)*VHYDROGEN_GH2_T(Y,IA,IHYDROGEN_GH2STO,IS3,T)))

* Variable Operation and maintainance cost of methanation-DAC:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GH2TOBIOMETH), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GH2TOBIOMETH) * SUM((IS3,T), IHOURSINST(IS3,T)*VGBIOMETH_T(Y,IA,IHYDROGEN_GH2TOBIOMETH,IS3,T)))

* Variable Operation and maintainance cost of biogas methanation:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GBIOGASMETHANATION), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GBIOGASMETHANATION) * SUM((IS3,T), IHOURSINST(IS3,T)*VGBIOGASMETHANATION_T(Y,IA,IHYDROGEN_GBIOGASMETHANATION,IS3,T)))

* Variable Operation and maintainance cost of biogas upgrading:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GBIOGASUPGRADING), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GBIOGASUPGRADING) * SUM((IS3,T), IHOURSINST(IS3,T)*VGBIOGASUPGRADING_T(Y,IA,IHYDROGEN_GBIOGASUPGRADING,IS3,T)))


* Fixed O&M and investment costs are included in
* Balmorel.gms


* H2 transmission cost:
+ SUM((IRE,IRI)$IXH2K_HASORPOT(Y,IRE,IRI),
SUM((IS3,T), IHOURFRAC*IHOURSINST(IS3,T) * (VXH2_T(Y,IRE,IRI,IS3,T) * XH2COST(IRE,IRI))))

* Investment costs, new H2 transmission capacity
* (the average of the annuities for the two countries in question is used for international transmission):
+ SUM((IRE,IRI)$((IXH2KN(Y,IRI,IRE) OR IXH2KN(Y,IRE,IRI)) AND (NOT (IXH2KN_ES(IRE,IRI) OR IXH2KN_ES(IRI,IRE)))),IOF05*VXH2KN(Y,IRE,IRI)*XH2INVCOST(Y,IRE,IRI)*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*SUM(IYALIAS2$(ORD(IYALIAS2) EQ ORD(Y)),IYHASANNUITYXH2(IYALIAS2,Y)))

+ SUM((IRE,IRI)$(IXH2KN_NGTOH2(Y,IRI,IRE) OR IXH2KN_NGTOH2(Y,IRE,IRI)),IOF05*VXH2KN_NGTOH2(Y,IRE,IRI)*XH2INVCOST_NGTOH2(Y,IRE,IRI)*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*SUM(IYALIAS2$(ORD(IYALIAS2) EQ ORD(Y)),IYHASANNUITYXH2(IYALIAS2,Y)))

*Investment costs, H2 transmission capacity invested in previous years
+ SUM((IYALIAS2,IRE,IRI)$((IXH2KN(IYALIAS2,IRI,IRE) OR IXH2KN(IYALIAS2,IRE,IRI)) AND (NOT (IXH2KN_ES(IRE,IRI) OR IXH2KN_ES(IRI,IRE))) AND (ORD(IYALIAS2) LT ORD(Y))),IOF05*VXH2KN(IYALIAS2,IRE,IRI)*XH2INVCOST(IYALIAS2,IRE,IRI)*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*IYHASANNUITYXH2(IYALIAS2,Y))

+ SUM((IYALIAS2,IRE,IRI)$((IXH2KN_NGTOH2(IYALIAS2,IRI,IRE) OR IXH2KN_NGTOH2(IYALIAS2,IRE,IRI)) AND (ORD(IYALIAS2) LT ORD(Y))),IOF05*VXH2KN_NGTOH2(IYALIAS2,IRE,IRI)*XH2INVCOST_NGTOH2(IYALIAS2,IRE,IRI)*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*IYHASANNUITYXH2(IYALIAS2,Y))


*ECONOMIES OF SCALE
* Investment costs, new transmission capacity

+ SUM((IRE,IRI,XES)$((IXH2KN(Y,IRI,IRE) OR IXH2KN(Y,IRE,IRI)) AND (IXH2KN_ES(IRE,IRI) OR IXH2KN_ES(IRI,IRE))),
VXH2LAMBDA(Y,IRE,IRI,XES)*XH2INVCOST_ES(Y,IRE,IRI,XES)*IOF05*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*SUM(IYALIAS2$(ORD(IYALIAS2) EQ ORD(Y)),IYHASANNUITYXH2(IYALIAS2,Y)))

*Investment costs, transmission capacity invested in previous years

+ SUM((IYALIAS2,IRE,IRI,XES)$((IXH2KN(IYALIAS2,IRI,IRE) OR IXH2KN(IYALIAS2,IRE,IRI)) AND (IXH2KN_ES(IRE,IRI) OR IXH2KN_ES(IRI,IRE)) AND (ORD(IYALIAS2) LT ORD(Y))),
VXH2LAMBDA(IYALIAS2,IRE,IRI,XES)*XH2INVCOST_ES(IYALIAS2,IRE,IRI,XES)*IOF05*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*IYHASANNUITYXH2(IYALIAS2,Y))
* -------- HYDROGEN COSTS -------- *

* Change in revenue when deviating from producing the fixed hydrogen demand
* in the transport sector specified by DH2_T_Y(AAA,S,T). Introduced to make
* it possible to specify more advanced hydrogen supply functions.
* SHOULD THE SUPPLY FUNCTION BE YEAR DEPENDANT?
*No steam reforming plants considered
$ontext
+ SUM(IA,
SUM((IS3,T), IHOURSINST(IS3,T)
* (SUM(DH2F_D,VDH2F_T(IA,IS3,T,DH2F_D)* IDEFP_T(IR,IS3,T,DEF_D1) )


)

)
)

- SUM(IR,
SUM((IS3,T), IHOURSINST(IS3,T)
* (SUM(DEF_U1, VDEF_T(IR,IS3,T,DEF_U1)* IDEFP_T(IR,IS3,T,DEF_U1) )
+ SUM(DEF_U2, VDEF_T(IR,IS3,T,DEF_U2)* IDEFP_T(IR,IS3,T,DEF_U2) ))
)
)

revenue sale of hydrogen to the transport sector
+ SUM(DH2F_U,VDH2F_T(IA,IS3,T,DH2F_U) )
* - SUM(DH2F_D,VDH2F_T(IA,IS3,T,DH2F_D) )
*
$offtext

* Variable Operation and maintainance cost of steam reforming:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GCH4TOH2), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GCH4TOH2) * SUM((IS3,T), IHOURSINST(IS3,T)*VHYDROGEN_GH2_T(Y,IA,IHYDROGEN_GCH4TOH2,IS3,T)))

* Variable Operation and maintainance cost of hydrogen storage:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GH2STO), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GH2STO) * SUM((IS3,T), IHOURSINST(IS3,T)*VHYDROGEN_GH2_T(Y,IA,IHYDROGEN_GH2STO,IS3,T)))

* Variable Operation and maintainance cost of methanation-DAC:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GH2TOBIOMETH), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GH2TOBIOMETH) * SUM((IS3,T), IHOURSINST(IS3,T)*VGBIOMETH_T(Y,IA,IHYDROGEN_GH2TOBIOMETH,IS3,T)))

* Variable Operation and maintainance cost of biogas methanation:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GBIOGASMETHANATION), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GBIOGASMETHANATION) * SUM((IS3,T), IHOURSINST(IS3,T)*VGBIOGASMETHANATION_T(Y,IA,IHYDROGEN_GBIOGASMETHANATION,IS3,T)))

* Variable Operation and maintainance cost of biogas upgrading:

+ SUM(IAGK_HASORPOT(Y,IA,IHYDROGEN_GBIOGASUPGRADING), IHOURFRAC*GOMVCOSTO(IA,IHYDROGEN_GBIOGASUPGRADING) * SUM((IS3,T), IHOURSINST(IS3,T)*VGBIOGASUPGRADING_T(Y,IA,IHYDROGEN_GBIOGASUPGRADING,IS3,T)))


* Fixed O&M and investment costs are included in
* Balmorel.gms


* H2 transmission cost:
+ SUM((IRE,IRI)$IXH2K_HASORPOT(Y,IRE,IRI),
SUM((IS3,T), IHOURFRAC*IHOURSINST(IS3,T) * (VXH2_T(Y,IRE,IRI,IS3,T) * XH2COST(IRE,IRI))))

* Investment costs, new H2 transmission capacity
* (the average of the annuities for the two countries in question is used for international transmission):
+ SUM((IRE,IRI)$((IXH2KN(Y,IRI,IRE) OR IXH2KN(Y,IRE,IRI)) AND (NOT (IXH2KN_ES(IRE,IRI) OR IXH2KN_ES(IRI,IRE)))),IOF05*VXH2KN(Y,IRE,IRI)*XH2INVCOST(Y,IRE,IRI)*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*SUM(IYALIAS2$(ORD(IYALIAS2) EQ ORD(Y)),IYHASANNUITYXH2(IYALIAS2,Y)))

+ SUM((IRE,IRI)$(IXH2KN_NGTOH2(Y,IRI,IRE) OR IXH2KN_NGTOH2(Y,IRE,IRI)),IOF05*VXH2KN_NGTOH2(Y,IRE,IRI)*XH2INVCOST_NGTOH2(Y,IRE,IRI)*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*SUM(IYALIAS2$(ORD(IYALIAS2) EQ ORD(Y)),IYHASANNUITYXH2(IYALIAS2,Y)))

*Investment costs, H2 transmission capacity invested in previous years
+ SUM((IYALIAS2,IRE,IRI)$((IXH2KN(IYALIAS2,IRI,IRE) OR IXH2KN(IYALIAS2,IRE,IRI)) AND (NOT (IXH2KN_ES(IRE,IRI) OR IXH2KN_ES(IRI,IRE))) AND (ORD(IYALIAS2) LT ORD(Y))),IOF05*VXH2KN(IYALIAS2,IRE,IRI)*XH2INVCOST(IYALIAS2,IRE,IRI)*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*IYHASANNUITYXH2(IYALIAS2,Y))

+ SUM((IYALIAS2,IRE,IRI)$((IXH2KN_NGTOH2(IYALIAS2,IRI,IRE) OR IXH2KN_NGTOH2(IYALIAS2,IRE,IRI)) AND (ORD(IYALIAS2) LT ORD(Y))),IOF05*VXH2KN_NGTOH2(IYALIAS2,IRE,IRI)*XH2INVCOST_NGTOH2(IYALIAS2,IRE,IRI)*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*IYHASANNUITYXH2(IYALIAS2,Y))


*ECONOMIES OF SCALE
* Investment costs, new transmission capacity
$ifi not %ES_H2TRANS%==yes $goto no_economy_of_scale
+ SUM((IRE,IRI,XES)$((IXH2KN(Y,IRI,IRE) OR IXH2KN(Y,IRE,IRI)) AND (IXH2KN_ES(IRE,IRI) OR IXH2KN_ES(IRI,IRE))),
VXH2LAMBDA(Y,IRE,IRI,XES)*XH2INVCOST_ES(Y,IRE,IRI,XES)*IOF05*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*SUM(IYALIAS2$(ORD(IYALIAS2) EQ ORD(Y)),IYHASANNUITYXH2(IYALIAS2,Y)))

*Investment costs, transmission capacity invested in previous years

+ SUM((IYALIAS2,IRE,IRI,XES)$((IXH2KN(IYALIAS2,IRI,IRE) OR IXH2KN(IYALIAS2,IRE,IRI)) AND (IXH2KN_ES(IRE,IRI) OR IXH2KN_ES(IRI,IRE)) AND (ORD(IYALIAS2) LT ORD(Y))),
VXH2LAMBDA(IYALIAS2,IRE,IRI,XES)*XH2INVCOST_ES(IYALIAS2,IRE,IRI,XES)*IOF05*
(IOF05* (SUM(C$CCCRRR(C,IRE),ANNUITYCXH2(C))+SUM(C$CCCRRR(C,IRI),ANNUITYCXH2(C))))*IYHASANNUITYXH2(IYALIAS2,Y))
$label no_economy_of_scale
14 changes: 7 additions & 7 deletions base/addons/hydrogen/bb4/hydrogen_varassign.inc
Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
* File hydrogen_varassign.inc for addon hydrogen.

$ifi %H2TransInvest%==yes VXH2KN.FX(IY411FIRST,IRE,IRI)$SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN(Y,IRE,IRI))= VXH2KN.L(IY411FIRST,IRE,IRI);
$ifi %H2TransInvest%==yes VXH2KNACCUMNET.FX(IY411FIRST,IRE,IRI)$SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN(Y,IRE,IRI))= VXH2KNACCUMNET.L(IY411FIRST,IRE,IRI);
$ifi %H2TransInvest%==yes VXH2KN_NGTOH2.FX(IY411FIRST,IRE,IRI)$SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN_NGTOH2(Y,IRE,IRI))= VXH2KN_NGTOH2.L(IY411FIRST,IRE,IRI);
$ifi %H2TransInvest%==yes VXH2KNACCUMNET_NGTOH2.FX(IY411FIRST,IRE,IRI)$SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN_NGTOH2(Y,IRE,IRI))= VXH2KNACCUMNET_NGTOH2.L(IY411FIRST,IRE,IRI);
$ifi %H2TransInvest%==yes VXH2LAMBDA.FX(IY411FIRST,IRE,IRI,XES)$(SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN(Y,IRE,IRI)) AND IXH2KN_ES(IRE,IRI))=VXH2LAMBDA.L(IY411FIRST,IRE,IRI,XES);
* File hydrogen_varassign.inc for addon hydrogen.
$ifi %H2TransInvest%==yes VXH2KN.FX(IY411FIRST,IRE,IRI)$SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN(Y,IRE,IRI))= VXH2KN.L(IY411FIRST,IRE,IRI);
$ifi %H2TransInvest%==yes VXH2KNACCUMNET.FX(IY411FIRST,IRE,IRI)$SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN(Y,IRE,IRI))= VXH2KNACCUMNET.L(IY411FIRST,IRE,IRI);
$ifi %H2TransInvest%==yes VXH2KN_NGTOH2.FX(IY411FIRST,IRE,IRI)$SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN_NGTOH2(Y,IRE,IRI))= VXH2KN_NGTOH2.L(IY411FIRST,IRE,IRI);
$ifi %H2TransInvest%==yes VXH2KNACCUMNET_NGTOH2.FX(IY411FIRST,IRE,IRI)$SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN_NGTOH2(Y,IRE,IRI))= VXH2KNACCUMNET_NGTOH2.L(IY411FIRST,IRE,IRI);
$ifi %H2TransInvest%==yes $ifi %ES_H2TRANS%==yes VXH2LAMBDA.FX(IY411FIRST,IRE,IRI,XES)$(SUM(Y$(YVALUE(Y) LE YVALUE(IY411FIRST)),IXH2KN(Y,IRE,IRI)) AND IXH2KN_ES(IRE,IRI))=VXH2LAMBDA.L(IY411FIRST,IRE,IRI,XES);
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