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Model.gms
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*###############################################################################
*
* Model
*
*###############################################################################
Variables
COST Total costs = objective value
COST_GEN(year_all) Yearly generation costs
COST_INV(year_all) Yearly investment costs
COST_FIX(year_all) Yearly fix costs
CAP_CONV_RAMP(country_all,conv,year_all,hour_all) Ramped capacity of conventional technologies
;
Positive Variables
GEN_CONV(country_all,conv,year_all,hour_all) Generation of conventional technologies
GEN_CONV_FULL(country_all,conv,year_all,hour_all) Generation of conventional technologies at full capacity
GEN_CONV_MIN(country_all,conv,year_all,hour_all) Generation of conventional technologies at full minimum capacity
CAP_CONV_RTO(country_all,conv,year_all,hour_all) Capacity ready-to-operate of conventional technologies
CAP_CONV_UP(country_all,conv,year_all,hour_all) Startup capacity of conventional technologies
CAP_CONV_DOWN(country_all,conv,year_all,hour_all) Shutdown capacity of conventional technologies
CAP_CONV_ADD(country_all,conv,year_all) Capacity investment in conventional technologies
CAP_CONV_SUB(country_all,conv,year_all) Capacity divestment in conventional technologies
CAP_CONV_INSTALL(country_all,conv,year_all) Installed capacity in year of conventional technology
GEN_RENEW(country_all,renew,year_all,hour_all) Generation of renewable technologies
CURT_RENEW(country_all,renew,year_all,hour_all) Renewable curtailment
CURT_LOAD(country_all,year_all,hour_all) Load curtailment
LEVEL(country_all,stor,year_all,hour_all) Energy level of the storage
CHARGE(country_all,stor,year_all,hour_all) Charge the storage
DISCHARGE(country_all,stor,year_all,hour_all) Discharge the storage
FLOW(country_all,country_all,year_all,hour_all) Export flow from A to B
;
Equations
DEF_COST Definition of COST
DEF_COST_GEN Definition of COST_GEN
DEF_COST_INV Definition of COST_INV
DEF_COST_FIX Definition of COST_FIX
MCC Market clearing condition (Energy balance)
DEF_CAP_CONV_RTO Definition of CAP_CONV_RTO
RES_CAP_CONV_RTO_up Upper bound for CAP_CONV_RTO
DEF_GEN_CONV Definition of GEN_CONV
RES_GEN_CONV_up Upper bound for GEN_CONV
RES_GEN_CONV_MIN_lo Lower bound for GEN_CONV_MIN
RES_GEN_CONV_lo Lower bound for GEN_CONV (due to chp production)
DEF_CAP_CONV_INSTALL Definition of CAP_CONV_INSTALL
DEF_CAP_CONV_INSTALL_start Definition of the start condition for CAP_CONV_INSTALL
RES_CAP_CONV_SUB_lo Lower bound for CAP_CONV_SUB
RES_GEN_RENEW_up Upper bound for GEN_RENEW
RES_GEN_RENEW_lo Lower bound for GEN_RENEW (due to chp production)
RES_GEN_RENEW_yearly_potential Restriction of renewable generation due to yearly fuel potential
RES_GEN_RENEW_monthly_potential Restriction of renewable generation due to monthly fuel potential
RES_GEN_RENEW_reservoir_up Upper bound for reservoir generation
RES_GEN_RENEW_reservoir_lo Lower bound for reservoir generation
DEF_GEN_RENEW_curt Definition of GEN_RENEW for curtailable technologies
DEF_GEN_RENEW_ncurt Definition of GEN_RENEW for non-curtailable technologies
DEF_LEVEL Definition of LEVEL
DEF_LEVEL_start Definition of the start condition for LEVEL
DEF_LEVEL_end Definition of the end condition for LEVEL
RES_LEVEL_up Upper bound for LEVEL
RES_LEVEL_lo Lower bound for LEVEL
RES_CHARGE_up Upper bound for CHARGE
RES_DISCHARGE_up Upper bound for DISCHARGE
RES_EMISSION_up Upper bound for total yearly co2 emissions
RES_FLOW_up Upper bound for FLOW (export congestion)
RES_CAP_CONV_ADD_up
RES_CAP_CONV_NUCLEAR_up
RES_CAP_HARDCOAL_DE_up
DEF_COST_dispatch Definition of COST for pure dispatch problem
DEF_CAP_CONV_INSTALL_dispatch Definition of CAP_CONV_INSTALL for pure dispatch problem
;
DEF_COST..
COST =E= sum(year, money_weighting_factor(year) * (COST_GEN(year) + COST_INV(year) + COST_FIX(year)))
;
DEF_COST_GEN(year)..
COST_GEN(year) =E=
sum(country,
sum(conv$( ( cap_conv_install_up(country,conv) gt 0 ) AND ( convyear_lo(conv) le yearnumber(year) ) ),
sum(hour_all$(hour(year,hour_all)),
cvar_conv_avg(country,conv,year) * GEN_CONV(country,conv,year,hour_all) * (1 - indicator_partload_country(country))
+
cvar_conv_full(country,conv,year) * GEN_CONV_FULL(country,conv,year,hour_all) * indicator_partload_country(country)
+
cvar_conv_min(country,conv,year) * GEN_CONV_MIN(country,conv,year,hour_all) * indicator_partload_country(country)
+
cramp_conv(country,conv,year) * ( CAP_CONV_UP(country,conv,year,hour_all) + CAP_CONV_DOWN(country,conv,year,hour_all) ) * indicator_ramping_country(country)
)
) * (8760 / sum(hour(year,hour_all), 1))
+
sum(renew$(cvar_renew(country,renew,year) gt 0),
sum(hour_all$(hour(year,hour_all)),
cvar_renew(country,renew,year) * GEN_RENEW(country,renew,year,hour_all)
)
) * (8760 / sum(hour(year,hour_all), 1))
+
sum(renew_curt$(cap_renew_install_exogen(country,renew_curt,year) gt 0),
sum(hour_all$(hour(year,hour_all)),
ccurt_renew_year(year) * CURT_RENEW(country,renew_curt,year,hour_all)
)
) * (8760 / sum(hour(year,hour_all), 1))
+
sum(hour_all$(hour(year,hour_all)),
ccurt_load_year(year) * CURT_LOAD(country,year,hour_all)
) * (8760 / sum(hour(year,hour_all), 1))$(indicator_loadcurt(country) eq 1)
)
;
DEF_COST_INV(year)..
COST_INV(year) =E=
sum(country,
* investment nur in technologien möglich die ab 2020 verfügbar sind
sum(conv$(convyear_lo(conv) ge 2020 ),
* Investitionen fallen zwischen dem Jahr der Installation (year2) und dem Ende der Lebenszeit an (year2 + lifetime) Technolofien können nur in einem bestimmten Zeitraum installiert werden
sum(year2$( ( yearnumber(year) ge yearnumber(year2) ) AND ( yearnumber(year) le (yearnumber(year2) + inputdata_conv(conv,'lifetime_tech')) ) AND ( yearnumber(year2) ge convyear_lo(conv) ) AND ( yearnumber(year2) le convyear_up(conv) ) ),
cinv_conv(conv,year2) * CAP_CONV_ADD(country,conv,year2)
)
)
)
;
DEF_COST_FIX(year)..
COST_FIX(year) =E=
* fix cost arise after year of investment
sum((country,conv)$( convyear_lo(conv) le yearnumber(year) ),
cfix_conv(conv,year) * CAP_CONV_INSTALL(country,conv,year)
)
;
MCC(country,year,hour_all)$(hour(year,hour_all))..
sum(conv$( ( cap_conv_install_up(country,conv) gt 0 ) AND ( convyear_lo(conv) le yearnumber(year) ) ),
GEN_CONV(country,conv,year,hour_all)
)
+
sum(renew$(cap_renew_install_exogen(country,renew,year) gt 0),
GEN_RENEW(country,renew,year,hour_all)
)
+
sum(stor$(cap_stor_install_exogen(country,stor,year) gt 0),
DISCHARGE(country,stor,year,hour_all) - CHARGE(country,stor,year,hour_all)
)
+
sum(country2$(ntc(country2,country,year) gt 0),
(1 - (grid_loss/2)) * FLOW(country2,country,year,hour_all)
)
=E=
load(country,year,hour_all)
-
CURT_LOAD(country,year,hour_all)$(indicator_loadcurt(country) eq 1)
+
sum(country2$(ntc(country,country2,year) gt 0),
(1 + (grid_loss/2)) * FLOW(country,country2,year,hour_all)
)
+
netexport_border(country,year,hour_all)
;
*###############################################################################
* Constraints for conventional (non-renewable) generation technologies
DEF_CAP_CONV_RTO(country,conv,year,hour_all)$(hour(year,hour_all) AND ( cap_conv_install_up(country,conv) gt 0 ) AND ( convyear_lo(conv) le yearnumber(year) ) )..
CAP_CONV_RTO(country,conv,year,hour_all) =E= CAP_CONV_RTO(country,conv,year,hour_all - step_hour(year,hour_all)) + ( CAP_CONV_UP(country,conv,year,hour_all) - CAP_CONV_DOWN(country,conv,year,hour_all) ) * indicator_ramping_country(country) + CAP_CONV_RAMP(country,conv,year,hour_all) * ( 1 - indicator_ramping_country(country) )
;
RES_CAP_CONV_RTO_up(country,conv,year,hour_all)$(hour(year,hour_all) AND ( cap_conv_install_up(country,conv) gt 0 ) AND ( convyear_lo(conv) le yearnumber(year) ) )..
CAP_CONV_RTO(country,conv,year,hour_all) =L= availability_conv(country,conv,year,hour_all) * CAP_CONV_INSTALL(country,conv,year)
;
DEF_GEN_CONV(country,conv,year,hour_all)$(hour(year,hour_all) AND ( cap_conv_install_up(country,conv) gt 0 ) AND ( convyear_lo(conv) le yearnumber(year) ) )..
GEN_CONV(country,conv,year,hour_all) =E= GEN_CONV_FULL(country,conv,year,hour_all) * indicator_partload_country(country) + GEN_CONV_MIN(country,conv,year,hour_all)
;
RES_GEN_CONV_up(country,conv,year,hour_all)$(hour(year,hour_all) AND ( cap_conv_install_up(country,conv) gt 0 ) AND ( convyear_lo(conv) le yearnumber(year) ) )..
GEN_CONV(country,conv,year,hour_all) =L= CAP_CONV_RTO(country,conv,year,hour_all)
;
RES_GEN_CONV_MIN_lo(country,conv,year,hour_all)$(hour(year,hour_all) AND ( cap_conv_install_up(country,conv) gt 0 ) AND ( convyear_lo(conv) le yearnumber(year) ) )..
GEN_CONV_MIN(country,conv,year,hour_all) =G= gmin_conv(conv) * ( CAP_CONV_RTO(country,conv,year,hour_all) * indicator_ramping_country(country) - GEN_CONV_FULL(country,conv,year,hour_all) * indicator_partload_country(country) )
;
RES_GEN_CONV_lo(country,conv,year,hour_all)$(hour(year,hour_all) AND ( flh_chp_conv(country,conv) gt 0 ) AND ( convyear_lo(conv) le yearnumber(year) ) )..
GEN_CONV(country,conv,year,hour_all) =G= flh_chp_conv(country,conv) * chp_structure_hour(country,year,hour_all) * CAP_CONV_INSTALL(country,conv,year) * indicator_chp
;
DEF_CAP_CONV_INSTALL(country,conv,year)$(yearnumber(year) gt 2020)..
CAP_CONV_INSTALL(country,conv,year)
=E=
CAP_CONV_INSTALL(country,conv,year - 1)$( yearnumber(year - 1) ge convyear_lo(conv) )
+
* Investment erst ab 2022 Investment in eine Technologie nur in einem bestimmten Zeitraum möglich Investment nur in zulässige Technologien möglich
CAP_CONV_ADD(country,conv,year)$( ( convyear_lo(conv) ge 2022 ) AND ( yearnumber(year) ge convyear_lo(conv) ) AND ( yearnumber(year) le convyear_up(conv) ) AND (cap_conv_add_forbidden(country,conv) eq 0) )
-
* Divestment
cap_conv_sub_old(country,conv,year) * (1 - indicator_divestment_country(country))
-
* Divestment einer Alterklasse erst ab der Folgeperiode des Investment möglich UND Divestment erst ab 2022 möglich
CAP_CONV_SUB(country,conv,year)$((convyear_lo(conv) lt yearnumber(year)) AND ( yearnumber(year) ge 2022 )) * indicator_divestment_country(country)
;
DEF_CAP_CONV_INSTALL_start(country,conv,year)$(yearnumber(year) le 2020)..
CAP_CONV_INSTALL(country,conv,year) =E=
cap_conv_install_old(country,conv,year)
;
RES_CAP_CONV_SUB_lo(country,conv,year)$((indicator_divestment_country(country) eq 1) AND ( yearnumber(year) ge 2022))..
sum(year2$(( yearnumber(year2) ge 2022 ) AND ( yearnumber(year2) le yearnumber(year) )),
CAP_CONV_SUB(country,conv,year2)$( yearnumber(year2) gt convyear_lo(conv) )
)
=G=
sum(year2$(( yearnumber(year2) ge 2022 ) AND ( yearnumber(year2) le yearnumber(year) )),
cap_conv_sub_old(country,conv,year2)$( yearnumber(year2) gt convyear_lo(conv) )
)
;
*###############################################################################
* Constraints for renewable generation technologies
*Constraints for dispatchable renewables
RES_GEN_RENEW_up(country,renew_disp,year,hour_all)$(hour(year,hour_all) AND (inputdata_renew(renew_disp,'avail') lt 1))..
GEN_RENEW(country,renew_disp,year,hour_all) =L= availability_renew(country,renew_disp,year,hour_all) * cap_renew_install_exogen(country,renew_disp,year)
;
RES_GEN_RENEW_lo(country,renew_disp,year,hour_all)$(hour(year,hour_all) AND (flh_chp_renew(country,renew_disp) gt 0))..
GEN_RENEW(country,renew_disp,year,hour_all) =G= flh_chp_renew(country,renew_disp) * chp_structure_hour(country,year,hour_all) * cap_renew_install_exogen(country,renew_disp,year) * indicator_chp
;
RES_GEN_RENEW_yearly_potential(country,renew,year)$((fuelpotential_renew(country,renew,year) gt 0) AND (sum(month2, gen_renew_structure_monthly(country,renew,year,month2)) eq 0))..
sum(hour_all$(hour(year,hour_all)),
( GEN_RENEW(country,renew,year,hour_all) / efficiency_renew(renew) )
) * (8760 / sum(hour(year,hour_all), 1))
=L=
fuelpotential_renew(country,renew,year)
;
RES_GEN_RENEW_monthly_potential(country,renew,year,month)$(sum(month2, gen_renew_structure_monthly(country,renew,year,month2)) gt 0)..
sum(hour_all$( hour(year,hour_all) AND map_hourmonth(year,hour_all,month) ),
( GEN_RENEW(country,renew,year,hour_all) / efficiency_renew(renew) )
) * ( sum(hour_all$(map_hourmonth(year,hour_all,month)), 1) / sum(hour_all$( hour(year,hour_all) AND map_hourmonth(year,hour_all,month) ), 1) )
=L=
fuelpotential_renew(country,renew,year) * gen_renew_structure_monthly(country,renew,year,month)
;
RES_GEN_RENEW_reservoir_up(country,year,hour_all)$(hour(year,hour_all))..
GEN_RENEW(country,'reservoir',year,hour_all) =L= capfactor_renew_max(country,'reservoir',year,hour_all) * cap_renew_install_exogen(country,'reservoir',year)
;
RES_GEN_RENEW_reservoir_lo(country,year,hour_all)$(hour(year,hour_all))..
GEN_RENEW(country,'reservoir',year,hour_all) =G= capfactor_renew_min(country,'reservoir',year,hour_all) * cap_renew_install_exogen(country,'reservoir',year)
;
*Constraints for non-dispatchable renewables
DEF_GEN_RENEW_curt(country,renew_curt,year,hour_all)$(hour(year,hour_all))..
GEN_RENEW(country,renew_curt,year,hour_all) + CURT_RENEW(country,renew_curt,year,hour_all) =E= capfactor_renew_max(country,renew_curt,year,hour_all) * cap_renew_install_exogen(country,renew_curt,year)
;
DEF_GEN_RENEW_ncurt(country,renew_ncurt,year,hour_all)$(hour(year,hour_all))..
GEN_RENEW(country,renew_ncurt,year,hour_all) =E= capfactor_renew_max(country,renew_ncurt,year,hour_all) * cap_renew_install_exogen(country,renew_ncurt,year)
;
*###############################################################################
* Constraints for storage technologies
DEF_LEVEL(country,stor,year,hour_all)$( hour(year,hour_all) AND ( ord(hour_all) gt first_hour(year) ) AND ( cap_stor_install_exogen(country,stor,year) gt 0 ) )..
LEVEL(country,stor,year,hour_all)
=E=
LEVEL(country,stor,year,hour_all - step_hour(year,hour_all))
+
CHARGE(country,stor,year,hour_all) * efficiency_stor(stor)
-
DISCHARGE(country,stor,year,hour_all) * ( 1 / efficiency_stor(stor) )
;
DEF_LEVEL_start(country,stor,year,hour_all)$( hour(year,hour_all) AND ( ord(hour_all) eq first_hour(year) ) AND ( cap_stor_install_exogen(country,stor,year) gt 0 ) )..
LEVEL(country,stor,year,hour_all)
=E=
cap_stor_install_exogen(country,stor,year) * duration_stor(country,stor) * 0.5 * (sum(hour(year,hour_all2), 1) / 8760)
+
CHARGE(country,stor,year,hour_all) * efficiency_stor(stor)
-
DISCHARGE(country,stor,year,hour_all) * ( 1 / efficiency_stor(stor) )
;
DEF_LEVEL_end(country,stor,year,hour_all)$( hour(year,hour_all) AND ( ord(hour_all) eq last_hour(year) ) AND ( cap_stor_install_exogen(country,stor,year) gt 0 ) )..
LEVEL(country,stor,year,hour_all)
=E=
cap_stor_install_exogen(country,stor,year) * duration_stor(country,stor) * 0.5 * (sum(hour(year,hour_all2), 1) / 8760)
;
RES_LEVEL_up(country,stor,year,hour_all)$( hour(year,hour_all) AND (cap_stor_install_exogen(country,stor,year) gt 0))..
LEVEL(country,stor,year,hour_all)
=L=
( 1 - 0.5 * ( 1 - avail_stor(stor) ) ) * cap_stor_install_exogen(country,stor,year) * duration_stor(country,stor) * (sum(hour(year,hour_all2), 1) / 8760)
;
RES_LEVEL_lo(country,stor,year,hour_all)$( hour(year,hour_all) AND (cap_stor_install_exogen(country,stor,year) gt 0))..
LEVEL(country,stor,year,hour_all)
=G=
0.5 * ( 1 - avail_stor(stor) ) * cap_stor_install_exogen(country,stor,year) * duration_stor(country,stor) * (sum(hour(year,hour_all2), 1) / 8760)
;
RES_CHARGE_up(country,stor,year,hour_all)$(hour(year,hour_all) AND (cap_stor_install_exogen(country,stor,year) gt 0))..
CHARGE(country,stor,year,hour_all)
=L=
avail_stor(stor) * cap_stor_install_exogen(country,stor,year)
;
RES_DISCHARGE_up(country,stor,year,hour_all)$(hour(year,hour_all) AND (cap_stor_install_exogen(country,stor,year) gt 0))..
DISCHARGE(country,stor,year,hour_all)
=L=
avail_stor(stor) * cap_stor_install_exogen(country,stor,year) * discharge_to_charge_ratio_stor(country,stor)
;
RES_FLOW_up(country,country2,year,hour_all)$(hour(year,hour_all) AND (ntc(country,country2,year) gt 0))..
FLOW(country,country2,year,hour_all) =L= ntc_hour(country,country2,year,hour_all)
;
RES_CAP_CONV_ADD_up(country,conv,year)$(convyear_lo(conv) ge 2020)..
CAP_CONV_ADD(country,conv,year) =L= cap_conv_add_up(country,conv,year)
;
RES_CAP_CONV_NUCLEAR_up(country,year)..
sum(conv$(map_convfuel(conv,'uranium')), CAP_CONV_INSTALL(country,conv,year))
=L=
sum(conv$(map_convfuel(conv,'uranium')), cap_conv_install_old(country,conv,'2017')) * 1.1
;
RES_CAP_HARDCOAL_DE_up(year)$(indicator_coalphaseout eq 1)..
sum(conv$(map_convfuel(conv,'hardcoal')), CAP_CONV_INSTALL('DE+LU',conv,year))
=L=
sum(conv$(map_convfuel(conv,'hardcoal')), cap_conv_install_old_phaseout('DE+LU',conv,year))
;
*###############################################
*Additional equations for pure dispatch problem
DEF_COST_dispatch..
COST =E= sum(year, money_weighting_factor(year) * COST_GEN(year) )
;
DEF_CAP_CONV_INSTALL_dispatch(country,conv,year)..
CAP_CONV_INSTALL(country,conv,year) =E=
cap_conv_install_L(country,conv,year)
;
MODEL Investment
/
DEF_COST
DEF_COST_GEN
DEF_COST_INV
DEF_COST_FIX
MCC
DEF_CAP_CONV_RTO
RES_CAP_CONV_RTO_up
DEF_GEN_CONV
RES_GEN_CONV_up
RES_GEN_CONV_MIN_lo
RES_GEN_CONV_lo
DEF_CAP_CONV_INSTALL
DEF_CAP_CONV_INSTALL_start
RES_CAP_CONV_SUB_lo
RES_GEN_RENEW_up
RES_GEN_RENEW_lo
RES_GEN_RENEW_yearly_potential
RES_GEN_RENEW_monthly_potential
RES_GEN_RENEW_reservoir_up
RES_GEN_RENEW_reservoir_lo
DEF_GEN_RENEW_curt
DEF_GEN_RENEW_ncurt
DEF_LEVEL
DEF_LEVEL_start
DEF_LEVEL_end
RES_LEVEL_up
RES_LEVEL_lo
RES_CHARGE_up
RES_DISCHARGE_up
RES_FLOW_up
RES_CAP_CONV_ADD_up
RES_CAP_CONV_NUCLEAR_up
RES_CAP_HARDCOAL_DE_up
/;
MODEL Dispatch
/
DEF_COST_dispatch
DEF_COST_GEN
MCC
DEF_CAP_CONV_RTO
RES_CAP_CONV_RTO_up
DEF_GEN_CONV
RES_GEN_CONV_up
RES_GEN_CONV_MIN_lo
RES_GEN_CONV_lo
DEF_CAP_CONV_INSTALL_dispatch
RES_GEN_RENEW_up
RES_GEN_RENEW_lo
RES_GEN_RENEW_yearly_potential
RES_GEN_RENEW_monthly_potential
RES_GEN_RENEW_reservoir_up
RES_GEN_RENEW_reservoir_lo
DEF_GEN_RENEW_curt
DEF_GEN_RENEW_ncurt
DEF_LEVEL
DEF_LEVEL_start
DEF_LEVEL_end
RES_LEVEL_up
RES_LEVEL_lo
RES_CHARGE_up
RES_DISCHARGE_up
RES_FLOW_up
/;