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Bilevel-Centralized-GEPM.gms
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Bilevel-Centralized-GEPM.gms
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$Title Deterministic Single-Node Static Generation Expansion Planning Model (GEPM)
$OnText
GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
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Developed by
Diego Alejandro Tejada Arango
dtejada@comillas.edu
November 23, 2020
$OffText
$OnText
The Bilevel formulation in this code is based on Chapter 3 of the Book:
Investment in Electricity Generation and Transmission
DOI: 10.1007/978-3-319-29501-5
Authors:
Antonio J. Conejo
Luis Baringo Morales
Kazempour Jalal
Afzal S. Siddiqui
$OffText
sets
c "candidate generating units" /gc1/
g "existing generating units" /ge1/
d "demands " /d1 /
o "operating conditions " /o1,o2/
;
parameters
CC (c) "Production cost of candidate generating unit c [$/MWh]" /gc1 25/
CE (g) "Production cost of existing generating unit g [$/MWh]" /ge1 35/
IC (c) "Annualized investment cost of candidate generating unit c [$/MW ]" /gc1 70000/
PCmax(c) "Maximum production capacity investment of candidate generating unit c [MW] " /gc1 500/
PEmax(g) "Production capacity of existing generating unit g [MW] " /ge1 400/
Rho (o) "Weight of operating condition o [h]"
/o1 6000
o2 2760/
price(o) "electricity prices [$/MWh]"
;
table PD (d,o) "load demand d at operating condition o [MW]"
o1 o2
d1 290 550
;
variable
of "objective function [$]"
lambda(o) "dual variable of balance equation"
positive variables
pc (c,o) "Power produced by candidate generating unit c [MW]"
pe (g,o) "Power produced by existing generating unit g [MW]"
cmax(c ) "Capacity of candidate generating unit c [MW]"
muEm(g,o) "dual variable of max production of candidate unit c"
muCm(c,o) "dual variable of max production of existing unit g"
;
equations
eTotalCost "Total cost (operating + investment cost)"
eBalance ( o) "balance equation at each operating condition o"
eCandProdLimit(c,o) "candidate production limit"
eDualConstE (g,o) "Dual constraint on existing generating unit g"
eDualConstC (c,o) "Dual constraint on candidate generating unit c"
eStrongDualEq ( o) "strong duality equalities"
;
eTotalCost.. of =e= sum[o,Rho(o)*[sum[g,CE(g)*pe(g,o)]+sum[c,CC(c)*pc(c,o)]]] + sum[c,IC(c)*cmax(c)] ;
eBalance(o).. sum[g,pe(g,o)]+sum[c,pc(c,o)] =e= sum[d,PD(d,o)] ;
eCandProdLimit(c,o).. pc(c,o) =l= cmax(c) ;
eDualConstE(g,o).. CE(g) - lambda(o) + muEm(g,o) =g= 0 ;
eDualConstC(c,o).. CC(c) - lambda(o) + muCm(c,o) =g= 0 ;
eStrongDualEq(o).. sum[g,CE(g)*pe(g,o)]+sum[c,CC(c)*pc(c,o)] =e= lambda(o)*sum[d,PD(d,o)]-sum[g,muEm(g,o)*PEmax(g)]-sum[c,muCm(c,o)*cmax(c)];
* constraints as bounds
cmax.up(c ) = PCmax(c);
pe.up (g,o) = PEmax(g);
Model bilevel_nlp /eTotalCost, eBalance, eCandProdLimit, eDualConstE, eDualConstC, eStrongDualEq /;
Model sglevel_lp /eTotalCost, eBalance, eCandProdLimit /;
* solve bilevel problem
solve bilevel_nlp using nlp minimizing of;
display pc.l, pe.l, cmax.l, lambda.l;
* solve single level problem
solve sglevel_lp using lp minimizing of;
price(o) = eBalance.m(o) / Rho(o) ;
display pc.l, pe.l, cmax.l, price;
* finding prices without dual information of investment
cmax.fx(c) = cmax.l(c);
solve sglevel_lp using lp minimizing of;
price(o) = eBalance.m(o) / Rho(o) ;
display price;