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Stochastic-GEP.gms
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Stochastic-GEP.gms
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*-------------------------------------------------------------------------
* Universidad Pontificia Comillas de Madrid
* Optimization Techniques
* Diego Alejandro Tejada Arango
*-------------------------------------------------------------------------
$TITLE Two-Stage Stochastic Generation Expansion Planning
* ========================================================================
* SETS DEFINITION
* ========================================================================
SETS
p "time periods (e.g., hours) " /h01 *h24 /
sc " scenarios " /sc01,sc02,sc03,sc_exp/
scu(sc) "uncertainty scenarios " /sc01,sc02,sc03/
sce(sc) "expected value of scenarios " /sc_exp/
g "generation technologies" / wind, solar, ccgt, ocgt /
r(g) "subset of renewable technologies" / wind, solar/
* dinamic set (to be defined depending on the input data)
sca(sc) "active scenarios"
;
* ========================================================================
* PARAMETERS AND SCALARS
* ========================================================================
SCALARS
pWeight "weight of representative period [days]" /365/
pENSCost "energy not supplied cost [kEUR/MWh]" /0.180/
;
PARAMETER
pScProb(sc) "scenario probability [p.u.]"
/sc01 0.2, sc02 0.5, sc03 0.3/
pDemand(p) "demand per time period [MW]"
/
h01 950
h02 870
h03 814
h04 779
h05 758
h06 751
h07 779
h08 834
h09 902
h10 956
h11 1010
h12 1023
h13 1018
h14 1010
h15 980
h16 965
h17 963
h18 997
h19 1093
h20 1114
h21 1115
h22 1107
h23 1053
h24 1035
/
;
TABLE pGenInfo(g,*) "generation information"
* kEUR/MWh kEUR/MW/year MW
VarCost InvCost UnitCap
ocgt 0.070 25 100
ccgt 0.050 40 400
wind 0.001 70 50
solar 0.000 50 10
;
TABLE pRenProf(p,r,sc) "renewable profile [p.u.]"
* sc01 -> low wind, high solar; sc02 -> avg wind and solar; sc03 -> high wind and low solar
wind.sc01 wind.sc02 wind.sc03 solar.sc01 solar.sc02 solar.sc03
h01 0.11 0.54 0.68 0.00 0.00 0.00
h02 0.11 0.54 0.69 0.00 0.00 0.00
h03 0.11 0.53 0.70 0.00 0.00 0.00
h04 0.11 0.52 0.71 0.00 0.00 0.00
h05 0.10 0.51 0.73 0.00 0.00 0.00
h06 0.10 0.50 0.74 0.02 0.00 0.00
h07 0.10 0.48 0.75 0.12 0.01 0.00
h08 0.09 0.47 0.76 0.30 0.07 0.01
h09 0.09 0.46 0.77 0.50 0.20 0.12
h10 0.09 0.45 0.78 0.66 0.36 0.28
h11 0.09 0.45 0.79 0.78 0.50 0.42
h12 0.09 0.45 0.80 0.83 0.57 0.51
h13 0.10 0.43 0.81 0.83 0.59 0.53
h14 0.12 0.41 0.81 0.78 0.54 0.50
h15 0.14 0.38 0.80 0.68 0.44 0.40
h16 0.15 0.35 0.79 0.53 0.29 0.23
h17 0.16 0.34 0.78 0.35 0.13 0.05
h18 0.16 0.35 0.77 0.17 0.03 0.00
h19 0.16 0.36 0.76 0.04 0.00 0.00
h20 0.15 0.38 0.75 0.00 0.00 0.00
h21 0.14 0.41 0.74 0.00 0.00 0.00
h22 0.13 0.43 0.74 0.00 0.00 0.00
h23 0.12 0.46 0.74 0.00 0.00 0.00
h24 0.12 0.48 0.74 0.00 0.00 0.00
;
* ========================================================================
* VARIABLES
* ========================================================================
INTEGER VARIABLE
vInstalUnits(g) "number of installed generation units [N]"
;
POSITIVE VARIABLE
vProduct(p,g,sc) "generation production per scenario [MW]"
vENS (p, sc) "energy not supplied per scenario [MW]"
;
FREE VARIABLES
vTotalCost "Total Cost = Investment + Operation [kEUR]"
vInvesCost "Total investment Cost [kEUR]"
vOperaCost "Total operating Cost [kEUR]"
;
* ========================================================================
* EQUATIONS AND MODEL DEFINITION
* ========================================================================
EQUATIONS
eTotalCost "Total Cost = Investment + Operation [kEUR]"
eInvesCost "Total investment Cost [kEUR]"
eOperaCost "Total operating Cost [kEUR]"
eBalance (p, sc) "power balance constriant [MW] "
eRenProd (p,g,sc) "renewable production constriant [MW] "
eMaxProd (p,g,sc) "generation production constraint [MW] "
;
eTotalCost.. vTotalCost =E= vInvesCost + vOperaCost
;
eInvesCost.. vInvesCost =E= SUM[g, pGenInfo(g,'InvCost')*pGenInfo(g,'UnitCap')*vInstalUnits(g)]
;
eOperaCost.. vOperaCost =E= pWeight * SUM[(p,g,sca),
pScProb(sca)*[
+ pGenInfo(g,'VarCost')*vProduct(p,g,sca)
+ pENSCost *vENS (p, sca)]]
;
eBalance(p,sca(sc))..
SUM[g,vProduct(p,g,sc)] + vENS(p,sc) =E= pDemand(p)
;
eRenProd(p,r,sca(sc))..
vProduct(p,r,sc) =L= pRenProf(p,r,sc) * pGenInfo(r,'UnitCap')*vInstalUnits(r)
;
eMaxProd(p,g,sca(sc))$[not r(g)]..
vProduct(p,g,sc) =L= pGenInfo(g,'UnitCap')*vInstalUnits(g)
;
MODEL TwoStageStochGEP / all /
;
* ========================================================================
* MODEL SOLUTION AND RESULTS
* ========================================================================
* option to find the solution to optimality
OPTION optcr=0;
* active only uncertainty scenarios with probability
sca(sc) $[scu(sc) AND pScProb(sc)] = YES ;
SOLVE TwoStageStochGEP USING MIP MINIMIZING vTotalCost
;
* result parameters
PARAMETERS
pInstalCap(g ) "installed capacity [MW] "
pScPrices (p,sc) "scenario prices [EUR/MWh]"
pEVPrices (p ) "expected value of prices [EUR/MWh]"
;
pInstalCap(g) = pGenInfo(g,'UnitCap')*vInstalUnits.L(g)
;
pScPrices (p,sca(sc)) = eBalance.M(p,sc) *1e3 / [pWeight * pScProb(sc)];
pEVPrices (p ) = SUM[sc, pScProb(sc) * pScPrices (p,sc)] ;
* gdx with all results
execute_unload 'TwoStageStochGEP.gdx'
*$stop
* ========================================================================
* STOCHASTIC MEASURES
* ========================================================================
;
PARAMETERS
pRP "Recourse Problem solution 'here and now' "
pWS "Wait and See solution "
pEVPI "Expected Value of Perfect Information "
pEV "Expect Value Problem result "
pEEV "Expected Result of Expect Value Problem "
pVSS "Value of the Stochastic solution "
pScProb_aux ( sc) "auxiliary parameter of scenario probabilities "
pDetTotCost ( sc) "total cost of each deterministic scenario "
pDetENS ( sc) "energy not supply of each deterministic scenario "
pDetInstalCap(g,sc) "installed capacity of each deterministic scenario "
pEEVTotCost ( sc) "total cost of each deterministic scenario using the EV solution"
pEVVENS ( sc) "energy not supply of each deterministic scenario using the EV solution"
pEEVInstalCap(g,sc) "installed capacity of each deterministic scenario using the EV solution"
pEVInstalCap (g ) "installed capacity of expected value problem "
;
* 1) save the solution from the stochastic model
pRP = vTotalCost.L ;
* 2) for the WS value we need the solution of each deterministic scenario
* 2.1) store the initial values of prob in a aux parameter and clean the initial values
pScProb_aux(sca(sc)) = pScProb(sc) ;
pScProb ( sc ) = 0 ;
* 2.2)loop over the uncertanty scenarios solving once at the time
sca(sc) = NO ;
loop(scu,
pScProb(scu) = 1 ;
sca (scu) = YES ;
SOLVE TwoStageStochGEP USING MIP MINIMIZING vTotalCost ;
pDetTotCost ( scu) = vTotalCost.L ;
pDetInstalCap(g,scu) = pGenInfo(g,'UnitCap')*vInstalUnits.L(g);
pDetENS ( scu) = SUM[p,vENS.L(p,scu)];
pScProb ( scu) = 0 ;
sca ( scu) = NO ;
);
* 2.3) we determine the wait and see solution
pWS = sum[scu, pScProb_aux(scu)*pDetTotCost(scu)]
;
* 3) we determine the EVPI
pEVPI = pRP - pWS
;
* 4) determine the expected value of scenarios
pRenProf(p,r,sce) = SUM[scu,pScProb_aux(scu)*pRenProf(p,r,scu)]
;
* 5) solve the model for the expected value and determine EEV
pScProb(sce) = 1 ;
sca (sce) = YES ;
SOLVE TwoStageStochGEP USING MIP MINIMIZING vTotalCost ;
pEV = vTotalCost.L ;
pDetInstalCap(g,sce) = pGenInfo(g,'UnitCap')*vInstalUnits.L(g)
;
* 6) save the solution of the expected value
pEVInstalCap(g) = vInstalUnits.L(g)
;
* 7) solve each deterministic scenario with this solution
sca(sc) = NO ;
loop(scu,
pScProb(scu) = 1 ;
sca (scu) = YES ;
vInstalUnits.FX(g) = pEVInstalCap(g) ;
SOLVE TwoStageStochGEP USING MIP MINIMIZING vTotalCost ;
pEEVTotCost ( scu) = vTotalCost.L ;
pEVVENS ( scu) = SUM[p,vENS.L(p,scu)];
pScProb ( scu) = 0 ;
sca ( scu) = NO ;
);
* 8) we determine the EEV
pEEV = sum[scu, pScProb_aux(scu)*pEEVTotCost(scu)]
;
* 9) Determine VSS
pVSS = pEEV - pRP
;
* gdx with stochastic measures
execute_unload 'TwoStageStochGEP-Stoch-Measures.gdx'
pRP, pWS, pEVPI, pEV, pEEV, pVSS, pDetTotCost, pDetENS
pDetInstalCap, pEEVTotCost, pEVVENS, pEVInstalCap, pRenProf
;