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fm_cong.gms
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$title GAMS/PSAT interface for solving the electricty market problem
$onempty
$offlisting
$offupper
$if exist psatglobs.gms $include psatglobs.gms
set B /1*%nBus%/,
L /1*%nLine%/,
G /1*%nPs%/,
C /1*%nPd%/,
W /1*%nSW%/,
U /1*%nPV%/,
busref(B) /%nBusref%/;
set supply /Ps0, Psmax, Psmin, Csa, Csb, Csc, Dsa, Dsb, Dsc, ksu, RGup, RGdw/,
demand /Pd0, Pdmax, Pdmin, tgphi, Cda, Cdb, Cdc, Dda, Ddb, Ddc, RDup, RDdw/,
data /V0, t0, Pg0, Qg0, Pl0, Ql0, Qgmax, Qgmin, Vmax, Vmin, ksw, kpv/,
lines /g, b, g0, b0, Pijmax, Pjimax/,
vsc /lmin, lmax, omega, line/;
alias (BB,B);
parameter S(G,supply) //,
D(C,demand) //,
X(B,data) //,
N(L,lines) //,
lambda(vsc) //,
Ps_idx(B,G) //,
Psc_idx(B,G) //,
Psm_idx(B,G) //,
Pd_idx(B,C) //,
SW_idx(B,W) //,
PV_idx(B,U) //,
Li(L,B) //,
Lj(L,B) //,
Gh(B,BB) //,
Bh(B,BB) //,
Ghc(B,BB) //,
Bhc(B,BB) //;
scalar MLC /0/,
pi /3.1416/;
$if exist psatdata.gms $include psatdata.gms
* =========================================================================
* ==================== C O M M O N V A R I A B L E S ===================
* =========================================================================
variables obj,
Pij(L),
Pji(L),
V(B),
a(B),
Ps(G),
Pd(C),
Qg(B),
Pijc(L),
Pjic(L),
DPGup(G),
DPGdw(G),
DPDup(C),
DPDdw(C),
Vc(B),
ac(B),
Qgc(B),
kg,
lambdac;
* -------------------------------------------------------------------------
* initial values
* -------------------------------------------------------------------------
Qg.l(B) = X(B,'Qg0');
V.l(B) = X(B,'V0');
a.l(B) = X(B,'t0');
Ps.l(G) = S(G,'Psmin');
Pd.l(C) = D(C,'Pdmin');
Qgc.l(B) = X(B,'Qg0');
Vc.l(B) = X(B,'V0');
ac.l(B) = X(B,'t0');
kg.l = 0;
* -------------------------------------------------------------------------
* limits
* -------------------------------------------------------------------------
* Bid Blocks
Ps.up(G) = S(G,'Psmax');
Pd.up(C) = D(C,'Pdmax');
Ps.lo(G) = S(G,'Psmin');
Pd.lo(C) = D(C,'Pdmin');
* Voltages & Voltage Limits
V.up(B) = X(B,'Vmax');
V.lo(B) = X(B,'Vmin');
a.up(B) = pi;
a.lo(B) = -pi;
* power variations
DPGup.lo(G) = 0;
DPGdw.lo(G) = 0;
DPDup.lo(C) = 0;
DPDdw.lo(C) = 0;
DPGup.up(G) = S(G,'Psmax');
DPGdw.up(G) = S(G,'Psmax');
DPDup.up(C) = D(C,'Pdmax');
DPDdw.up(C) = D(C,'Pdmax');
* Generator Reactive Power Limits
Qg.up(B) = X(B,'Qgmax');
Qg.lo(B) = X(B,'Qgmin');
* Flow limits on transmission lines
Pij.up(L) = N(L,'Pijmax');
Pij.lo(L) = -N(L,'Pijmax');
Pji.up(L) = N(L,'Pijmax');
Pji.lo(L) = -N(L,'Pijmax');
* Voltages & Voltage Limits
Vc.up(B) = X(B,'Vmax');
Vc.lo(B) = X(B,'Vmin');
ac.up(B) = pi;
ac.lo(B) = -pi;
kg.lo = -1;
kg.up = 1;
* Generator Reactive Power Limits
Qgc.up(B) = X(B,'Qgmax');
Qgc.lo(B) = X(B,'Qgmin');
* Flow limits on transmission lines
Pijc.up(L) = N(L,'Pijmax');
Pijc.lo(L) = -N(L,'Pijmax');
Pjic.up(L) = N(L,'Pijmax');
Pjic.lo(L) = -N(L,'Pijmax');
lambdac.up = lambda('lmax');
lambdac.lo = lambda('lmin');
* -------------------------------------------------------------------------
* define equations
* -------------------------------------------------------------------------
equations cost,
Pseq(G),
Pdeq(C),
Peq(B),
Qeq(B),
Thetaref(B),
Pceq(B),
Qceq(B),
Thetacref(B);
$if %flow% == 0 $goto noflows
equations Pijeq(L),
Pjieq(L),
Pijceq(L),
Pjiceq(L);
$label noflows
* =========================================================================
* ====== V O L T A G E S T A B I L I T Y C O N S T R A I N E D ======
* ================== O P T I M A L P O W E R F L O W =================
* =========================================================================
* -------------------------------------------------------------------------
* objective function
cost.. obj =e= sum(G,DPGup(G)*S(G,'RGup'))+
sum(G,DPGdw(G)*S(G,'RGdw'))+
sum(C,DPDup(C)*D(C,'RDup'))+
sum(C,DPDdw(C)*D(C,'RDdw'));
* -------------------------------------------------------------------------
Pseq(G).. Ps(G) =e= S(G,'Ps0') + DPGup(G) - DPGdw(G);
Pdeq(C).. Pd(C) =e= D(C,'Pd0') + DPDup(C) - DPDdw(C);
Peq(B).. sum(G,Ps_idx(B,G)*Ps(G)) -
sum(C,Pd_idx(B,C)*Pd(C)) + X(B,'Pg0') - X(B,'Pl0') -
V(B)*sum(BB,V(BB)*(Gh(B,BB)*cos(a(B)-a(BB)) +
Bh(B,BB)*sin(a(B)-a(BB)))) =e= 0;
Qeq(B).. Qg(B) - X(B,'Ql0') - sum(C,Pd_idx(B,C)*(D(C,'tgphi')*Pd(C))) -
V(B)*sum(BB,V(BB)*(Gh(B,BB)*sin(a(B)-a(BB)) -
Bh(B,BB)*cos(a(B)-a(BB)))) =e= 0;
Thetaref(B)$busref(B).. a(B) =e= 0;
Pceq(B).. (1+lambdac+kg)*(sum(G,Psc_idx(B,G)*(S(G,'ksu')*Ps(G))) + X(B,'Pg0')) +
(sum(W,SW_idx(B,W)*(X(B,'ksw')*X(B,'Pg0')))) +
(sum(U,PV_idx(B,U)*(X(B,'kpv')*X(B,'Pg0')))) +
sum(G,Psm_idx(B,G)*S(G,'Psmax')) -
(1+lambdac)*(sum(C,Pd_idx(B,C)*Pd(C)) + X(B,'Pl0')) -
Vc(B)*sum(BB,Vc(BB)*(Ghc(B,BB)*cos(ac(B)-ac(BB)) +
Bhc(B,BB)*sin(ac(B)-ac(BB)))) =e= 0;
* (sum(G,Ps_idx(B,G)*(S(G,'ksu')*Ps(G)))) +
Qceq(B).. Qgc(B) - (1+lambdac)*(X(B,'Ql0') +
sum(C,Pd_idx(B,C)*(D(C,'tgphi')*Pd(C)))) -
Vc(B)*sum(BB,Vc(BB)*(Ghc(B,BB)*sin(ac(B)-ac(BB)) -
Bhc(B,BB)*cos(ac(B)-ac(BB)))) =e= 0;
Thetacref(B)$busref(B).. ac(B) =e= 0;
$if %flow% == 0 $goto solvestat
$if %flow% == 1 $goto iflows
$if %flow% == 2 $goto pflows
$if %flow% == 3 $goto sflows
$label pflows
Pijeq(L).. Pij(L) =e= N(L,'g0')*sum(B,Li(L,B)*V(B)*V(B)) -
N(L,'b')*sum(B,Li(L,B)*V(B)*sin(a(B)))*
sum(B,Lj(L,B)*V(B)*cos(a(B))) +
N(L,'b')*sum(B,Li(L,B)*V(B)*cos(a(B)))*
sum(B,Lj(L,B)*V(B)*sin(a(B))) -
N(L,'g')*sum(B,Li(L,B)*V(B)*cos(a(B)))*
sum(B,Lj(L,B)*V(B)*cos(a(B))) -
N(L,'g')*sum(B,Li(L,B)*V(B)*sin(a(B)))*
sum(B,Lj(L,B)*V(B)*sin(a(B)));
Pjieq(L).. Pji(L) =e= N(L,'g0')*sum(B,Lj(L,B)*V(B)*V(B)) -
N(L,'b')*sum(B,Lj(L,B)*V(B)*sin(a(B)))*
sum(B,Li(L,B)*V(B)*cos(a(B))) +
N(L,'b')*sum(B,Lj(L,B)*V(B)*cos(a(B)))*
sum(B,Li(L,B)*V(B)*sin(a(B))) -
N(L,'g')*sum(B,Lj(L,B)*V(B)*cos(a(B)))*
sum(B,Li(L,B)*V(B)*cos(a(B))) -
N(L,'g')*sum(B,Lj(L,B)*V(B)*sin(a(B)))*
sum(B,Li(L,B)*V(B)*sin(a(B)));
N(L,'b')$(ord(L) eq lambda('line')) = -1E-6;
N(L,'g')$(ord(L) eq lambda('line')) = 0;
N(L,'b0')$(ord(L) eq lambda('line')) = 0;
N(L,'g0')$(ord(L) eq lambda('line')) = 0;
Pijceq(L).. Pijc(L) =e= N(L,'g0')*sum(B,Li(L,B)*Vc(B)*Vc(B)) -
N(L,'b')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))*
sum(B,Lj(L,B)*Vc(B)*cos(ac(B))) +
N(L,'b')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))*
sum(B,Lj(L,B)*Vc(B)*sin(ac(B))) -
N(L,'g')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))*
sum(B,Lj(L,B)*Vc(B)*cos(ac(B))) -
N(L,'g')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))*
sum(B,Lj(L,B)*Vc(B)*sin(ac(B)));
Pjiceq(L).. Pjic(L) =e= N(L,'g0')*sum(B,Lj(L,B)*Vc(B)*Vc(B)) -
N(L,'b')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))*
sum(B,Li(L,B)*Vc(B)*cos(ac(B))) +
N(L,'b')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))*
sum(B,Li(L,B)*Vc(B)*sin(ac(B))) -
N(L,'g')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))*
sum(B,Li(L,B)*Vc(B)*cos(ac(B))) -
N(L,'g')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))*
sum(B,Li(L,B)*Vc(B)*sin(ac(B)));
$goto solvestat
$label iflows
Pijeq(L).. Pij(L) =e= sqrt(
sqr(N(L,'g')*sum(B,Li(L,B)*V(B)*cos(a(B)))-
N(L,'g')*sum(B,Lj(L,B)*V(B)*cos(a(B)))-
N(L,'b')*sum(B,Li(L,B)*V(B)*sin(a(B)))+
N(L,'b')*sum(B,Lj(L,B)*V(B)*sin(a(B)))-
N(L,'b0')*sum(B,Li(L,B)*V(B)*sin(a(B))))+
sqr(N(L,'b')*sum(B,Li(L,B)*V(B)*cos(a(B)))-
N(L,'b')*sum(B,Lj(L,B)*V(B)*cos(a(B)))+
N(L,'g')*sum(B,Li(L,B)*V(B)*sin(a(B)))-
N(L,'g')*sum(B,Lj(L,B)*V(B)*sin(a(B)))+
N(L,'b0')*sum(B,Li(L,B)*V(B)*cos(a(B)))));
Pjieq(L).. Pji(L) =e= sqrt(
sqr(N(L,'g')*sum(B,Lj(L,B)*V(B)*cos(a(B)))-
N(L,'g')*sum(B,Li(L,B)*V(B)*cos(a(B)))-
N(L,'b')*sum(B,Lj(L,B)*V(B)*sin(a(B)))+
N(L,'b')*sum(B,Li(L,B)*V(B)*sin(a(B)))-
N(L,'b0')*sum(B,Lj(L,B)*V(B)*sin(a(B))))+
sqr(N(L,'b')*sum(B,Lj(L,B)*V(B)*cos(a(B)))-
N(L,'b')*sum(B,Li(L,B)*V(B)*cos(a(B)))+
N(L,'g')*sum(B,Lj(L,B)*V(B)*sin(a(B)))-
N(L,'g')*sum(B,Li(L,B)*V(B)*sin(a(B)))+
N(L,'b0')*sum(B,Lj(L,B)*V(B)*cos(a(B)))));
N(L,'b')$(ord(L) eq lambda('line')) = -1E-6;
N(L,'g')$(ord(L) eq lambda('line')) = 0;
N(L,'b0')$(ord(L) eq lambda('line')) = 0;
N(L,'g0')$(ord(L) eq lambda('line')) = 0;
Pijceq(L).. Pijc(L) =e= sqrt(
sqr(N(L,'g')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))-
N(L,'g')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))-
N(L,'b')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))+
N(L,'b')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))-
N(L,'b0')*sum(B,Li(L,B)*Vc(B)*sin(ac(B))))+
sqr(N(L,'b')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))-
N(L,'b')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))+
N(L,'g')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))-
N(L,'g')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))+
N(L,'b0')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))));
Pjiceq(L).. Pjic(L) =e= sqrt(
sqr(N(L,'g')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))-
N(L,'g')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))-
N(L,'b')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))+
N(L,'b')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))-
N(L,'b0')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B))))+
sqr(N(L,'b')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))-
N(L,'b')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))+
N(L,'g')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))-
N(L,'g')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))+
N(L,'b0')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))));
$goto solvestat
$label sflows
Pijeq(L).. Pij(L) =e= sum(B,Li(L,B)*V(B))*sqrt(
sqr(N(L,'g')*sum(B,Li(L,B)*V(B)*cos(a(B)))-
N(L,'g')*sum(B,Lj(L,B)*V(B)*cos(a(B)))-
N(L,'b')*sum(B,Li(L,B)*V(B)*sin(a(B)))+
N(L,'b')*sum(B,Lj(L,B)*V(B)*sin(a(B)))-
N(L,'b0')*sum(B,Li(L,B)*V(B)*sin(a(B))))+
sqr(N(L,'b')*sum(B,Li(L,B)*V(B)*cos(a(B)))-
N(L,'b')*sum(B,Lj(L,B)*V(B)*cos(a(B)))+
N(L,'g')*sum(B,Li(L,B)*V(B)*sin(a(B)))-
N(L,'g')*sum(B,Lj(L,B)*V(B)*sin(a(B)))+
N(L,'b0')*sum(B,Li(L,B)*V(B)*cos(a(B)))));
Pjieq(L).. Pji(L) =e= sum(B,Lj(L,B)*V(B))*sqrt(
sqr(N(L,'g')*sum(B,Lj(L,B)*V(B)*cos(a(B)))-
N(L,'g')*sum(B,Li(L,B)*V(B)*cos(a(B)))-
N(L,'b')*sum(B,Lj(L,B)*V(B)*sin(a(B)))+
N(L,'b')*sum(B,Li(L,B)*V(B)*sin(a(B)))-
N(L,'b0')*sum(B,Lj(L,B)*V(B)*sin(a(B))))+
sqr(N(L,'b')*sum(B,Lj(L,B)*V(B)*cos(a(B)))-
N(L,'b')*sum(B,Li(L,B)*V(B)*cos(a(B)))+
N(L,'g')*sum(B,Lj(L,B)*V(B)*sin(a(B)))-
N(L,'g')*sum(B,Li(L,B)*V(B)*sin(a(B)))+
N(L,'b0')*sum(B,Lj(L,B)*V(B)*cos(a(B)))));
N(L,'b')$(ord(L) eq lambda('line')) = -1E-6;
N(L,'g')$(ord(L) eq lambda('line')) = 0;
N(L,'b0')$(ord(L) eq lambda('line')) = 0;
N(L,'g0')$(ord(L) eq lambda('line')) = 0;
Pijceq(L).. Pijc(L) =e= sum(B,Li(L,B)*Vc(B))*sqrt(
sqr(N(L,'g')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))-
N(L,'g')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))-
N(L,'b')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))+
N(L,'b')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))-
N(L,'b0')*sum(B,Li(L,B)*Vc(B)*sin(ac(B))))+
sqr(N(L,'b')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))-
N(L,'b')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))+
N(L,'g')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))-
N(L,'g')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))+
N(L,'b0')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))));
Pjiceq(L).. Pjic(L) =e= sum(B,Lj(L,B)*Vc(B))*sqrt(
sqr(N(L,'g')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))-
N(L,'g')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))-
N(L,'b')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))+
N(L,'b')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))-
N(L,'b0')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B))))+
sqr(N(L,'b')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))-
N(L,'b')*sum(B,Li(L,B)*Vc(B)*cos(ac(B)))+
N(L,'g')*sum(B,Lj(L,B)*Vc(B)*sin(ac(B)))-
N(L,'g')*sum(B,Li(L,B)*Vc(B)*sin(ac(B)))+
N(L,'b0')*sum(B,Lj(L,B)*Vc(B)*cos(ac(B)))));
$goto solvestat
* -------------------------------------------------------------------------
* Solve Market Problem
* -------------------------------------------------------------------------
$label solvestat
model market /all/;
option nlp = minos;
option iterlim = 50000;
solve market using nlp minimizing obj;
scalar mstatus /0/;
scalar sstatus /0/;
if ((market.modelstat eq 1), mstatus = 1;);
if ((market.modelstat eq 2), mstatus = 2;);
if ((market.modelstat eq 3), mstatus = 3;);
if ((market.modelstat eq 4), mstatus = 4;);
if ((market.modelstat eq 5), mstatus = 5;);
if ((market.modelstat eq 6), mstatus = 6;);
if ((market.modelstat eq 7), mstatus = 7;);
if ((market.modelstat eq 8), mstatus = 8;);
if ((market.modelstat eq 9), mstatus = 9;);
if ((market.modelstat eq 10), mstatus = 10;);
if ((market.modelstat eq 11), mstatus = 11;);
if ((market.modelstat eq 12), mstatus = 12;);
if ((market.modelstat eq 13), mstatus = 13;);
if ((market.solvestat eq 1), sstatus = 1;);
if ((market.solvestat eq 2), sstatus = 2;);
if ((market.solvestat eq 3), sstatus = 3;);
if ((market.solvestat eq 4), sstatus = 4;);
if ((market.solvestat eq 5), sstatus = 5;);
if ((market.solvestat eq 6), sstatus = 6;);
if ((market.solvestat eq 7), sstatus = 7;);
if ((market.solvestat eq 8), sstatus = 8;);
if ((market.solvestat eq 9), sstatus = 9;);
if ((market.solvestat eq 10), sstatus = 10;);
if ((market.solvestat eq 11), sstatus = 11;);
if ((market.solvestat eq 12), sstatus = 12;);
if ((market.solvestat eq 13), sstatus = 13;);
$libinclude psatout Ps.l G
$libinclude psatout Pd.l C
$libinclude psatout DPGup.l G
$libinclude psatout DPGdw.l G
$libinclude psatout DPDup.l C
$libinclude psatout DPDdw.l C
$libinclude psatout V.l B
$libinclude psatout a.l B
$libinclude psatout Qg.l B
$libinclude psatout Peq.m B
$libinclude psatout Pij.l L
$libinclude psatout Pji.l L
$libinclude psatout V.m B
$libinclude psatout Pij.m L
$libinclude psatout Pji.m L
$libinclude psatout lambdac.l
$libinclude psatout kg.l
$libinclude psatout Vc.l B
$libinclude psatout ac.l B
$libinclude psatout Qgc.l B
$libinclude psatout Pijc.l L
$libinclude psatout Pjic.l L
$libinclude psatout Pceq.m B
$libinclude psatout lambdac.m
$libinclude psatout mstatus
$libinclude psatout sstatus