GAMS Code

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GAMS code:simple
parameters
y l / 9.95037190209989/
a l / -1.47112767430373/;
variables
z , p1,p2, q1, q2, v1, v2, v3, d1, d2;
p1.lo = 0; p2.lo = 0;
p1.up = 3; p2.up = 0.8;
q1.lo = - 2 ; q2.lo = - 2 ;
q1.up = 2; q2.up = 2;
v1.lo = .9 5; v2.lo = . 95; v3.l o = .95;
v1.up = 1 .1; v2.up = 1. 1 ; v3.up = 1.1;
d 1 . lo = - pi ; d2. l o = - p i ;
d1.up = pi ; d2.up = p i ;
v1.l=1; v2.l=1; v3.l=1;
d1.l=0; d2.l=0;

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GAMS code:simple
bp1.. p1 =e=
bp2.. p2 =e=
bp3.. -0.8 =e=
bq1.. q1 =e=
bq2.. q2 =e=
bq3.. -0.6 =e=
equations
o f , bp1, bp2, bp3, bq1, bq2, bq3, l12, l 21, l13, l3 1, l 23, l32;
o f . . z =e= 2*p1 + p2;
yl*cos(al)*(v1)**2-yl*v1*v2*cos(d1-d2-al)+
yl*cos(al)*(v1)**2-yl*v1*v3*cos(d1- 0 - a l ) ;
yl*cos(al)*(v2)**2-yl*v2*v1*cos(d2-d1-al)+
yl*cos(al)*(v2)**2-yl*v2*v3*cos(d2- 0 - a l ) ;
yl*cos(al)*(v3)**2-yl*v3*v1*cos( 0-d1-al)+
yl*cos(al)*(v3)**2-yl*v3*v2*cos( 0-d2-al);
-yl*sin(al)*(v1)**2-yl*v1*v2*sin(d1-d2-al)-
y l*si n(al ) * ( v 1 ) * * 2- y l*v1*v3* sin(d1- 0- al ) ;
-yl*sin(al)*(v2)**2-yl*v2*v1*sin(d2-d1-al)-
yl*sin(al)*(v2)**2-yl*v2*v3*sin(d2- 0 - a l ) ;
- y l*si n(al ) * ( v 3 ) * * 2- y l*v3*v1* s in( 0- d1- al ) -
y l*si n(al ) * ( v 3 ) * * 2- y l*v3*v2* s in( 0- d2- al ) ;

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GAMS code:simple
l 1 2 . . sqrt(sqr(yl*cos(al)*(v1)**2-yl*v1*v2*cos(d1-d2-al))+
sqr(-yl*sin(al)*(v1)**2-yl*v1*v2*sin(d1-d2-al))) =l= 0.25;
l 2 1 . . sqrt(sqr(yl*cos(al)*(v2)**2-yl*v2*v1*cos(d2-d1-al))+
sqr(-yl*sin(al)*(v2)**2-yl*v2*v1*sin(d2-d1-al))) =l= 0.25;
l 1 3 . . sqrt(sqr(yl*cos(al)*(v1)**2-yl*v1*v3*cos(d1- 0-al))+
sqr(-yl*sin(al)*(v1)**2-yl*v1*v3*sin(d1- 0-al))) =l= 2;
l 3 1 . . sqrt(sqr(yl*cos(al)*(v3)**2-yl*v3*v1*cos( 0-d1-al))+
sqr(-yl*sin(al)*(v3)**2-yl*v3*v1*sin( 0-d1-al))) =l= 2;
l 2 3 . . sqrt(sqr(yl*cos(al)*(v2)**2-yl*v2*v3*cos(d2- 0-al))+
sqr(-yl*sin(al)*(v2)**2-yl*v2*v3*sin(d2- 0-al))) =l= 2;
l 3 2 . . sqrt(sqr(yl*cos(al)*(v3)**2-yl*v3*v2*cos( 0-d2-al))+
sqr(-yl*sin(al)*(v3)**2-yl*v3*v2*sin( 0-d2-al))) =l= 2;

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GAMS code:simple
model simpleopf / a l l / ;
solve simpl eopf using nlp mini m izing z ;
option decimals = 8;
display p 1 . l , p 2 . l , q 1 . l , q 2 . l , v 1 . l ,
v 2 . l , v 3 . l , d 1 . l , d 2 . l ;

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GAMS code
$ t it l e opf
set
g index of units /g1*g2/
n index of nodes /n1*n3/
g2n(g,n) units to nodes /g1.n1,g2.n2/;
a l ias( n ,np) ;

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GAMS code
table Gdat (g, * ) uni t data
Pmin Pmax Qmin Qmax Cost
g1 0.0 3.0 -2.0 2.0 2
g2 0.0 0.8 -2.0 2.0 1;
table Ndat (n, * ) node data
Vmin Vmax Pd Qd
n1 0.95 1.10 0.0 0.0
n2 0.95 1.10 0.0 0.0
n3 0.95 1.10 0.8 0.6;

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GAMS code
table Ldat(n,np,*) line
y l
data
t hel yshalf thes cap
n1.n2 9.95037190209989 -1.47112767430373 0 0 0.25
n1.n3 9.95037190209989 -1.47112767430373 0 0 2
n2.n3 9.95037190209989 -1.47112767430373 0 0 2;
L d a t ( n , n p , ' y l ' ) $(ord(n) gt ord(np))=Ldat(np,n,'yl');
Ldat(n,np,'thel')$(ord(n) gt ord(np))=Ldat(np,n,'thel');
Ldat(n,np, 'yshalf') $(ord(n) gt ord(np))=Ldat(np,n,'yshalf');
Ldat(n,np,'thes')$(ord(n) gt ord(np))=Ldat(np,n,'thes');
Ldat(n,np,'cap') $(ord(n) gt ord(np))=Ldat(np,n,'cap');

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GAMS code
variables
z objective function
p(g) un it g P gener a tion
q(g) un it g Q gener a tion
v(n) node n volta ge m
agni t ude
d(n) node n angle
pf(n,np) P flow per l i n e
qf( n,np) Q f low per l ine;

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GAMS code
p.lo(g)=Gdat(g,'Pmin');
p.up(g)=Gdat(g,'Pmax');
q.lo(g)=Gdat(g,'Qmin');
q.up(g)=Gdat(g,'Qmax');
v.lo(n)=Ndat(n,'Vmin');
v.up(n)=Ndat(n,'Vmax');
d. lo( n) = - pi;
d.up(n)= p i ;
d . fx( ' n3' )=0;

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GAMS code
equations
cost objective function
Pfcal(n,np) P flow calculation
Qfcal(n,np) Qflow calculation
Pbal(n)
Qbal(n)
S l im(n,n p)
P node balance
Q node balance
Sflow l i m i t ;

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GAMS code
Pfcal(n,np)..pf(n,np)=e=
v(n)**2*Ldat(n,np, 'yl')*cos(-Ldat(n,np, 'thel'))-
v(n)*v(np)*Ldat(n,np, 'yl')*cos(d(n)-d(np)-Ldat(n,np,'thel'))+
(1/2)*v(n)**2*Ldat(n,np, 'yshalf')*cos(-Ldat(n,np,'thes'));
Qfcal(n,np)..qf(n,np)=e=
v( n) **2*Ldat ( n, np, 'yl' ) *sin( - Ldat ( n, np, 't hel' ) ) -
v(n)*v(np)*Ldat(n,np, 'yl')*sin(d(n)-d(np)-Ldat(n,np,'thel'))+
(1/2)*v(n)**2*Ldat(n,np, 'yshalf')*sin(-Ldat(n,np, 'thes'));

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GAMS code
c o s t . . z =e= sum(g,Gdat(g,'cost')*p(g));
Pbal(n).. sum(g$g2n(g,n),p(g))-Ndat(n,'Pd')=e=sum(np,pf(n,np));
Qbal(n).. sum(g$g2n(g,n),q(g))-Ndat(n,'Qd')=e=sum(np,qf(n,np));
Slim(n,np).. sqrt(power(pf(n,np),2)+power(qf(n,np),2))=l=Ldat(n,np, 'cap');

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GAMS code
model opf /all/;
solve opf using nlp minimizing z ;
option decimals = 8
display p . l, q. l , v.l , d .l , pf . l , qf . l ;

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