$title Optimal power flow for a Five-bus system

$onText
For more details please refer to Chapter 6 (Gcode6.3), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
--------------------------------------------------------------------------------
Model type: LP
--------------------------------------------------------------------------------
Contributed by
Dr. Alireza Soroudi
IEEE Senior Member
email: alireza.soroudi@gmail.com
We do request that publications derived from the use of the developed GAMS code
explicitly acknowledge that fact by citing
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
DOI: doi.org/10.1007/978-3-319-62350-4
$offText

Set
   bus        / 1*5   /
   slack(bus) / 1     /
   Gen        / g1*g5 /;

Scalar Sbase / 100 /;

Alias (bus,node);

Table GenData(Gen,*) 'generating units characteristics'
       b   pmin  pmax
   g1  14  0     40
   g2  15  0     170
   g3  30  0     520
   g4  40  0     200
   g5  10  0     600 ;
* -----------------------------------------------------

Set GBconect(bus,Gen) 'connectivity index of each generating unit to each bus'
/
   1.g1
   1.g2
   3.g3
   4.g4
   5.g5
/;
****************************************************

Table BusData(bus,*) 'demands of each bus in MW'
      Pd
   2  300
   3  300
   4  400;
****************************************************

Set conex 'bus connectivity matrix'
/
   1.2
   2.3
   3.4
   4.1
   4.5
   5.1
/;
* -----------------------------------------------------
conex(bus,node)$(conex(node,bus)) = 1;

Table branch(bus,node,*) 'network technical characteristics'
        x       Limit
   1.2  0.0281  400
   1.4  0.0304  400
   1.5  0.0064  400
   2.3  0.0108  400
   3.4  0.0297  400
   4.5  0.0297  240;

branch(bus,node,'x')$(branch(bus,node,'x')=0)         =   branch(node,bus,'x');
branch(bus,node,'Limit')$(branch(bus,node,'Limit')=0) =   branch(node,bus,'Limit');
branch(bus,node,'bij')$conex(bus,node)                = 1/branch(bus,node,'x');
*****************************************************

Variable OF, Pij(bus,node), Pg(Gen), delta(bus);
Equation const1, const2, const3;
*********************************************

const1(bus,node)$(conex(bus,node))..
   Pij(bus,node) =e= branch(bus,node,'bij')*(delta(bus) - delta(node));

const2(bus)..
   sum(Gen$GBconect(bus,Gen), Pg(Gen)) - BusData(bus,'pd')/Sbase =e= sum(node$conex(node,bus), Pij(bus,node));

const3..
   OF =g= sum(Gen, Pg(Gen)*GenData(Gen,'b')*Sbase);

Model loadflow / const1, const2, const3 /;

Pg.lo(Gen) = GenData(Gen,'Pmin')/Sbase;
Pg.up(Gen) = GenData(Gen,'Pmax')/Sbase;
delta.up(bus)   = pi;
delta.lo(bus)   =-pi;
delta.fx(slack) = 0;
Pij.up(bus,node)$((conex(bus,node)))= 1*branch(bus,node,'Limit')/Sbase;
Pij.lo(bus,node)$((conex(bus,node)))=-1*branch(bus,node,'Limit')/Sbase;

solve loadflow minimizing OF using lp;

Parameter report(bus,*), Congestioncost;
report(bus,'Gen(MW)')    = sum(Gen$GBconect(bus,Gen), Pg.l(Gen))*sbase;
report(bus,'Angle')      = delta.l(bus);
report(bus,'load(MW)')   = BusData(bus,'pd');
report(bus,'LMP($/MWh)') = const2.m(bus)/sbase ;
Congestioncost = sum((bus,node), Pij.l(bus,node)*(-const2.m(bus) + const2.m(node)))/2;
display report, Pij.l, Congestioncost;