Reference
Alireza Soroudi, Power System Optimization Modelling in GAMS, Model OPF2bus (Gcode6.1) in chapter Multi-Period Optimal Power Flow, 2017
$title Optimal power flow for a simple two-bus system

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For more details please refer to Chapter 6 (Gcode6.1), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
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Model type: QCP
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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
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Set
   Gen / g1*g2 /
   bus /  1*2  /;

Scalar
   L2      / 400 /
   X12     / 0.2 /
   Sbase   / 100 /
   P12_max / 1.5 /;

Table data(Gen,*)
       a     b      c      Pmin  Pmax
   G1  3     20     100    28    206
   G2  4.05  18.07  98.87  90    284;

Variable P(gen), OF, delta(bus), P12;
Equation eq1, eq2, eq3, eq4;

eq1.. OF =e= sum(gen, data(gen,'a')*P(gen)*P(gen) + data(gen,'b')*P(gen) + data(gen,'c'));
eq2.. P('G1') =e= P12;
eq3.. P('G2') + P12 =e= L2/Sbase;
eq4.. P12 =e= (delta('1') - delta('2'))/X12;

P.lo(gen) = data(gen,'Pmin')/Sbase;
P.up(gen) = data(gen,'Pmax')/Sbase;
P12.lo    =-P12_max;
P12.up    = P12_max;
delta.fx('1')=0;

Model OPF / all /;
solve OPF using qcp minimizing of;