Non linear constraint in a convex optimization.
Posted: Thu Aug 01, 2019 6:23 pm
Hello,
I am intending to formulate a convex optimization for a distribution system containing size of 13 bus of example. The variables are as such,
set: bi=bj=/bus1*bus13/;
voltage squared: v(bi)
line current: il(bi,bj)
line active power: pl(bi,bj)
line reactive power: ql(bi,bj)
line resistance: R(bi,bj)
line reactance: X(bi,bj)
connection matrix of the buses: c(bi,bj)
Now, I am trying to represent the following equation:
V_i^2 - V_j^2 = 2(P_ij*R_ij + Q_ij*X_ij) - Z_ij^2*I_ij^2
in the form of,
c(bi,bj)*(v(bi)-v(bj)) =e= c(bi,bj)*(2*(pl(bi,bj)*R(bi,bj) + ql(bi,bj)*X(bi,bj)) - (sqr(R(bi,bj))+sqr(X(bi,bj)))*il(bi,bj));
after including this constraint the GAMS solver gives me an error saying
"The problem contains both conic and non-linear constraints."
Btw, I have a conic constraint in my formulation, but I couldn't see how the aforementioned equation is non-linear and how can I resolve it. Please help me in this regard. Thank you.
I am intending to formulate a convex optimization for a distribution system containing size of 13 bus of example. The variables are as such,
set: bi=bj=/bus1*bus13/;
voltage squared: v(bi)
line current: il(bi,bj)
line active power: pl(bi,bj)
line reactive power: ql(bi,bj)
line resistance: R(bi,bj)
line reactance: X(bi,bj)
connection matrix of the buses: c(bi,bj)
Now, I am trying to represent the following equation:
V_i^2 - V_j^2 = 2(P_ij*R_ij + Q_ij*X_ij) - Z_ij^2*I_ij^2
in the form of,
c(bi,bj)*(v(bi)-v(bj)) =e= c(bi,bj)*(2*(pl(bi,bj)*R(bi,bj) + ql(bi,bj)*X(bi,bj)) - (sqr(R(bi,bj))+sqr(X(bi,bj)))*il(bi,bj));
after including this constraint the GAMS solver gives me an error saying
"The problem contains both conic and non-linear constraints."
Btw, I have a conic constraint in my formulation, but I couldn't see how the aforementioned equation is non-linear and how can I resolve it. Please help me in this regard. Thank you.