### 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.