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### 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.

### Re: Non linear constraint in a convex optimization.

Posted: Sat Aug 03, 2019 10:09 am
Hi
The square of a variable is non-linear, so you now have an NLP. I don't know how to make the square (approximately) linear except for using Taylor series.
Cheers
Renger

### Re: Non linear constraint in a convex optimization.

Posted: Sat Aug 03, 2019 3:50 pm
Thank you sir for your reply. But I defined the squared of voltage magnitude V_i^2 with a new variable v(bi) and current squared with il(bi,bj). So, in the equation
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));
there isn't any squared variable. R(bi,bj) and X(bi,bj) are parameters with fixed values not variables. That's why I was confused.

### Re: Non linear constraint in a convex optimization.

Posted: Sat Aug 03, 2019 4:07 pm
Hi
In that case you should not write "the variables are such that... including X and R.
It is good practice to make a clear distinction between variables and parameters in your code (e.g. variables in capitals and parameters in lower case).

You have also a product of c * v and c * pl, so if these are variables, this is non-linear.
Cheers
Renger

### Re: Non linear constraint in a convex optimization.

Posted: Sat Aug 03, 2019 4:12 pm
c(bi,bj) is also a parameter which denotes the connection between nodes. To re-write the equations as you said, variables as capital and parameters as small,

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));

Thank you.

### Re: Non linear constraint in a convex optimization.

Posted: Sat Aug 03, 2019 8:32 pm
Hi j
Please send the complete code as attachment.
Cheers
Renger