## Coding second order cone constraint in GAMS

Problems with modeling
bbiswas
User Posts: 14
Joined: 11 months ago

### Coding second order cone constraint in GAMS

Hi,
I'm working on second order cone programming for power distribution system problems. Suppose my system includes 5 buses and 4 lines. So,
set bi /bus1*bus5/
set li /line1*line4/
alias(bi,bj)

Now the vector V(bi) stands for voltage magnitude squared of a node, P(bi,bj) and Q(bi,bj) stand for the active and reactive power flow from bus bi to bj. My second order cone equation is

V(bi) + V(bj) >= || 2P(bi,bj), 2Q(bi,bj), (V(bi)-V(bj)) ||

I wrote this equation in GAMS as,

conic(bi).. V(bi)+V(bj) =C= sum(bj, (2*P(bi,bj) + 2*Q(bi,bj)))

I'm getting error for uncontrolled set. I will appreciate highly if anyone help to write the equation properly for GAMS mosek solver. Thanks.

Renger
Posts: 422
Joined: 3 years ago

### Re: Coding second order cone constraint in GAMS

Hi
You define the equation over bi, but the equation itself is over bi and bj on the left hand side:

Code: Select all

``````conic(bi).. V(bi)+V(bj) =C= sum(bj, (2*P(bi,bj) + 2*Q(bi,bj)))
``````
In this equation, Gams has to use one V(bj) but is not clear which bj to choose. Then on the RHS you use at the same time the sum over all bj.

This would work

Code: Select all

``````alias(bj, bjj);
conic(bi,bj).. V(bi)+V(bj) =C= sum(bjj, (2*P(bi,bjj) + 2*Q(bi,bjj)))
* or
conic(bi).. V(bi) =C= sum(bjj, (2*P(bi,bjj) + 2*Q(bi,bjj)))
``````
but that is probably not what you want to achieve.
Over which bj should be summed?
Cheeers
Renger
____________________________________
Enjoy modeling even more: Read my blog on modeling at The lazy economist

bbiswas
User Posts: 14
Joined: 11 months ago

### Re: Coding second order cone constraint in GAMS

Thank you for your response sir. In fact I need to know how to write conic constraints in GAMS language.
Like I mention in my case, let's assume V is a vector of variables which stands for the voltage magnitude squared of nodes. P and Q are also variable matrices stands for the active and reactive power flow among the nodes. The number of nodes of my system for example is 5.
So, the dimensions,
V is (5*1)
P is (5*5)
Q is (5*5)

Now, my conic equation is

V(i) + V(j) >= sqrt ((2*P(i,j))^2 + (2*Q(i,j))^2 + (V(i) - V(j))^2)

how can I write it as a conic constraint using "=C=" in GAMS language?
Thank you.

Renger
Posts: 422
Joined: 3 years ago

### Re: Coding second order cone constraint in GAMS

Hi
Did you have a look at the documentation on conic programming: Conic programming?
Cheers
Renger
____________________________________
Enjoy modeling even more: Read my blog on modeling at The lazy economist