Variable enters more than one =C= equation

GAMS
1

Hey all,

I need your help. I develop a SOCP formulation for optimal power flow. However, The following error shows

**** Variable enters more than one =C= equation
X(i1)

**** Variable enters more than one =C= equation
X(i2)

**** Variable enters more than one =C= equation
X(i3)

**** Variable enters more than one =C= equation
X(i4)

**** Variable enters more than one =C= equation
X(i5)

Here is the model

*** SETS

set i bus /i1*i5/;
alias (i,j);

*** PARAMETERS

table G(i,j)
$include g.txt
;
table B(i,j)
$include b.txt
;

*** VARIABLES

variable obj
variable P(i)
variable Q(i)
variable X(i)
variable R(i,j)
variable Y(i,j)

*** EQUATION DECLARATION

equations
power_loss
active_power(i)
reactive_power(i)
cone(i,j)
;

*** EQUATION

X.fx(i)$(ord(i)=1)=1.061.06/sqrt(2);
power_loss…
obj =e= sum((i,j),G(i,j)(sqrt(2)*X(i)+sqrt(2)X(j)-2R(i,j)));
active_power(i)…
P(i) =e= sum(j,G(i,j)*R(i,j)+B(i,j)*Y(i,j));
reactive_power(i)…
Q(i) =e= sum(j,-B(i,j)*R(i,j)+G(i,j)*Y(i,j));
cone(i,j)…
X(i)+X(j) =C= R(i,j)+Y(i,j);
model ep /all/;
option limrow = 10000;
option lp=mosek;
solve ep using lp minimizing obj;
g.txt (758 Bytes)
b.txt (766 Bytes)

2

Hi
You might have a closer look here: https://www.gams.com/latest/docs/UG_LanguageFeatures.html#UG_LanguageFeatures_ConicProgramming.

Cheers
Renger

3

Hi Renger,

Thanks for your response. I read this document carefully and realize that each decision variables is a member of at most one set in SOCP. Therefore, It seems that one decision variable can only be in one =C= equation.

Do you think my model is a SOCP formulation? and how do I reformulate it as a SOCP one?

Thanks.