Imposing Radiality Constraints in Distribution System Optimization Problems

@article{lavorato2012imposing,
  title={Imposing Radiality Constraints in Distribution System Optimization Problems},
  author={Lavorato, M. and Franco, J.F. and Rider, M.J. and Romero, R.},
  journal={Power Systems, IEEE Transactions on},
  number={99},
  pages={1--1},
  year={2012},
  publisher={IEEE}
}

set

     Powerchar    Power characteristics 
/Pg,Pd/

     GenPchar     Generator active power characteristics  /puplim,plowlim/

set i Bus Node /1*5/

alias(i,j);

set 
PConNode(i)     Active power control node/1/

     PGeneralNode(i) General active power node /2*5/;

set ij(i,j)/

    1.2

    1.3

    1.4

    2.3

    2.5

    3.4

    3.5

    4.5/;

set ji(j,i)/

    1.2

    1.3

    1.4

    2.3

    2.5

    3.4

    3.5

    4.5/;

Table 
Power(i,Powerchar)       Power of node

   Pd   Pg

2  25   0

3  30   0

4  20   0

5  60   0

Table 
GenP(i,GenPchar)  Generators active power output limits

         plowlim      puplim

1        0            150

Parameters

          Pd                    Active demand

;

          Pd(i)= Power(i,'Pd');

display Pd;

Variables

          Pg(i)                 Active power output ;

          Pg.up(i) = GenP(i,"puplim");

Variables

          v      cost

          f(i,j) brabch power;

          f.up(i,j)=100;



binary Variables

          x(i,j) output;

Equations

      Pfn       Pg-Pd-Ploss=0

      xfn

      vfn

      maxbfn_pos

      maxbfn_neg

;

     Pfn(i).. 0 =e= Pg(i)-Pd(i)+sum(j$ji(j,i),f(j,i))-sum(j$ij(i,j),f(i,j));

     xfn.. card(i)-1
=e= sum(ij(i,j),x(i,j));

     maxbfn_pos(i,j)..
f.up(i,j)*x(i,j)=g= f(i,j);

     maxbfn_neg(i,j)..
f.up(i,j)*x(i,j)=g= -f(i,j);

     vfn.. v =e= sum(ij(i,j),
f(i,j)*f(i,j) );

option limrow=100, limcol=100;

option MINLP=BARON;

*option MINLP=SBB;

*option rminlp=conopt;

* option MINLP=CONOPT;

* option NLP=CONOPT;

Model Optimal /
all /;

Solve Optimal minimizing v using MINLP;

*Solve Optimal minimizing v using XA;

display v.l, x.l, f.l, Pg.l;