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updating sdpopf formulation
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@hhijazi
hhijazi committed Jan 10, 2018
1 parent 943dc40 commit ec613b0
Showing 1 changed file with 43 additions and 41 deletions.
84 changes: 43 additions & 41 deletions examples/MINLP/Power/SDPOPF/SDPOPF_main.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -218,74 +218,76 @@ int main (int argc, char * argv[]) {
/** Objective */
auto obj = product(grid->c1, Pg) + product(grid->c2, power(Pg,2)) + sum(grid->c0);
SDP.min(obj.in(grid->gens));



/** Constraints */
/* Second-order cone constraints */
Constraint SOC("SOC");
SOC = power(R_Wij, 2) + power(Im_Wij, 2) - Wii.from()*Wii.to() ;
SOC = power(R_Wij, 2) + power(Im_Wij, 2) - Wii.from()*Wii.to();
SDP.add_constraint(SOC.in(bus_pairs) <= 0);

/* Flow conservation */
Constraint KCL_P("KCL_P");
Constraint KCL_Q("KCL_Q");
KCL_P = sum(Pf_from.out_arcs()) + sum(Pf_to.in_arcs()) + grid->pl - sum(Pg.in_gens());
KCL_Q = sum(Qf_from.out_arcs()) + sum(Qf_to.in_arcs()) + grid->ql - sum(Qg.in_gens());
/* Shunts */
KCL_P += grid->gs*Wii;
KCL_Q -= grid->bs*Wii;
KCL_P = sum(Pf_from.out_arcs()) + sum(Pf_to.in_arcs()) + grid->pl - sum(Pg.in_gens()) + grid->gs*Wii;
SDP.add_constraint(KCL_P.in(grid->nodes) == 0);

Constraint KCL_Q("KCL_Q");
KCL_Q = sum(Qf_from.out_arcs()) + sum(Qf_to.in_arcs()) + grid->ql - sum(Qg.in_gens()) - grid->bs*Wii;
SDP.add_constraint(KCL_Q.in(grid->nodes) == 0);

/* AC Power Flow */
Constraint Flow_P_From("Flow_P_From");
Flow_P_From += Pf_from;
Flow_P_From -= grid->g_ff*Wii.from();
Flow_P_From -= grid->g_ft*R_Wij.in_pairs();
Flow_P_From -= grid->b_ft*Im_Wij.in_pairs();
Flow_P_From = Pf_from - (grid->g_ff*Wii.from() + grid->g_ft*R_Wij.in_pairs() + grid->b_ft*Im_Wij.in_pairs());
SDP.add_constraint(Flow_P_From.in(grid->arcs) == 0);

Constraint Flow_P_To("Flow_P_To");
Flow_P_To += Pf_to;
Flow_P_To -= grid->g_tt*Wii.to();
Flow_P_To -= grid->g_tf*R_Wij.in_pairs();
Flow_P_To += grid->b_tf*Im_Wij.in_pairs();
Flow_P_To = Pf_to - (grid->g_tt*Wii.to() + grid->g_tf*R_Wij.in_pairs() - grid->b_tf*Im_Wij.in_pairs());
SDP.add_constraint(Flow_P_To.in(grid->arcs) == 0);

Constraint Flow_Q_From("Flow_Q_From");
Flow_Q_From += Qf_from;
Flow_Q_From += grid->b_ff*Wii.from();
Flow_Q_From += grid->b_ft*R_Wij.in_pairs();
Flow_Q_From -= grid->g_ft*Im_Wij.in_pairs();
Flow_Q_From = Qf_from - (grid->g_ft*Im_Wij.in_pairs() - grid->b_ff*Wii.from() - grid->b_ft*R_Wij.in_pairs());
SDP.add_constraint(Flow_Q_From.in(grid->arcs) == 0);

Constraint Flow_Q_To("Flow_Q_To");
Flow_Q_To += Qf_to;
Flow_Q_To += grid->b_tt*Wii.to();
Flow_Q_To += grid->b_tf*R_Wij.in_pairs();
Flow_Q_To += grid->g_tf*Im_Wij.in_pairs();
Flow_Q_To = Qf_to + (grid->b_tt*Wii.to() + grid->b_tf*R_Wij.in_pairs() + grid->g_tf*Im_Wij.in_pairs());
SDP.add_constraint(Flow_Q_To.in(grid->arcs) == 0);

/* Phase Angle Bounds constraints */
Constraint PAD_UB("PAD_UB");
PAD_UB = Im_Wij - (grid->tan_th_max)*R_Wij;
SDP.add_constraint(PAD_UB.in(bus_pairs) <= 0);
PAD_UB = Im_Wij;
PAD_UB <= grid->tan_th_max*R_Wij;
SDP.add_constraint(PAD_UB.in(bus_pairs));

Constraint PAD_LB("PAD_LB");
PAD_LB = Im_Wij - grid->tan_th_min*R_Wij;
SDP.add_constraint(PAD_LB.in(bus_pairs) >= 0);

PAD_LB = Im_Wij;
PAD_LB >= grid->tan_th_min*R_Wij;
SDP.add_constraint(PAD_LB.in(bus_pairs));

/* Thermal Limit Constraints */
Constraint Thermal_Limit_from("Thermal_Limit_from");
Thermal_Limit_from += power(Pf_from, 2) + power(Qf_from, 2);
Thermal_Limit_from -= power(grid->S_max,2);
SDP.add_constraint(Thermal_Limit_from.in(grid->arcs) <= 0);

Thermal_Limit_from = power(Pf_from, 2) + power(Qf_from, 2);
Thermal_Limit_from <= power(grid->S_max,2);
SDP.add_constraint(Thermal_Limit_from.in(grid->arcs));


Constraint Thermal_Limit_to("Thermal_Limit_to");
Thermal_Limit_to += power(Pf_to, 2) + power(Qf_to, 2);
Thermal_Limit_to -= power(grid->S_max,2);
SDP.add_constraint(Thermal_Limit_to.in(grid->arcs) <= 0);

Thermal_Limit_to = power(Pf_to, 2) + power(Qf_to, 2);
Thermal_Limit_to <= power(grid->S_max,2);
SDP.add_constraint(Thermal_Limit_to.in(grid->arcs));

/* Lifted Nonlinear Cuts */
Constraint LNC1("LNC1");
LNC1 = (grid->v_min.from()+grid->v_max.from())*(grid->v_min.to()+grid->v_max.to())*(sin(0.5*(grid->th_max+grid->th_min))*Im_Wij + cos(0.5*(grid->th_max+grid->th_min))*R_Wij);
LNC1 -= grid->v_max.to()*cos(0.5*(grid->th_max-grid->th_min))*(grid->v_min.to()+grid->v_max.to())*Wii.from();
LNC1 -= grid->v_max.from()*cos(0.5*(grid->th_max-grid->th_min))*(grid->v_min.from()+grid->v_max.from())*Wii.to();
LNC1 -= grid->v_max.from()*grid->v_max.to()*cos(0.5*(grid->th_max-grid->th_min))*(grid->v_min.from()*grid->v_min.to() - grid->v_max.from()*grid->v_max.to());
SDP.add_constraint(LNC1.in(bus_pairs) >= 0);

Constraint LNC2("LNC2");
LNC2 = (grid->v_min.from()+grid->v_max.from())*(grid->v_min.to()+grid->v_max.to())*(sin(0.5*(grid->th_max+grid->th_min))*Im_Wij + cos(0.5*(grid->th_max+grid->th_min))*R_Wij);
LNC2 -= grid->v_min.to()*cos(0.5*(grid->th_max-grid->th_min))*(grid->v_min.to()+grid->v_max.to())*Wii.from();
LNC2 -= grid->v_min.from()*cos(0.5*(grid->th_max-grid->th_min))*(grid->v_min.from()+grid->v_max.from())*Wii.to();
LNC2 += grid->v_min.from()*grid->v_min.to()*cos(0.5*(grid->th_max-grid->th_min))*(grid->v_min.from()*grid->v_min.to() - grid->v_max.from()*grid->v_max.to());
SDP.add_constraint(LNC2.in(bus_pairs) >= 0);

/* Solver selection */
solver SDPOPF(SDP,ipopt);
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