opf_current_balance_fcn

OPF_CURRENT_BALANCE_FCN  Evaluates AC current balance constraints and their gradients.
   [G, DG] = OPF_CURRENT_BALANCE_FCN(X, OM, YBUS, MPOPT)

   Computes the real or imaginary current balance equality constraints for
   AC optimal power flow. Computes constraint vectors and their gradients.

   Inputs:
     X : optimization vector
     MPC : MATPOWER case struct
     YBUS : bus admittance matrix
     MPOPT : MATPOWER options struct

   Outputs:
     G  : vector of equality constraint values (real/imaginary current balances)
     DG : (optional) equality constraint gradients

   Examples:
       g = opf_current_balance_fcn(x, mpc, Ybus, mpopt);
       [g, dg] = opf_current_balance_fcn(x, mpc, Ybus, mpopt);

   See also OPF_POWER_BALANCE_HESS

0001 function [g, dg] = opf_current_balance_fcn(x, mpc, Ybus, mpopt)
0002 %OPF_CURRENT_BALANCE_FCN  Evaluates AC current balance constraints and their gradients.
0003 %   [G, DG] = OPF_CURRENT_BALANCE_FCN(X, OM, YBUS, MPOPT)
0004 %
0005 %   Computes the real or imaginary current balance equality constraints for
0006 %   AC optimal power flow. Computes constraint vectors and their gradients.
0007 %
0008 %   Inputs:
0009 %     X : optimization vector
0010 %     MPC : MATPOWER case struct
0011 %     YBUS : bus admittance matrix
0012 %     MPOPT : MATPOWER options struct
0013 %
0014 %   Outputs:
0015 %     G  : vector of equality constraint values (real/imaginary current balances)
0016 %     DG : (optional) equality constraint gradients
0017 %
0018 %   Examples:
0019 %       g = opf_current_balance_fcn(x, mpc, Ybus, mpopt);
0020 %       [g, dg] = opf_current_balance_fcn(x, mpc, Ybus, mpopt);
0021 %
0022 %   See also OPF_POWER_BALANCE_HESS
0023 
0024 %   MATPOWER
0025 %   Copyright (c) 1996-2018, Power Systems Engineering Research Center (PSERC)
0026 %   by Baljinnyam Sereeter, Delft University of Technology
0027 %   and Ray Zimmerman, PSERC Cornell
0028 %
0029 %   This file is part of MATPOWER.
0030 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0031 %   See https://matpower.org for more info.
0032 
0033 %%----- initialize -----
0034 %% define named indices into data matrices
0035 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0036     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0037     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0038 
0039 %% unpack data
0040 [baseMVA, bus, gen] = deal(mpc.baseMVA, mpc.bus, mpc.gen);
0041 if mpopt.opf.v_cartesian
0042     [Vr, Vi, Pg, Qg] = deal(x{:});
0043     V = Vr + 1j* Vi;        %% reconstruct V
0044 else
0045     [Va, Vm, Pg, Qg] = deal(x{:});
0046     V = Vm .* exp(1j * Va); %% reconstruct V
0047 end
0048 
0049 %% problem dimensions
0050 nb = length(V);             %% number of buses
0051 ng = length(Pg);            %% number of dispatchable injections
0052 
0053 %% ----- evaluate constraints -----
0054 %% put Pg, Qg back in gen
0055 gen(:, PG) = Pg * baseMVA;  %% active generation in MW
0056 gen(:, QG) = Qg * baseMVA;  %% reactive generation in MVAr
0057 
0058 %% rebuild Sbus
0059 Sbus = makeSbus(baseMVA, bus, gen);  %% net injected power in p.u.
0060 
0061 %% evaluate complex current balance mismatches
0062 mis = Ybus*V - conj(Sbus./V);
0063 
0064 %% assemble real and imaginary current balance constraints
0065 g = [ real(mis);    %% real current mismatch
0066       imag(mis) ];  %% imaginary current mismatch
0067 
0068 %%----- evaluate constraint gradients -----
0069 if nargout > 1
0070     %% compute partials of injected bus powers
0071     Cg = sparse(gen(:, GEN_BUS), 1:ng, 1, nb, ng);
0072     InvConjV = sparse(1:nb, 1:nb, 1./conj(V), nb, nb);
0073     dImis_dPg = -InvConjV * Cg;     %% dImis w.r.t. Pg
0074     dImis_dQg = -1j * dImis_dPg;    %% dImis w.r.t. Qg
0075     [dImis_dV1, dImis_dV2] = dImis_dV(Sbus, Ybus, V, mpopt.opf.v_cartesian);     %% w.r.t. V
0076     dg = [
0077         real([dImis_dV1 dImis_dV2 dImis_dPg dImis_dQg]);    %% Ir mismatch w.r.t V1, V2, Pg, Qg
0078         imag([dImis_dV1 dImis_dV2 dImis_dPg dImis_dQg]) ;   %% Ii mismatch w.r.t V1, V2, Pg, Qg
0079     ];
0080 end