GAUSSPF Solves the power flow using a Gauss-Seidel method. [V, CONVERGED, I] = GAUSSPF(YBUS, SBUS, V0, REF, PV, PQ, MPOPT) solves for bus voltages given the full system admittance matrix (for all buses), the complex bus power injection vector (for all buses), the initial vector of complex bus voltages, and column vectors with the lists of bus indices for the swing bus, PV buses, and PQ buses, respectively. The bus voltage vector contains the set point for generator (including ref bus) buses, and the reference angle of the swing bus, as well as an initial guess for remaining magnitudes and angles. MPOPT is a MATPOWER options struct which can be used to set the termination tolerance, maximum number of iterations, and output options (see MPOPTION for details). Uses default options if this parameter is not given. Returns the final complex voltages, a flag which indicates whether it converged or not, and the number of iterations performed. See also RUNPF.
0001 function [V, converged, i] = gausspf(Ybus, Sbus, V0, ref, pv, pq, mpopt) 0002 %GAUSSPF Solves the power flow using a Gauss-Seidel method. 0003 % [V, CONVERGED, I] = GAUSSPF(YBUS, SBUS, V0, REF, PV, PQ, MPOPT) 0004 % solves for bus voltages given the full system admittance matrix (for 0005 % all buses), the complex bus power injection vector (for all buses), 0006 % the initial vector of complex bus voltages, and column vectors with 0007 % the lists of bus indices for the swing bus, PV buses, and PQ buses, 0008 % respectively. The bus voltage vector contains the set point for 0009 % generator (including ref bus) buses, and the reference angle of the 0010 % swing bus, as well as an initial guess for remaining magnitudes and 0011 % angles. MPOPT is a MATPOWER options struct which can be used to 0012 % set the termination tolerance, maximum number of iterations, and 0013 % output options (see MPOPTION for details). Uses default options 0014 % if this parameter is not given. Returns the final complex voltages, 0015 % a flag which indicates whether it converged or not, and the number 0016 % of iterations performed. 0017 % 0018 % See also RUNPF. 0019 0020 % MATPOWER 0021 % $Id: gausspf.m 2229 2013-12-11 01:28:09Z ray $ 0022 % by Ray Zimmerman, PSERC Cornell 0023 % and Alberto Borghetti, University of Bologna, Italy 0024 % Copyright (c) 1996-2011 by Power System Engineering Research Center (PSERC) 0025 % 0026 % This file is part of MATPOWER. 0027 % See http://www.pserc.cornell.edu/matpower/ for more info. 0028 % 0029 % MATPOWER is free software: you can redistribute it and/or modify 0030 % it under the terms of the GNU General Public License as published 0031 % by the Free Software Foundation, either version 3 of the License, 0032 % or (at your option) any later version. 0033 % 0034 % MATPOWER is distributed in the hope that it will be useful, 0035 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0036 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0037 % GNU General Public License for more details. 0038 % 0039 % You should have received a copy of the GNU General Public License 0040 % along with MATPOWER. If not, see <http://www.gnu.org/licenses/>. 0041 % 0042 % Additional permission under GNU GPL version 3 section 7 0043 % 0044 % If you modify MATPOWER, or any covered work, to interface with 0045 % other modules (such as MATLAB code and MEX-files) available in a 0046 % MATLAB(R) or comparable environment containing parts covered 0047 % under other licensing terms, the licensors of MATPOWER grant 0048 % you additional permission to convey the resulting work. 0049 0050 %% default arguments 0051 if nargin < 7 0052 mpopt = mpoption; 0053 end 0054 0055 %% options 0056 tol = mpopt.pf.tol; 0057 max_it = mpopt.pf.gs.max_it; 0058 0059 %% initialize 0060 converged = 0; 0061 i = 0; 0062 V = V0; 0063 Vm = abs(V); 0064 0065 %% set up indexing for updating V 0066 npv = length(pv); 0067 npq = length(pq); 0068 0069 %% evaluate F(x0) 0070 mis = V .* conj(Ybus * V) - Sbus; 0071 F = [ real(mis([pv; pq])); 0072 imag(mis(pq)) ]; 0073 0074 %% check tolerance 0075 normF = norm(F, inf); 0076 if mpopt.verbose > 1 0077 fprintf('\n it max P & Q mismatch (p.u.)'); 0078 fprintf('\n---- ---------------------------'); 0079 fprintf('\n%3d %10.3e', i, normF); 0080 end 0081 if normF < tol 0082 converged = 1; 0083 if mpopt.verbose > 1 0084 fprintf('\nConverged!\n'); 0085 end 0086 end 0087 0088 %% do Gauss-Seidel iterations 0089 while (~converged && i < max_it) 0090 %% update iteration counter 0091 i = i + 1; 0092 0093 %% update voltage 0094 %% at PQ buses 0095 for k = pq(1:npq)' 0096 V(k) = V(k) + (conj(Sbus(k) / V(k)) - Ybus(k,:) * V ) / Ybus(k,k); 0097 end 0098 0099 %% at PV buses 0100 if npv 0101 for k = pv(1:npv)' 0102 Sbus(k) = real(Sbus(k)) + 1j * imag( V(k) .* conj(Ybus(k,:) * V)); 0103 V(k) = V(k) + (conj(Sbus(k) / V(k)) - Ybus(k,:) * V ) / Ybus(k,k); 0104 % V(k) = Vm(k) * V(k) / abs(V(k)); 0105 end 0106 V(pv) = Vm(pv) .* V(pv) ./ abs(V(pv)); 0107 end 0108 0109 %% evalute F(x) 0110 mis = V .* conj(Ybus * V) - Sbus; 0111 F = [ real(mis(pv)); 0112 real(mis(pq)); 0113 imag(mis(pq)) ]; 0114 0115 %% check for convergence 0116 normF = norm(F, inf); 0117 if mpopt.verbose > 1 0118 fprintf('\n%3d %10.3e', i, normF); 0119 end 0120 if normF < tol 0121 converged = 1; 0122 if mpopt.verbose 0123 fprintf('\nGauss-Seidel power flow converged in %d iterations.\n', i); 0124 end 0125 end 0126 end 0127 0128 if mpopt.verbose 0129 if ~converged 0130 fprintf('\nGauss-Seidel power flow did not converge in %d iterations.\n', i); 0131 end 0132 end