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 vector 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 vector 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,v 1.11 2011/12/14 17:05:18 cvs Exp $ 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(2); 0057 max_it = mpopt(5); 0058 verbose = mpopt(31); 0059 0060 %% initialize 0061 converged = 0; 0062 i = 0; 0063 V = V0; 0064 Vm = abs(V); 0065 0066 %% set up indexing for updating V 0067 npv = length(pv); 0068 npq = length(pq); 0069 0070 %% evaluate F(x0) 0071 mis = V .* conj(Ybus * V) - Sbus; 0072 F = [ real(mis([pv; pq])); 0073 imag(mis(pq)) ]; 0074 0075 %% check tolerance 0076 normF = norm(F, inf); 0077 if verbose > 1 0078 fprintf('\n it max P & Q mismatch (p.u.)'); 0079 fprintf('\n---- ---------------------------'); 0080 fprintf('\n%3d %10.3e', i, normF); 0081 end 0082 if normF < tol 0083 converged = 1; 0084 if verbose > 1 0085 fprintf('\nConverged!\n'); 0086 end 0087 end 0088 0089 %% do Gauss-Seidel iterations 0090 while (~converged && i < max_it) 0091 %% update iteration counter 0092 i = i + 1; 0093 0094 %% update voltage 0095 %% at PQ buses 0096 for k = pq(1:npq)' 0097 V(k) = V(k) + (conj(Sbus(k) / V(k)) - Ybus(k,:) * V ) / Ybus(k,k); 0098 end 0099 0100 %% at PV buses 0101 if npv 0102 for k = pv(1:npv)' 0103 Sbus(k) = real(Sbus(k)) + 1j * imag( V(k) .* conj(Ybus(k,:) * V)); 0104 V(k) = V(k) + (conj(Sbus(k) / V(k)) - Ybus(k,:) * V ) / Ybus(k,k); 0105 % V(k) = Vm(k) * V(k) / abs(V(k)); 0106 end 0107 V(pv) = Vm(pv) .* V(pv) ./ abs(V(pv)); 0108 end 0109 0110 %% evalute F(x) 0111 mis = V .* conj(Ybus * V) - Sbus; 0112 F = [ real(mis(pv)); 0113 real(mis(pq)); 0114 imag(mis(pq)) ]; 0115 0116 %% check for convergence 0117 normF = norm(F, inf); 0118 if verbose > 1 0119 fprintf('\n%3d %10.3e', i, normF); 0120 end 0121 if normF < tol 0122 converged = 1; 0123 if verbose 0124 fprintf('\nGauss-Seidel power flow converged in %d iterations.\n', i); 0125 end 0126 end 0127 end 0128 0129 if verbose 0130 if ~converged 0131 fprintf('\nGauss-Seidel power did not converge in %d iterations.\n', i); 0132 end 0133 end