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gausspf

PURPOSE ^

GAUSSPF Solves the power flow using a Gauss-Seidel method.

SYNOPSIS ^

function [V, converged, i] = gausspf(Ybus, Sbus, V0, ref, pv, pq, mpopt)

DESCRIPTION ^

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.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

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

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