NEWTONPF Solves the power flow using a full Newton's method. [V, CONVERGED, I] = NEWTONPF(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] = newtonpf(Ybus, Sbus, V0, ref, pv, pq, mpopt) 0002 %NEWTONPF Solves the power flow using a full Newton's method. 0003 % [V, CONVERGED, I] = NEWTONPF(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 if 0014 % this parameter is not given. Returns the final complex voltages, a 0015 % flag which indicates whether it converged or not, and the number of 0016 % iterations performed. 0017 % 0018 % See also RUNPF. 0019 0020 % MATPOWER 0021 % $Id: newtonpf.m 2229 2013-12-11 01:28:09Z ray $ 0022 % by Ray Zimmerman, PSERC Cornell 0023 % Copyright (c) 1996-2011 by Power System Engineering Research Center (PSERC) 0024 % 0025 % This file is part of MATPOWER. 0026 % See http://www.pserc.cornell.edu/matpower/ for more info. 0027 % 0028 % MATPOWER is free software: you can redistribute it and/or modify 0029 % it under the terms of the GNU General Public License as published 0030 % by the Free Software Foundation, either version 3 of the License, 0031 % or (at your option) any later version. 0032 % 0033 % MATPOWER is distributed in the hope that it will be useful, 0034 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0035 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0036 % GNU General Public License for more details. 0037 % 0038 % You should have received a copy of the GNU General Public License 0039 % along with MATPOWER. If not, see <http://www.gnu.org/licenses/>. 0040 % 0041 % Additional permission under GNU GPL version 3 section 7 0042 % 0043 % If you modify MATPOWER, or any covered work, to interface with 0044 % other modules (such as MATLAB code and MEX-files) available in a 0045 % MATLAB(R) or comparable environment containing parts covered 0046 % under other licensing terms, the licensors of MATPOWER grant 0047 % you additional permission to convey the resulting work. 0048 0049 %% default arguments 0050 if nargin < 7 0051 mpopt = mpoption; 0052 end 0053 0054 %% options 0055 tol = mpopt.pf.tol; 0056 max_it = mpopt.pf.nr.max_it; 0057 0058 %% initialize 0059 converged = 0; 0060 i = 0; 0061 V = V0; 0062 Va = angle(V); 0063 Vm = abs(V); 0064 0065 %% set up indexing for updating V 0066 npv = length(pv); 0067 npq = length(pq); 0068 j1 = 1; j2 = npv; %% j1:j2 - V angle of pv buses 0069 j3 = j2 + 1; j4 = j2 + npq; %% j3:j4 - V angle of pq buses 0070 j5 = j4 + 1; j6 = j4 + npq; %% j5:j6 - V mag of pq buses 0071 0072 %% evaluate F(x0) 0073 mis = V .* conj(Ybus * V) - Sbus; 0074 F = [ real(mis([pv; pq])); 0075 imag(mis(pq)) ]; 0076 0077 %% check tolerance 0078 normF = norm(F, inf); 0079 if mpopt.verbose > 1 0080 fprintf('\n it max P & Q mismatch (p.u.)'); 0081 fprintf('\n---- ---------------------------'); 0082 fprintf('\n%3d %10.3e', i, normF); 0083 end 0084 if normF < tol 0085 converged = 1; 0086 if mpopt.verbose > 1 0087 fprintf('\nConverged!\n'); 0088 end 0089 end 0090 0091 %% do Newton iterations 0092 while (~converged && i < max_it) 0093 %% update iteration counter 0094 i = i + 1; 0095 0096 %% evaluate Jacobian 0097 [dSbus_dVm, dSbus_dVa] = dSbus_dV(Ybus, V); 0098 0099 j11 = real(dSbus_dVa([pv; pq], [pv; pq])); 0100 j12 = real(dSbus_dVm([pv; pq], pq)); 0101 j21 = imag(dSbus_dVa(pq, [pv; pq])); 0102 j22 = imag(dSbus_dVm(pq, pq)); 0103 0104 J = [ j11 j12; 0105 j21 j22; ]; 0106 0107 %% compute update step 0108 dx = -(J \ F); 0109 0110 %% update voltage 0111 if npv 0112 Va(pv) = Va(pv) + dx(j1:j2); 0113 end 0114 if npq 0115 Va(pq) = Va(pq) + dx(j3:j4); 0116 Vm(pq) = Vm(pq) + dx(j5:j6); 0117 end 0118 V = Vm .* exp(1j * Va); 0119 Vm = abs(V); %% update Vm and Va again in case 0120 Va = angle(V); %% we wrapped around with a negative Vm 0121 0122 %% evalute F(x) 0123 mis = V .* conj(Ybus * V) - Sbus; 0124 F = [ real(mis(pv)); 0125 real(mis(pq)); 0126 imag(mis(pq)) ]; 0127 0128 %% check for convergence 0129 normF = norm(F, inf); 0130 if mpopt.verbose > 1 0131 fprintf('\n%3d %10.3e', i, normF); 0132 end 0133 if normF < tol 0134 converged = 1; 0135 if mpopt.verbose 0136 fprintf('\nNewton''s method power flow converged in %d iterations.\n', i); 0137 end 0138 end 0139 end 0140 0141 if mpopt.verbose 0142 if ~converged 0143 fprintf('\nNewton''s method power flow did not converge in %d iterations.\n', i); 0144 end 0145 end