Home > matpower6.0 > extras > se > doSE.m

doSE

PURPOSE ^

DOSE Do state estimation.

SYNOPSIS ^

function [V, converged, iterNum, z, z_est, error_sqrsum] = doSE(baseMVA, bus, gen, branch, Ybus, Yf, Yt, V0, ref, pv, pq, measure, idx, sigma)

DESCRIPTION ^

DOSE  Do state estimation.
   created by Rui Bo on 2007/11/12

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [V, converged, iterNum, z, z_est, error_sqrsum] = doSE(baseMVA, bus, gen, branch, Ybus, Yf, Yt, V0, ref, pv, pq, measure, idx, sigma)
0002 %DOSE  Do state estimation.
0003 %   created by Rui Bo on 2007/11/12
0004 
0005 %   MATPOWER
0006 %   Copyright (c) 1996-2016, Power Systems Engineering Research Center (PSERC)
0007 %   by Rui Bo
0008 %   and Ray Zimmerman, PSERC Cornell
0009 %
0010 %   This file is part of MATPOWER.
0011 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0012 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0013 
0014 %% define named indices into bus, gen, branch matrices
0015 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0016     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0017 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, ...
0018     RATE_C, TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST] = idx_brch;
0019 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, ...
0020     GEN_STATUS, PMAX, PMIN, MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN] = idx_gen;
0021 
0022 %% options
0023 tol     = 1e-5; % mpopt.pf.tol;
0024 max_it  = 100;  % mpopt.pf.nr.max_it;
0025 verbose = 0;
0026 
0027 %% initialize
0028 j = sqrt(-1);
0029 converged = 0;
0030 i = 0;
0031 V = V0;
0032 Va = angle(V);
0033 Vm = abs(V);
0034 
0035 nb = size(Ybus, 1);
0036 f = branch(:, F_BUS);       %% list of "from" buses
0037 t = branch(:, T_BUS);       %% list of "to" buses
0038 
0039 %% get non reference buses
0040 nonref = [pv;pq];
0041 
0042 %% form measurement vector 'z'. NOTE: all are p.u. values
0043 z = [
0044     measure.PF
0045     measure.PT
0046     measure.PG
0047     measure.Va
0048     measure.QF
0049     measure.QT
0050     measure.QG
0051     measure.Vm
0052     ];
0053 
0054 %% form measurement index vectors
0055 idx_zPF = idx.idx_zPF;
0056 idx_zPT = idx.idx_zPT;
0057 idx_zPG = idx.idx_zPG;
0058 idx_zVa = idx.idx_zVa;
0059 idx_zQF = idx.idx_zQF;
0060 idx_zQT = idx.idx_zQT;
0061 idx_zQG = idx.idx_zQG;
0062 idx_zVm = idx.idx_zVm;
0063 
0064 %% get R inverse matrix
0065 sigma_vector = [
0066     sigma.sigma_PF*ones(size(idx_zPF, 1), 1)
0067     sigma.sigma_PT*ones(size(idx_zPT, 1), 1)
0068     sigma.sigma_PG*ones(size(idx_zPG, 1), 1)
0069     sigma.sigma_Va*ones(size(idx_zVa, 1), 1)
0070     sigma.sigma_QF*ones(size(idx_zQF, 1), 1)
0071     sigma.sigma_QT*ones(size(idx_zQT, 1), 1)
0072     sigma.sigma_QG*ones(size(idx_zQG, 1), 1)
0073     sigma.sigma_Vm*ones(size(idx_zVm, 1), 1)
0074     ]; % NOTE: zero-valued elements of simga are skipped
0075 sigma_square = sigma_vector.^2;
0076 R_inv = diag(1./sigma_square);
0077 
0078 %% do Newton iterations
0079 while (~converged & i < max_it)
0080     %% update iteration counter
0081     i = i + 1;
0082     
0083     %% --- compute estimated measurement ---
0084     Sfe = V(f) .* conj(Yf * V);
0085     Ste = V(t) .* conj(Yt * V);
0086     %% compute net injection at generator buses
0087     gbus = gen(:, GEN_BUS);
0088     Sgbus = V(gbus) .* conj(Ybus(gbus, :) * V);
0089     Sgen = Sgbus * baseMVA + (bus(gbus, PD) + j*bus(gbus, QD));   %% inj S + local Sd
0090     Sgen = Sgen/baseMVA;
0091     z_est = [ % NOTE: all are p.u. values
0092         real(Sfe(idx_zPF));
0093         real(Ste(idx_zPT));
0094         real(Sgen(idx_zPG));
0095         angle(V(idx_zVa));
0096         imag(Sfe(idx_zQF));
0097         imag(Ste(idx_zQT));
0098         imag(Sgen(idx_zQG));
0099         abs(V(idx_zVm));
0100     ];
0101 
0102     %% --- get H matrix ---
0103     [dSbus_dVm, dSbus_dVa] = dSbus_dV(Ybus, V);
0104     [dSf_dVa, dSf_dVm, dSt_dVa, dSt_dVm, Sf, St] = dSbr_dV(branch, Yf, Yt, V);
0105 %     genbus_row = findBusRowByIdx(bus, gbus);
0106     genbus_row = gbus;  %% rdz, this should be fine if using internal bus numbering
0107 
0108     %% get sub-matrix of H relating to line flow
0109     dPF_dVa = real(dSf_dVa); % from end
0110     dQF_dVa = imag(dSf_dVa);   
0111     dPF_dVm = real(dSf_dVm);
0112     dQF_dVm = imag(dSf_dVm);
0113     dPT_dVa = real(dSt_dVa);% to end
0114     dQT_dVa = imag(dSt_dVa);   
0115     dPT_dVm = real(dSt_dVm);
0116     dQT_dVm = imag(dSt_dVm);   
0117     %% get sub-matrix of H relating to generator output
0118     dPG_dVa = real(dSbus_dVa(genbus_row, :));
0119     dQG_dVa = imag(dSbus_dVa(genbus_row, :));
0120     dPG_dVm = real(dSbus_dVm(genbus_row, :));
0121     dQG_dVm = imag(dSbus_dVm(genbus_row, :));
0122     %% get sub-matrix of H relating to voltage angle
0123     dVa_dVa = eye(nb);
0124     dVa_dVm = zeros(nb, nb);
0125     %% get sub-matrix of H relating to voltage magnitude
0126     dVm_dVa = zeros(nb, nb);
0127     dVm_dVm = eye(nb);
0128     H = [
0129         dPF_dVa(idx_zPF, nonref)   dPF_dVm(idx_zPF, nonref);
0130         dPT_dVa(idx_zPT, nonref)   dPT_dVm(idx_zPT, nonref);
0131         dPG_dVa(idx_zPG, nonref)   dPG_dVm(idx_zPG, nonref);
0132         dVa_dVa(idx_zVa, nonref)   dVa_dVm(idx_zVa, nonref);
0133         dQF_dVa(idx_zQF, nonref)   dQF_dVm(idx_zQF, nonref);
0134         dQT_dVa(idx_zQT, nonref)   dQT_dVm(idx_zQT, nonref);
0135         dQG_dVa(idx_zQG, nonref)   dQG_dVm(idx_zQG, nonref);
0136         dVm_dVa(idx_zVm, nonref)   dVm_dVm(idx_zVm, nonref);
0137         ];
0138     
0139     %% compute update step
0140     J = H'*R_inv*H;
0141     F = H'*R_inv*(z-z_est); % evalute F(x)
0142     if ~isobservable(H, pv, pq)
0143         error('doSE: system is not observable');
0144     end
0145     dx = (J \ F);
0146 
0147     %% check for convergence
0148     normF = norm(F, inf);
0149     if verbose > 1
0150         fprintf('\niteration [%3d]\t\tnorm of mismatch: %10.3e', i, normF);
0151     end
0152     if normF < tol
0153         converged = 1;
0154     end
0155     
0156     %% update voltage
0157     Va(nonref) = Va(nonref) + dx(1:size(nonref, 1));
0158     Vm(nonref) = Vm(nonref) + dx(size(nonref, 1)+1:2*size(nonref, 1));
0159     V = Vm .* exp(j * Va); % NOTE: angle is in radians in pf solver, but in degree in case data
0160     Vm = abs(V);            %% update Vm and Va again in case
0161     Va = angle(V);          %% we wrapped around with a negative Vm
0162 end
0163 
0164 iterNum = i;
0165 
0166 %% get weighted sum of squared errors
0167 error_sqrsum = sum((z - z_est).^2./sigma_square);
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