Home > matpower4.1 > extras > se > isobservable.m

isobservable

PURPOSE ^

ISOBSERVABLE Test for observability.

SYNOPSIS ^

function TorF = isobservable(H, pv, pq)

DESCRIPTION ^

ISOBSERVABLE  Test for observability.
   returns 1 if the system is observable, 0 otherwise.
   created by Rui Bo on Jan 9, 2010

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function TorF = isobservable(H, pv, pq)
0002 %ISOBSERVABLE  Test for observability.
0003 %   returns 1 if the system is observable, 0 otherwise.
0004 %   created by Rui Bo on Jan 9, 2010
0005 
0006 %   MATPOWER
0007 %   $Id: isobservable.m,v 1.3 2010/04/26 19:45:26 ray Exp $
0008 %   by Rui Bo
0009 %   Copyright (c) 2009-2010 by Rui Bo
0010 %
0011 %   This file is part of MATPOWER.
0012 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0013 %
0014 %   MATPOWER is free software: you can redistribute it and/or modify
0015 %   it under the terms of the GNU General Public License as published
0016 %   by the Free Software Foundation, either version 3 of the License,
0017 %   or (at your option) any later version.
0018 %
0019 %   MATPOWER is distributed in the hope that it will be useful,
0020 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0021 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
0022 %   GNU General Public License for more details.
0023 %
0024 %   You should have received a copy of the GNU General Public License
0025 %   along with MATPOWER. If not, see <http://www.gnu.org/licenses/>.
0026 %
0027 %   Additional permission under GNU GPL version 3 section 7
0028 %
0029 %   If you modify MATPOWER, or any covered work, to interface with
0030 %   other modules (such as MATLAB code and MEX-files) available in a
0031 %   MATLAB(R) or comparable environment containing parts covered
0032 %   under other licensing terms, the licensors of MATPOWER grant
0033 %   you additional permission to convey the resulting work.
0034 
0035 %% options
0036 tol     = 1e-5; % mpopt(2);
0037 check_reason = 1;    % check reason for system being not observable
0038                     % 0: no check
0039                     % 1: check (NOTE: may be time consuming due to svd calculation)
0040 
0041 %% test if H is full rank
0042 [m, n]  = size(H);
0043 r       = rank(H);
0044 if r < min(m, n)
0045     TorF = 0;
0046 else
0047     TorF = 1;
0048 end
0049 
0050 %% look for reasons for system being not observable
0051 if check_reason && ~TorF
0052     %% look for variables not being observed
0053     idx_trivialColumns = [];
0054     varNames = {};
0055     for j = 1:n
0056         normJ = norm(H(:, j), inf);
0057         if normJ < tol % found a zero column
0058             idx_trivialColumns = [idx_trivialColumns j];
0059             varName = getVarName(j, pv, pq);
0060             varNames{length(idx_trivialColumns)} = varName;
0061         end
0062     end
0063 
0064     if ~isempty(idx_trivialColumns) % found zero-valued column vector
0065         fprintf('Warning: The following variables are not observable since they are not related with any measurement!');
0066         varNames
0067         idx_trivialColumns
0068     else % no zero-valued column vector
0069         %% look for dependent column vectors
0070         for j = 1:n
0071             rr = rank(H(:, 1:j));
0072             if rr ~= j % found dependent column vector
0073                 %% look for linearly depedent vector
0074                 colJ = H(:, j); % j(th) column of H
0075                 varJName = getVarName(j, pv, pq);
0076                 for k = 1:j-1
0077                     colK = H(:, k);
0078                     if rank([colK colJ]) < 2 % k(th) column vector is linearly dependent of j(th) column vector
0079                         varKName = getVarName(k, pv, pq);
0080                         fprintf('Warning: %d(th) column vector (w.r.t. %s) of H is linearly dependent of %d(th) column vector (w.r.t. %s)!\n', j, varJName, k, varKName);
0081                         return;
0082                     end
0083                 end
0084             end
0085         end
0086     fprintf('Warning: No specific reason was found for system being not observable.\n');
0087     end
0088 end

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