fm_hessian.m

电力系统的psat

function H = fm_hessian(ro)
% FM_HESSIAN compute the Hessian matrix of PF equations
%
% HESSIAN =FM_HESSIAN(RHO)
%
%     RHO = Lagrangian multipliers
%     HESSIAN = Hessian matrix
%
%Author:    Federico Milano
%Date:      11-Nov-2002
%Version:   1.0.0
%
%E-mail:    [e-mail]
%Web-site:  http://thunderbox.uwaterloo.ca/~fmilano
%
% Copyright (C) 2002-2005 Federico Milano
%
% This toolbox is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2.0 of the License, or
% (at your option) any later version.
%
% This toolbox is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANDABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
% General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this toolbox; if not, write to the Free Software
% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307,
% USA.

global DAE Line Bus jay

ang = exp(jay*DAE.a);
V = ones(1,Bus.n);
Ma = ang*V;
MM = ro(Bus.n+1:2*Bus.n)*V;
MW = ro(1:Bus.n)*V;

S1 = Ma.*conj(Line.Y).*Ma';
S2 = conj(Ma.*Line.Y.*Ma');

A1 = real(S1);
B1 = imag(S1);

A2 = real(S2);
B2 = imag(S2);

H22 = MW.*A1 + MW'.*A2 + MM.*B1 + MM'.*B2;
H11 = (DAE.V*DAE.V').*H22;
H11 = H11 - diag(sum(H11));
H21 = (V'*DAE.V').*(MW.*B1 - MW'.*B2 - MM.*A1 + MM'.*A2);
H21 = H21 - diag(sum(H21'));
H = [H11,H21';H21,H22];