dsbr_dv.m

比较经典的matlab的电力系统潮流计算程序

function [dSf_dVa, dSf_dVm, dSt_dVa, dSt_dVm, Sf, St] = dSbr_dV(branch, Yf, Yt, V)
%DSBR_DV   Computes partial derivatives of power flows w.r.t. voltage.
%   [dSf_dVa, dSf_dVm, dSt_dVa, dSt_dVm, Sf, St] = dSbr_dV(branch, Yf, Yt, V)
%   returns four matrices containing partial derivatives of the complex
%   branch power flows at "from" and "to" ends of each branch w.r.t voltage
%   magnitude and voltage angle respectively (for all buses). If Yf is a
%   sparse matrix, the partial derivative matrices will be as well. Optionally
%   returns vectors containing the power flows themselves. The following
%   explains the expressions used to form the matrices:
%
%   If = Yf * V;
%   Sf = diag(Vf) * conj(If) = diag(conj(If)) * Vf
%
%   Partials of V, Vf & If w.r.t. voltage angles
%       dV/dVa  = j * diag(V)
%       dVf/dVa = sparse(1:nl, f, j * V(f)) = j * sparse(1:nl, f, V(f))
%       dIf/dVa = Yf * dV/dVa = Yf * j * diag(V)
%
%   Partials of V, Vf & If w.r.t. voltage magnitudes
%       dV/dVm  = diag(V./abs(V))
%       dVf/dVm = sparse(1:nl, f, V(f)./abs(V(f))
%       dIf/dVm = Yf * dV/dVm = Yf * diag(V./abs(V))
%
%   Partials of Sf w.r.t. voltage angles
%       dSf/dVa = diag(Vf) * conj(dIf/dVa)              + diag(conj(If)) * dVf/dVa
%               = diag(Vf) * conj(Yf * j * diag(V))     + conj(diag(If)) * j * sparse(1:nl, f, V(f))
%               = -j * diag(Vf) * conj(Yf * diag(V))    + j * conj(diag(If)) * sparse(1:nl, f, V(f))
%               = j * (conj(diag(If)) * sparse(1:nl, f, V(f)) - diag(Vf) * conj(Yf * diag(V)))
%
%   Partials of Sf w.r.t. voltage magnitudes
%       dSf/dVm = diag(Vf) * conj(dIf/dVm)              + diag(conj(If)) * dVf/dVm
%               = diag(Vf) * conj(Yf * diag(V./abs(V))) + conj(diag(If)) * sparse(1:nl, f, V(f)./abs(V(f)))
%
%   Derivations for "to" bus are similar.
%

%   MATPOWER Version 2.0
%   by Ray Zimmerman, PSERC Cornell    9/19/97
%   Copyright (c) 1996, 1997 by Power System Engineering Research Center (PSERC)
%   See http://www.pserc.cornell.edu/ for more info.

%% constant
j = sqrt(-1);

%% define named indices into bus, gen, branch matrices
[F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, ...
	RATE_C, TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST] = idx_brch;

%% define
f = branch(:, F_BUS);		%% list of "from" buses
t = branch(:, T_BUS);		%% list of "to" buses
nl = length(f);
nb = length(V);

%% compute currents
If = Yf * V;
It = Yt * V;

Vnorm = V ./ abs(V);
if issparse(Yf)				%% sparse version (if Yf is sparse)
	diagVf		= spdiags(V(f), 0, nl, nl);
	diagIf		= spdiags(If, 0, nl, nl);
	diagVt		= spdiags(V(t), 0, nl, nl);
	diagIt		= spdiags(It, 0, nl, nl);
	diagV		= spdiags(V, 0, nb, nb);
	diagVnorm	= spdiags(Vnorm, 0, nb, nb);
	
	dSf_dVa = j * (conj(diagIf) * sparse(1:nl, f, V(f), nl, nb) - diagVf * conj(Yf * diagV));
	dSf_dVm = diagVf * conj(Yf * diagVnorm)	+ conj(diagIf) * sparse(1:nl, f, Vnorm(f), nl, nb);
	dSt_dVa = j * (conj(diagIt) * sparse(1:nl, t, V(t), nl, nb) - diagVt * conj(Yt * diagV));
	dSt_dVm = diagVt * conj(Yt * diagVnorm)	+ conj(diagIt) * sparse(1:nl, t, Vnorm(t), nl, nb);
else						%% dense version
	diagVf		= diag(V(f));
	diagIf		= diag(If);
	diagVt		= diag(V(t));
	diagIt		= diag(It);
	diagV		= diag(V);
	diagVnorm	= diag(Vnorm);
	temp1		= zeros(nl, nb);	temp1(1:nl, f) = V(f);
	temp2		= zeros(nl, nb);	temp2(1:nl, f) = Vnorm(f);
	temp3		= zeros(nl, nb);	temp3(1:nl, t) = V(t);
	temp4		= zeros(nl, nb);	temp4(1:nl, t) = Vnorm(t);
	
	dSf_dVa = j * (conj(diagIf) * temp1 - diagVf * conj(Yf * diagV));
	dSf_dVm = diagVf * conj(Yf * diagVnorm)	+ conj(diagIf) * temp2;
	dSt_dVa = j * (conj(diagIt) * temp3 - diagVt * conj(Yt * diagV));
	dSt_dVm = diagVt * conj(Yt * diagVnorm)	+ conj(diagIt) * temp4;
end

if nargout > 4
	Sf = V(f) .* conj(If);
	St = V(t) .* conj(It);
end

return;