gusucode.com > matpower工具箱源码程序 > matpower工具箱源码程序/MP2_0/dSbr_dV.m
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;