gusucode.com > matpower工具箱源码程序 > matpower工具箱源码程序/MP2_0/dSbus_dV.m
function [dSbus_dVm, dSbus_dVa] = dSbus_dV(Ybus, V) %DSBUS_DV Computes partial derivatives of power injection w.r.t. voltage. % [dSbus_dVm, dSbus_dVa] = dSbus_dV(Ybus, V) returns two matrices containing % partial derivatives of the complex bus power injections w.r.t voltage % magnitude and voltage angle respectively (for all buses). If Ybus is a % sparse matrix, the return values will be also. The following explains % the expressions used to form the matrices: % % S = diag(V) * conj(Ibus) = diag(conj(Ibus)) * V % % Partials of V & Ibus w.r.t. voltage magnitudes % dV/dVm = diag(V./abs(V)) % dI/dVm = Ybus * dV/dVm = Ybus * diag(V./abs(V)) % % Partials of V & Ibus w.r.t. voltage angles % dV/dVa = j * diag(V) % dI/dVa = Ybus * dV/dVa = Ybus * j * diag(V) % % Partials of S w.r.t. voltage magnitudes % dS/dVm = diag(V) * conj(dI/dVm) + diag(conj(Ibus)) * dV/dVm % = diag(V) * conj(Ybus * diag(V./abs(V))) % + conj(diag(Ibus)) * diag(V./abs(V)) % % Partials of S w.r.t. voltage angles % dS/dVa = diag(V) * conj(dI/dVa) + diag(conj(Ibus)) * dV/dVa % = diag(V) * conj(Ybus * j * diag(V)) % + conj(diag(Ibus)) * j * diag(V) % = -j * diag(V) * conj(Ybus * diag(V)) % + conj(diag(Ibus)) * j * diag(V) % = j * diag(V) * conj(diag(Ibus) - Ybus * diag(V)) % % 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. j = sqrt(-1); n = length(V); Ibus = Ybus * V; if issparse(Ybus) %% sparse version (if Ybus is sparse) diagV = spdiags(V, 0, n, n); diagIbus = spdiags(Ibus, 0, n, n); diagVnorm = spdiags(V./abs(V), 0, n, n); else %% dense version diagV = diag(V); diagIbus = diag(Ibus); diagVnorm = diag(V./abs(V)); end dSbus_dVm = diagV * conj(Ybus * diagVnorm) + conj(diagIbus) * diagVnorm; dSbus_dVa = j * diagV * conj(diagIbus - Ybus * diagV); return;