CPF_P_JAC Computes partial derivatives of CPF parameterization function. [DP_DV, DP_DLAM ] = CPF_P_JAC(PARAMETERIZATION, Z, V, LAM, ... VPRV, LAMPRV, PV, PQ) Computes the partial derivatives of the continuation power flow parameterization function w.r.t. bus voltages and the continuation parameter lambda. Inputs: PARAMETERIZATION : Value of cpf.parameterization option. Z : normalized tangent prediction vector from previous step V : complex bus voltage vector at current solution LAM : scalar lambda value at current solution VPRV : complex bus voltage vector at previous solution LAMPRV : scalar lambda value at previous solution PV : vector of indices of PV buses PQ : vector of indices of PQ buses Outputs: DP_DV : partial of parameterization function w.r.t. voltages DP_DLAM : partial of parameterization function w.r.t. lambda See also CPF_PREDICTOR, CPF_CORRECTOR.
0001 function [dP_dV, dP_dlam] = cpf_p_jac(parameterization, z, V, lam, Vprv, lamprv, pv, pq) 0002 %CPF_P_JAC Computes partial derivatives of CPF parameterization function. 0003 % [DP_DV, DP_DLAM ] = CPF_P_JAC(PARAMETERIZATION, Z, V, LAM, ... 0004 % VPRV, LAMPRV, PV, PQ) 0005 % 0006 % Computes the partial derivatives of the continuation power flow 0007 % parameterization function w.r.t. bus voltages and the continuation 0008 % parameter lambda. 0009 % 0010 % Inputs: 0011 % PARAMETERIZATION : Value of cpf.parameterization option. 0012 % Z : normalized tangent prediction vector from previous step 0013 % V : complex bus voltage vector at current solution 0014 % LAM : scalar lambda value at current solution 0015 % VPRV : complex bus voltage vector at previous solution 0016 % LAMPRV : scalar lambda value at previous solution 0017 % PV : vector of indices of PV buses 0018 % PQ : vector of indices of PQ buses 0019 % 0020 % Outputs: 0021 % DP_DV : partial of parameterization function w.r.t. voltages 0022 % DP_DLAM : partial of parameterization function w.r.t. lambda 0023 % 0024 % See also CPF_PREDICTOR, CPF_CORRECTOR. 0025 0026 % MATPOWER 0027 % Copyright (c) 1996-2016, Power Systems Engineering Research Center (PSERC) 0028 % by Shrirang Abhyankar, Argonne National Laboratory 0029 % and Ray Zimmerman, PSERC Cornell 0030 % 0031 % This file is part of MATPOWER. 0032 % Covered by the 3-clause BSD License (see LICENSE file for details). 0033 % See http://www.pserc.cornell.edu/matpower/ for more info. 0034 0035 if parameterization == 1 %% natural 0036 npv = length(pv); 0037 npq = length(pq); 0038 dP_dV = zeros(1, npv+2*npq); 0039 if lam >= lamprv 0040 dP_dlam = 1.0; 0041 else 0042 dP_dlam = -1.0; 0043 end 0044 elseif parameterization == 2 %% arc length 0045 Va = angle(V); 0046 Vm = abs(V); 0047 Vaprv = angle(Vprv); 0048 Vmprv = abs(Vprv); 0049 dP_dV = 2*([Va([pv; pq]); Vm(pq)] - [Vaprv([pv; pq]); Vmprv(pq)])'; 0050 if lam == lamprv %% first step 0051 dP_dlam = 1.0; %% avoid singular Jacobian that would result 0052 %% from [dP_dV, dP_dlam] = 0 0053 else 0054 dP_dlam = 2*(lam-lamprv); 0055 end 0056 elseif parameterization == 3 %% pseudo arc length 0057 nb = length(V); 0058 dP_dV = z([pv; pq; nb+pq])'; 0059 dP_dlam = z(2*nb+1); 0060 end