cpf_tangent

CPF_TANGENT  Computes normalized tangent predictor for continuation power flow
   Z = CPF_TANGENT(V, LAM, YBUS, SBUSB, SBUST, PV, PQ, ...
                                 ZPRV, VPRV, LAMPRV, PARAMETERIZATION, DIRECTION)

   Computes a normalized tangent predictor for the continuation power flow.

   Inputs:
       V : complex bus voltage vector at current solution
       LAM : scalar lambda value at current solution
       YBUS : complex bus admittance matrix
       SBUSB : handle of function returning nb x 1 vector of complex
               base case injections in p.u. and derivatives w.r.t. |V|
       SBUST : handle of function returning nb x 1 vector of complex
               target case injections in p.u. and derivatives w.r.t. |V|
       PV : vector of indices of PV buses
       PQ : vector of indices of PQ buses
       ZPRV : normalized tangent prediction vector from previous step
       VPRV : complex bus voltage vector at previous solution
       LAMPRV : scalar lambda value at previous solution
       PARAMETERIZATION : value of cpf.parameterization option.
       DIRECTION: continuation direction (+1 for postive lambda
                  increase, -1 otherwise)

   Outputs:
       Z : the normalized tangent prediction vector

0001 function z = cpf_tangent(V, lam, Ybus, Sbusb, Sbust, pv, pq, ...
0002                             zprv, Vprv, lamprv, parameterization, direction)
0003 %CPF_TANGENT  Computes normalized tangent predictor for continuation power flow
0004 %   Z = CPF_TANGENT(V, LAM, YBUS, SBUSB, SBUST, PV, PQ, ...
0005 %                                 ZPRV, VPRV, LAMPRV, PARAMETERIZATION, DIRECTION)
0006 %
0007 %   Computes a normalized tangent predictor for the continuation power flow.
0008 %
0009 %   Inputs:
0010 %       V : complex bus voltage vector at current solution
0011 %       LAM : scalar lambda value at current solution
0012 %       YBUS : complex bus admittance matrix
0013 %       SBUSB : handle of function returning nb x 1 vector of complex
0014 %               base case injections in p.u. and derivatives w.r.t. |V|
0015 %       SBUST : handle of function returning nb x 1 vector of complex
0016 %               target case injections in p.u. and derivatives w.r.t. |V|
0017 %       PV : vector of indices of PV buses
0018 %       PQ : vector of indices of PQ buses
0019 %       ZPRV : normalized tangent prediction vector from previous step
0020 %       VPRV : complex bus voltage vector at previous solution
0021 %       LAMPRV : scalar lambda value at previous solution
0022 %       PARAMETERIZATION : value of cpf.parameterization option.
0023 %       DIRECTION: continuation direction (+1 for postive lambda
0024 %                  increase, -1 otherwise)
0025 %
0026 %   Outputs:
0027 %       Z : the normalized tangent prediction vector
0028 
0029 %   MATPOWER
0030 %   Copyright (c) 1996-2016, Power Systems Engineering Research Center (PSERC)
0031 %   by Shrirang Abhyankar, Argonne National Laboratory
0032 %   and Ray Zimmerman, PSERC Cornell
0033 %
0034 %   This file is part of MATPOWER.
0035 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0036 %   See https://matpower.org for more info.
0037 
0038 %% sizes
0039 nb = length(V);
0040 npv = length(pv);
0041 npq = length(pq);
0042 
0043 Vm = abs(V);
0044 
0045 %% compute Jacobian for the power flow equations
0046 [dSbus_dVa, dSbus_dVm] = dSbus_dV(Ybus, V);
0047 [dummy, neg_dSdb_dVm] = Sbusb(Vm);
0048 [dummy, neg_dSdt_dVm] = Sbust(Vm);
0049 dSbus_dVm = dSbus_dVm - neg_dSdb_dVm - lam * (neg_dSdt_dVm - neg_dSdb_dVm);
0050 
0051 j11 = real(dSbus_dVa([pv; pq], [pv; pq]));
0052 j12 = real(dSbus_dVm([pv; pq], pq));
0053 j21 = imag(dSbus_dVa(pq, [pv; pq]));
0054 j22 = imag(dSbus_dVm(pq, pq));
0055 
0056 J = [   j11 j12;
0057         j21 j22;    ];
0058 
0059 Sxf = Sbust(Vm) - Sbusb(Vm);    %% "transfer" at current voltage level
0060 dF_dlam = -[real(Sxf([pv; pq])); imag(Sxf(pq))];
0061 [dP_dV, dP_dlam] = cpf_p_jac(parameterization, zprv, V, lam, Vprv, lamprv, pv, pq);
0062 
0063 %% linear operator for computing the tangent predictor
0064 J = [   J   dF_dlam; 
0065       dP_dV dP_dlam ];
0066 
0067 % J = [ J, dF_dlam;
0068 %       z([pv; pq; nb+pq; 2*nb+1])'];
0069 
0070 %% compute normalized tangent predictor
0071 z = zprv;
0072 s = zeros(npv+2*npq+1, 1);
0073 s(end,1) = sign(direction);
0074 z([pv; pq; nb+pq; 2*nb+1]) = J\s;   %% tangent vector
0075 z = z/norm(z);                      %% normalize tangent predictor