cpf_p

CPF_P Computes the value of the CPF parameterization function.
   P = CPF_P(PARAMETERIZATION, STEP, Z, V, LAM, VPRV, LAMPRV, PV, PQ)

   Computes the value of the parameterization function at the current
   solution point.

   Inputs:
       PARAMETERIZATION : Value of cpf.parameterization option
       STEP : continuation step size
       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:
       P : value of the parameterization function at the current point

   See also CPF_PREDICTOR, CPF_CORRECTOR.

0001 function P = cpf_p(parameterization, step, z, V, lam, Vprv, lamprv, pv, pq)
0002 %CPF_P Computes the value of the CPF parameterization function.
0003 %   P = CPF_P(PARAMETERIZATION, STEP, Z, V, LAM, VPRV, LAMPRV, PV, PQ)
0004 %
0005 %   Computes the value of the parameterization function at the current
0006 %   solution point.
0007 %
0008 %   Inputs:
0009 %       PARAMETERIZATION : Value of cpf.parameterization option
0010 %       STEP : continuation step size
0011 %       Z : normalized tangent prediction vector from previous step
0012 %       V : complex bus voltage vector at current solution
0013 %       LAM : scalar lambda value at current solution
0014 %       VPRV : complex bus voltage vector at previous solution
0015 %       LAMPRV : scalar lambda value at previous solution
0016 %       PV : vector of indices of PV buses
0017 %       PQ : vector of indices of PQ buses
0018 %
0019 %   Outputs:
0020 %       P : value of the parameterization function at the current point
0021 %
0022 %   See also CPF_PREDICTOR, CPF_CORRECTOR.
0023 
0024 %   MATPOWER
0025 %   Copyright (c) 1996-2016, Power Systems Engineering Research Center (PSERC)
0026 %   by Shrirang Abhyankar, Argonne National Laboratory
0027 %   and Ray Zimmerman, PSERC Cornell
0028 %
0029 %   This file is part of MATPOWER.
0030 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0031 %   See https://matpower.org for more info.
0032 
0033 %% evaluate P(x0, lambda0)
0034 if parameterization == 1        %% natural
0035     if lam >= lamprv
0036         P = lam - lamprv - step;
0037     else
0038         P = lamprv - lam - step;
0039     end
0040 elseif parameterization == 2    %% arc length
0041     Va = angle(V);
0042     Vm = abs(V);
0043     Vaprv = angle(Vprv);
0044     Vmprv = abs(Vprv);
0045     P = sum(([Va([pv; pq]); Vm(pq); lam] - [Vaprv([pv; pq]); Vmprv(pq); lamprv]).^2) - step^2;
0046 elseif parameterization == 3    %% pseudo arc length
0047     nb = length(V);
0048     Va = angle(V);
0049     Vm = abs(V);
0050     Vaprv = angle(Vprv);
0051     Vmprv = abs(Vprv);
0052     P = z([pv; pq; nb+pq; 2*nb+1])' * ...
0053         ( [Va([pv; pq]); Vm(pq); lam] - [Vaprv([pv; pq]); Vmprv(pq); lamprv] )...
0054         - step;
0055 end