opf_branch_ang_fcn

OPF_BRANCH_ANG_FCN  Evaluates branch angle difference constraints and gradients.
   [VADIF, DVADIF] = OPF_BRANCH_ANG_FCN(X, AANG, LANG, UANG);

   Computes the lower and upper constraints on branch angle differences
   for voltages in cartesian coordinates. Computes constraint vectors and
   their gradients. The constraints are of the form:
       Aang * Va >= lang
       Aang * Va <= uang
   where Va is the voltage angle, a non-linear function of the Vr and Vi.

   Inputs:
     X : optimization vector
     AANG : constraint matrix, see MAKEAANG
     LANG : lower bound vector, see MAKEAANG
     UANG : upper bound vector, see MAKEAANG

   Outputs:
     VADIF  : constraint vector [ lang - Aang * Va; Aang * Va - uang ]
     DVADIF : (optional) constraint gradients

   Examples:
       VaDif = opf_branch_ang_fcn(x, Aang, lang, uang);
       [VaDif, dVaDif] = opf_branch_ang_fcn(x, Aang, lang, uang);

   See also OPF_BRANCH_ANG_HESS

0001 function [VaDif, dVaDif] = opf_branch_ang_fcn(x, Aang, lang, uang);
0002 %OPF_BRANCH_ANG_FCN  Evaluates branch angle difference constraints and gradients.
0003 %   [VADIF, DVADIF] = OPF_BRANCH_ANG_FCN(X, AANG, LANG, UANG);
0004 %
0005 %   Computes the lower and upper constraints on branch angle differences
0006 %   for voltages in cartesian coordinates. Computes constraint vectors and
0007 %   their gradients. The constraints are of the form:
0008 %       Aang * Va >= lang
0009 %       Aang * Va <= uang
0010 %   where Va is the voltage angle, a non-linear function of the Vr and Vi.
0011 %
0012 %   Inputs:
0013 %     X : optimization vector
0014 %     AANG : constraint matrix, see MAKEAANG
0015 %     LANG : lower bound vector, see MAKEAANG
0016 %     UANG : upper bound vector, see MAKEAANG
0017 %
0018 %   Outputs:
0019 %     VADIF  : constraint vector [ lang - Aang * Va; Aang * Va - uang ]
0020 %     DVADIF : (optional) constraint gradients
0021 %
0022 %   Examples:
0023 %       VaDif = opf_branch_ang_fcn(x, Aang, lang, uang);
0024 %       [VaDif, dVaDif] = opf_branch_ang_fcn(x, Aang, lang, uang);
0025 %
0026 %   See also OPF_BRANCH_ANG_HESS
0027 
0028 %   MATPOWER
0029 %   Copyright (c) 2018-2020, Power Systems Engineering Research Center (PSERC)
0030 %   by Baljinnyam Sereeter, Delft University of Technology
0031 %   and Ray Zimmerman, PSERC Cornell
0032 %
0033 %   This file is part of MATPOWER.
0034 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0035 %   See https://matpower.org for more info.
0036 
0037 %% unpack data
0038 [Vr, Vi] = deal(x{:});
0039 
0040 %% problem dimensions
0041 nb = length(Vi);            %% number of buses
0042 
0043 %% compute branch angle difference
0044 Va = angle(Vr + 1j* Vi);
0045 Ax = Aang * Va;
0046 VaDif = [ lang - Ax;
0047           Ax - uang ];
0048 
0049 if nargout > 1
0050     %% compute partials of branch angle difference w.r.t Vr and Vi
0051     Vm2 = Vr.^2 + Vi.^2;
0052     AangdVa_dVr = Aang * sparse(1:nb, 1:nb, -Vi./Vm2, nb, nb);
0053     AangdVa_dVi = Aang * sparse(1:nb, 1:nb,  Vr./Vm2, nb, nb);
0054     dVaDif = [ -AangdVa_dVr -AangdVa_dVi;   %% VaDif w.r.t Vr, Vi
0055                 AangdVa_dVr  AangdVa_dVi ];
0056 end