makeAang

MAKEAANG  Construct constraints for branch angle difference limits.
   [AANG, LANG, UANG, IANG]  = MAKEAANG(BASEMVA, BRANCH, NB, MPOPT)

   Constructs the parameters for the following linear constraint limiting
   the voltage angle differences across branches, where Va is the vector
   of bus voltage angles. NB is the number of buses.

       LANG <= AANG * Va <= UANG

   IANG is the vector of indices of branches with angle difference limits.
   The limits are given in the ANGMIN and ANGMAX columns of the branch
   matrix. Voltage angle differences are taken to be unbounded below if
   ANGMIN < -360 and unbounded above if ANGMAX > 360. If both ANGMIN and
   ANGMAX are zero, the angle difference is assumed to be unconstrained.

   Example:
       [Aang, lang, uang, iang]  = makeAang(baseMVA, branch, nb, mpopt);

0001 function [Aang, lang, uang, iang]  = makeAang(baseMVA, branch, nb, mpopt)
0002 %MAKEAANG  Construct constraints for branch angle difference limits.
0003 %   [AANG, LANG, UANG, IANG]  = MAKEAANG(BASEMVA, BRANCH, NB, MPOPT)
0004 %
0005 %   Constructs the parameters for the following linear constraint limiting
0006 %   the voltage angle differences across branches, where Va is the vector
0007 %   of bus voltage angles. NB is the number of buses.
0008 %
0009 %       LANG <= AANG * Va <= UANG
0010 %
0011 %   IANG is the vector of indices of branches with angle difference limits.
0012 %   The limits are given in the ANGMIN and ANGMAX columns of the branch
0013 %   matrix. Voltage angle differences are taken to be unbounded below if
0014 %   ANGMIN < -360 and unbounded above if ANGMAX > 360. If both ANGMIN and
0015 %   ANGMAX are zero, the angle difference is assumed to be unconstrained.
0016 %
0017 %   Example:
0018 %       [Aang, lang, uang, iang]  = makeAang(baseMVA, branch, nb, mpopt);
0019 
0020 %   MATPOWER
0021 %   Copyright (c) 1996-2016, Power Systems Engineering Research Center (PSERC)
0022 %   by Ray Zimmerman, PSERC Cornell
0023 %   and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Nacional de Colombia
0024 %
0025 %   This file is part of MATPOWER.
0026 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0027 %   See https://matpower.org for more info.
0028 
0029 %% define named indices into data matrices
0030 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0031     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0032     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0033 
0034 if mpopt.opf.ignore_angle_lim
0035   Aang  = sparse(0, nb);
0036   lang  = [];
0037   uang  = [];
0038   iang  = [];
0039 else
0040   iang = find( (branch(:, ANGMIN) & branch(:, ANGMIN) > -360) | ...
0041                (branch(:, ANGMAX) & branch(:, ANGMAX) <  360) | ...
0042                ( branch(:, ANGMIN) & ~branch(:, ANGMAX)) | ...
0043                (~branch(:, ANGMIN) &  branch(:, ANGMAX)) );
0044   nang = length(iang);
0045 
0046   if nang > 0
0047     ii = [(1:nang)'; (1:nang)'];
0048     jj = [branch(iang, F_BUS); branch(iang, T_BUS)];
0049     Aang = sparse(ii, jj, [ones(nang, 1); -ones(nang, 1)], nang, nb);
0050     lang = branch(iang, ANGMIN);
0051     uang = branch(iang, ANGMAX);
0052     lang(lang < -360) = -Inf;
0053     uang(uang >  360) =  Inf;
0054     lang = lang * pi/180;
0055     uang = uang * pi/180;
0056   else
0057     Aang = sparse(0, nb);
0058     lang =[];
0059     uang =[];
0060   end
0061 end