makeAy

MAKEAY  Make the A matrix and RHS for the CCV formulation.
   [AY, BY]  = MAKEAY(BASEMVA, NG, GENCOST, PGBAS, QGBAS, YBAS)

   Constructs the parameters for linear "basin constraints" on Pg, Qg
   and Y used by the CCV cost formulation, expressed as

       AY * X <= BY

   where X is the vector of optimization variables. The starting index
   within the X vector for the active, reactive sources and the Y
   variables should be provided in arguments PGBAS, QGBAS, YBAS. The
   number of generators is NG.

   Assumptions: All generators are in-service.  Filter any generators
   that are offline from the GENCOST matrix before calling MAKEAY.
   Efficiency depends on Qg variables being after Pg variables, and
   the Y variables must be the last variables within the vector X for
   the dimensions of the resulting AY to be conformable with X.

   Example:
       [Ay, by]  = makeAy(baseMVA, ng, gencost, pgbas, qgbas, ybas);

0001 function [Ay, by]  = makeAy(baseMVA, ng, gencost, pgbas, qgbas, ybas)
0002 %MAKEAY  Make the A matrix and RHS for the CCV formulation.
0003 %   [AY, BY]  = MAKEAY(BASEMVA, NG, GENCOST, PGBAS, QGBAS, YBAS)
0004 %
0005 %   Constructs the parameters for linear "basin constraints" on Pg, Qg
0006 %   and Y used by the CCV cost formulation, expressed as
0007 %
0008 %       AY * X <= BY
0009 %
0010 %   where X is the vector of optimization variables. The starting index
0011 %   within the X vector for the active, reactive sources and the Y
0012 %   variables should be provided in arguments PGBAS, QGBAS, YBAS. The
0013 %   number of generators is NG.
0014 %
0015 %   Assumptions: All generators are in-service.  Filter any generators
0016 %   that are offline from the GENCOST matrix before calling MAKEAY.
0017 %   Efficiency depends on Qg variables being after Pg variables, and
0018 %   the Y variables must be the last variables within the vector X for
0019 %   the dimensions of the resulting AY to be conformable with X.
0020 %
0021 %   Example:
0022 %       [Ay, by]  = makeAy(baseMVA, ng, gencost, pgbas, qgbas, ybas);
0023 
0024 %   MATPOWER
0025 %   Copyright (c) 1996-2016, Power Systems Engineering Research Center (PSERC)
0026 %   by Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Nacional de Colombia
0027 %
0028 %   This file is part of MATPOWER.
0029 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0030 %   See https://matpower.org for more info.
0031 
0032 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0033 
0034 % find all pwl cost rows in gencost, either real or reactive
0035 iycost = find(gencost(:, MODEL) == PW_LINEAR);
0036 
0037 % this is the number of extra "y" variables needed to model those costs
0038 ny = size(iycost, 1);
0039 
0040 if ny == 0
0041    Ay = sparse([], [], [], 0, ybas+ny-1, 0);
0042    by = [];
0043    return
0044 end
0045 
0046 % if p(i),p(i+1),c(i),c(i+1) define one of the cost segments, then
0047 % the corresponding constraint on Pg (or Qg) and Y is
0048 %                                             c(i+1) - c(i)
0049 %  Y   >=   c(i) + m * (Pg - p(i)),      m = ---------------
0050 %                                             p(i+1) - p(i)
0051 %
0052 % this becomes   m * Pg - Y   <=   m*p(i) - c(i)
0053 
0054 % Form A matrix.  Use two different loops, one for the Pg/Qg coeffs,
0055 % then another for the y coeffs so that everything is filled in the
0056 % same order as the compressed column sparse format used by MATLAB;
0057 % this should be the quickest.
0058 
0059 m = sum(gencost(iycost, NCOST));  % total number of cost points
0060 Ay = sparse([], [], [], m-ny, ybas+ny-1, 2*(m-ny)); 
0061 by = [];
0062 % First fill the Pg or Qg coefficients (since their columns come first)
0063 % and the rhs
0064 k = 1;
0065 for i=iycost'
0066    ns = gencost(i, NCOST);                % # of cost points; segments = ns-1
0067    p = gencost(i, COST:2:COST+2*ns-1) / baseMVA;
0068    c = gencost(i, COST+1:2:COST+2*ns);
0069    m = diff(c) ./ diff(p);                % slopes for Pg (or Qg)
0070    if any(diff(p) == 0)
0071      fprintf('\nmakeAy: bad x axis data in row %i of gencost matrix\n',i);
0072    end
0073    b = m .* p(1:ns-1) - c(1:ns-1);        % and rhs
0074    by = [by;  b'];
0075    if i > ng
0076      sidx = qgbas + (i-ng) - 1;           % this was for a q cost
0077    else
0078      sidx = pgbas + i - 1;                % this was for a p cost
0079    end
0080    Ay(k:k+ns-2, sidx) = m';
0081    k = k + ns - 1;
0082 end
0083 % Now fill the y columns with -1's
0084 k = 1;
0085 j = 1;
0086 for i=iycost'
0087    ns = gencost(i, NCOST);
0088    Ay(k:k+ns-2, ybas+j-1) = -ones(ns-1,1);
0089    k = k + ns - 1;
0090    j = j + 1;
0091 end