function [Ay, by]  = makeAy(baseMVA, ng, gencost, pgbas, qgbas, ybas)% makeAy:  Make the A matrix and RHS for the CCV formulation.%% [Ay, by]  = makeAy(baseMVA, ng, gencost, pgbas, qgbas, ybas) constructs% a matrix Ay and vector by such that the "basin constraints" on Pg,% Qg and Y that the CCV cost formulation uses are expressed as%  Ay * x <= by% where x are the 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 committed.  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 .%   MATPOWER%   $Id: makeAy.m,v 1.5 2004/09/17 13:42:20 ray Exp $%   by Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de Manizales%   Copyright (c) 1996-2004 by Power System Engineering Research Center (PSERC)%   See http://www.pserc.cornell.edu/matpower/ for more info.[PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;% find all pwl cost rows in gencost, either real or reactiveiycost = find(gencost(:, MODEL) == PW_LINEAR);% this is the number of extra "y" variables needed to model those costsny = size(iycost, 1);if ny == 0   Ay = sparse([], [], [], 0, 0, 0);;   by = [];   returnend% if p(i),p(i+1),c(i),c(i+1) define one of the cost segments, then% the corresponding constraint on Pg (or Qg) and Y is%                                             c(i+1) - c(i)%  Y   >=   c(i) + m * (Pg - p(i)),      m = ---------------%                                             p(i+1) - p(i)%% this becomes   m * Pg - Y   <=   m*p(i) - c(i)% Form A matrix.  Use two different loops, one for the PG/Qg coefs,% then another for the y coefs so that everything is filled in the% same order as the compressed column sparse format used by matlab;% this should be the quickest.m = sum(gencost(iycost, NCOST));  % total number of cost pointsAy = sparse([], [], [], m-ny, ybas+ny-1, 2*(m-ny)); by = [];% First fill the Pg or Qg coefficients (since their columns come first)% and the rhsk = 1;for i=iycost'   ns = gencost(i, NCOST);                % # of cost points; segments = ns-1   p = gencost(i, COST:2:COST+2*ns-1) / baseMVA;   c = gencost(i, COST+1:2:COST+2*ns);   m = diff(c) ./ diff(p);                % slopes for Pg (or Qg)   if any(diff(p) == 0)     fprintf('\nmakeAy: bad x axis data in row %i of gencost matrix\n',i);   end   b = m .* p(1:ns-1) - c(1:ns-1);        % and rhs   by = [by;  b'];   if i > ng     sidx = qgbas + (i-ng) - 1;           % this was for a q cost   else     sidx = pgbas + i - 1;                % this was for a p cost   end   Ay(k:k+ns-2, sidx) = m';   k = k + ns - 1;end% Now fill the y columns with -1'sk = 1;j = 1;for i=iycost'   ns = gencost(i, NCOST);   Ay(k:k+ns-2, ybas+j-1) = -ones(ns-1,1);   k = k + ns - 1;   j = j + 1;endreturn;