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 % $Id: makeAy.m 1635 2010-04-26 19:45:26Z ray $ 0026 % by Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de Manizales 0027 % Copyright (c) 1996-2010 by Power System Engineering Research Center (PSERC) 0028 % 0029 % This file is part of MATPOWER. 0030 % See http://www.pserc.cornell.edu/matpower/ for more info. 0031 % 0032 % MATPOWER is free software: you can redistribute it and/or modify 0033 % it under the terms of the GNU General Public License as published 0034 % by the Free Software Foundation, either version 3 of the License, 0035 % or (at your option) any later version. 0036 % 0037 % MATPOWER is distributed in the hope that it will be useful, 0038 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0039 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0040 % GNU General Public License for more details. 0041 % 0042 % You should have received a copy of the GNU General Public License 0043 % along with MATPOWER. If not, see <http://www.gnu.org/licenses/>. 0044 % 0045 % Additional permission under GNU GPL version 3 section 7 0046 % 0047 % If you modify MATPOWER, or any covered work, to interface with 0048 % other modules (such as MATLAB code and MEX-files) available in a 0049 % MATLAB(R) or comparable environment containing parts covered 0050 % under other licensing terms, the licensors of MATPOWER grant 0051 % you additional permission to convey the resulting work. 0052 0053 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost; 0054 0055 % find all pwl cost rows in gencost, either real or reactive 0056 iycost = find(gencost(:, MODEL) == PW_LINEAR); 0057 0058 % this is the number of extra "y" variables needed to model those costs 0059 ny = size(iycost, 1); 0060 0061 if ny == 0 0062 Ay = sparse([], [], [], 0, ybas+ny-1, 0); 0063 by = []; 0064 return 0065 end 0066 0067 % if p(i),p(i+1),c(i),c(i+1) define one of the cost segments, then 0068 % the corresponding constraint on Pg (or Qg) and Y is 0069 % c(i+1) - c(i) 0070 % Y >= c(i) + m * (Pg - p(i)), m = --------------- 0071 % p(i+1) - p(i) 0072 % 0073 % this becomes m * Pg - Y <= m*p(i) - c(i) 0074 0075 % Form A matrix. Use two different loops, one for the PG/Qg coefs, 0076 % then another for the y coefs so that everything is filled in the 0077 % same order as the compressed column sparse format used by matlab; 0078 % this should be the quickest. 0079 0080 m = sum(gencost(iycost, NCOST)); % total number of cost points 0081 Ay = sparse([], [], [], m-ny, ybas+ny-1, 2*(m-ny)); 0082 by = []; 0083 % First fill the Pg or Qg coefficients (since their columns come first) 0084 % and the rhs 0085 k = 1; 0086 for i=iycost' 0087 ns = gencost(i, NCOST); % # of cost points; segments = ns-1 0088 p = gencost(i, COST:2:COST+2*ns-1) / baseMVA; 0089 c = gencost(i, COST+1:2:COST+2*ns); 0090 m = diff(c) ./ diff(p); % slopes for Pg (or Qg) 0091 if any(diff(p) == 0) 0092 fprintf('\nmakeAy: bad x axis data in row %i of gencost matrix\n',i); 0093 end 0094 b = m .* p(1:ns-1) - c(1:ns-1); % and rhs 0095 by = [by; b']; 0096 if i > ng 0097 sidx = qgbas + (i-ng) - 1; % this was for a q cost 0098 else 0099 sidx = pgbas + i - 1; % this was for a p cost 0100 end 0101 Ay(k:k+ns-2, sidx) = m'; 0102 k = k + ns - 1; 0103 end 0104 % Now fill the y columns with -1's 0105 k = 1; 0106 j = 1; 0107 for i=iycost' 0108 ns = gencost(i, NCOST); 0109 Ay(k:k+ns-2, ybas+j-1) = -ones(ns-1,1); 0110 k = k + ns - 1; 0111 j = j + 1; 0112 end