Home > matpower4.1 > @opf_model > compute_cost.m

compute_cost

PURPOSE ^

COMPUTE_COST Computes a user-defined cost.

SYNOPSIS ^

function f = compute_cost(om, x, name)

DESCRIPTION ^

COMPUTE_COST  Computes a user-defined cost.
   F_U = COMPUTE_COST(OM, X)
   F_U = COMPUTE_COST(OM, X, NAME)

   Computes the value of a user defined cost, either for all user
   defined costs or for a named set of costs. Requires calling
   BUILD_COST_PARAMS first to build the full set of parameters.

   Let X be the full set of optimization variables and F_U(X, CP) be the
   user-defined cost at X, corresponding to the set of cost parameters in
   the CP struct returned by GET_COST_PARAMS, where CP is a struct with the
   following fields:
       N      - nw x nx sparse matrix
       Cw     - nw x 1 vector
       H      - nw x nw sparse matrix (optional, all zeros by default)
       dd, mm - nw x 1 vectors (optional, all ones by default)
       rh, kk - nw x 1 vectors (optional, all zeros by default)

   These parameters are used as follows to compute F_U(X, CP)

       R  = N*x - rh

               /  kk(i),  R(i) < -kk(i)
       K(i) = <   0,     -kk(i) <= R(i) <= kk(i)
               \ -kk(i),  R(i) > kk(i)

       RR = R + K

       U(i) =  /  0, -kk(i) <= R(i) <= kk(i)
               \  1, otherwise

       DDL(i) = /  1, dd(i) = 1
                \  0, otherwise

       DDQ(i) = /  1, dd(i) = 2
                \  0, otherwise

       Dl = diag(mm) * diag(U) * diag(DDL)
       Dq = diag(mm) * diag(U) * diag(DDQ)

       w = (Dl + Dq * diag(RR)) * RR

       F_U(X, CP) = 1/2 * w'*H*w + Cw'*w

   See also OPF_MODEL, ADD_COSTS, BUILD_COST_PARAMS, GET_COST_PARAMS.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function f = compute_cost(om, x, name)
0002 %COMPUTE_COST  Computes a user-defined cost.
0003 %   F_U = COMPUTE_COST(OM, X)
0004 %   F_U = COMPUTE_COST(OM, X, NAME)
0005 %
0006 %   Computes the value of a user defined cost, either for all user
0007 %   defined costs or for a named set of costs. Requires calling
0008 %   BUILD_COST_PARAMS first to build the full set of parameters.
0009 %
0010 %   Let X be the full set of optimization variables and F_U(X, CP) be the
0011 %   user-defined cost at X, corresponding to the set of cost parameters in
0012 %   the CP struct returned by GET_COST_PARAMS, where CP is a struct with the
0013 %   following fields:
0014 %       N      - nw x nx sparse matrix
0015 %       Cw     - nw x 1 vector
0016 %       H      - nw x nw sparse matrix (optional, all zeros by default)
0017 %       dd, mm - nw x 1 vectors (optional, all ones by default)
0018 %       rh, kk - nw x 1 vectors (optional, all zeros by default)
0019 %
0020 %   These parameters are used as follows to compute F_U(X, CP)
0021 %
0022 %       R  = N*x - rh
0023 %
0024 %               /  kk(i),  R(i) < -kk(i)
0025 %       K(i) = <   0,     -kk(i) <= R(i) <= kk(i)
0026 %               \ -kk(i),  R(i) > kk(i)
0027 %
0028 %       RR = R + K
0029 %
0030 %       U(i) =  /  0, -kk(i) <= R(i) <= kk(i)
0031 %               \  1, otherwise
0032 %
0033 %       DDL(i) = /  1, dd(i) = 1
0034 %                \  0, otherwise
0035 %
0036 %       DDQ(i) = /  1, dd(i) = 2
0037 %                \  0, otherwise
0038 %
0039 %       Dl = diag(mm) * diag(U) * diag(DDL)
0040 %       Dq = diag(mm) * diag(U) * diag(DDQ)
0041 %
0042 %       w = (Dl + Dq * diag(RR)) * RR
0043 %
0044 %       F_U(X, CP) = 1/2 * w'*H*w + Cw'*w
0045 %
0046 %   See also OPF_MODEL, ADD_COSTS, BUILD_COST_PARAMS, GET_COST_PARAMS.
0047 
0048 %   MATPOWER
0049 %   $Id: compute_cost.m,v 1.6 2011/12/01 17:03:59 cvs Exp $
0050 %   by Ray Zimmerman, PSERC Cornell
0051 %   Copyright (c) 2008-2010 by Power System Engineering Research Center (PSERC)
0052 %
0053 %   This file is part of MATPOWER.
0054 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0055 %
0056 %   MATPOWER is free software: you can redistribute it and/or modify
0057 %   it under the terms of the GNU General Public License as published
0058 %   by the Free Software Foundation, either version 3 of the License,
0059 %   or (at your option) any later version.
0060 %
0061 %   MATPOWER is distributed in the hope that it will be useful,
0062 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0063 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
0064 %   GNU General Public License for more details.
0065 %
0066 %   You should have received a copy of the GNU General Public License
0067 %   along with MATPOWER. If not, see <http://www.gnu.org/licenses/>.
0068 %
0069 %   Additional permission under GNU GPL version 3 section 7
0070 %
0071 %   If you modify MATPOWER, or any covered work, to interface with
0072 %   other modules (such as MATLAB code and MEX-files) available in a
0073 %   MATLAB(R) or comparable environment containing parts covered
0074 %   under other licensing terms, the licensors of MATPOWER grant
0075 %   you additional permission to convey the resulting work.
0076 
0077 if nargin < 3
0078     cp = get_cost_params(om);
0079 else
0080     cp = get_cost_params(om, name);
0081 end
0082 
0083 [N, Cw, H, dd, rh, kk, mm] = deal(cp.N, cp.Cw, cp.H, cp.dd, ...
0084                                     cp.rh, cp.kk, cp.mm);
0085 nw = size(N, 1);
0086 r = N * x - rh;                 %% Nx - rhat
0087 iLT = find(r < -kk);            %% below dead zone
0088 iEQ = find(r == 0 & kk == 0);   %% dead zone doesn't exist
0089 iGT = find(r > kk);             %% above dead zone
0090 iND = [iLT; iEQ; iGT];          %% rows that are Not in the Dead region
0091 iL = find(dd == 1);             %% rows using linear function
0092 iQ = find(dd == 2);             %% rows using quadratic function
0093 LL = sparse(iL, iL, 1, nw, nw);
0094 QQ = sparse(iQ, iQ, 1, nw, nw);
0095 kbar = sparse(iND, iND, [   ones(length(iLT), 1);
0096                             zeros(length(iEQ), 1);
0097                             -ones(length(iGT), 1)], nw, nw) * kk;
0098 rr = r + kbar;                  %% apply non-dead zone shift
0099 M = sparse(iND, iND, mm(iND), nw, nw);  %% dead zone or scale
0100 diagrr = sparse(1:nw, 1:nw, rr, nw, nw);
0101 
0102 %% linear rows multiplied by rr(i), quadratic rows by rr(i)^2
0103 w = M * (LL + QQ * diagrr) * rr;
0104 
0105 f = full((w' * H * w) / 2 + Cw' * w);

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