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opf

PURPOSE ^

OPF Solves an optimal power flow.

SYNOPSIS ^

function [busout, genout, branchout, f, success, info, et, g, jac, xr, pimul] =opf(varargin)

DESCRIPTION ^

OPF  Solves an optimal power flow.
   [RESULTS, SUCCESS] = OPF(MPC, MPOPT)

   Returns either a RESULTS struct and an optional SUCCESS flag, or individual
   data matrices, the objective function value and a SUCCESS flag. In the
   latter case, there are additional optional return values. See Examples
   below for the possible calling syntax options.

   Examples:
       Output argument options:

       results = opf(...)
       [results, success] = opf(...)
       [bus, gen, branch, f, success] = opf(...)
       [bus, gen, branch, f, success, info, et, g, jac, xr, pimul] = opf(...)

       Input arguments options:

       opf(mpc)
       opf(mpc, mpopt)
       opf(mpc, userfcn, mpopt)
       opf(mpc, A, l, u)
       opf(mpc, A, l, u, mpopt)
       opf(mpc, A, l, u, mpopt, N, fparm, H, Cw)
       opf(mpc, A, l, u, mpopt, N, fparm, H, Cw, z0, zl, zu)

       opf(baseMVA, bus, gen, branch, areas, gencost)
       opf(baseMVA, bus, gen, branch, areas, gencost, mpopt)
       opf(baseMVA, bus, gen, branch, areas, gencost, userfcn, mpopt)
       opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u)
       opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u, mpopt)
       opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u, ...
                                   mpopt, N, fparm, H, Cw)
       opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u, ...
                                   mpopt, N, fparm, H, Cw, z0, zl, zu)

   The data for the problem can be specified in one of three ways:
   (1) a string (mpc) containing the file name of a MATPOWER case
     which defines the data matrices baseMVA, bus, gen, branch, and
     gencost (areas is not used at all, it is only included for
     backward compatibility of the API).
   (2) a struct (mpc) containing the data matrices as fields.
   (3) the individual data matrices themselves.
   
   The optional user parameters for user constraints (A, l, u), user costs
   (N, fparm, H, Cw), user variable initializer (z0), and user variable
   limits (zl, zu) can also be specified as fields in a case struct,
   either passed in directly or defined in a case file referenced by name.
   
   When specified, A, l, u represent additional linear constraints on the
   optimization variables, l <= A*[x; z] <= u. If the user specifies an A
   matrix that has more columns than the number of "x" (OPF) variables,
   then there are extra linearly constrained "z" variables. For an
   explanation of the formulation used and instructions for forming the
   A matrix, see the manual.

   A generalized cost on all variables can be applied if input arguments
   N, fparm, H and Cw are specified.  First, a linear transformation
   of the optimization variables is defined by means of r = N * [x; z].
   Then, to each element of r a function is applied as encoded in the
   fparm matrix (see manual). If the resulting vector is named w,
   then H and Cw define a quadratic cost on w: (1/2)*w'*H*w + Cw * w .
   H and N should be sparse matrices and H should also be symmetric.

   The optional mpopt vector specifies MATPOWER options. If the OPF
   algorithm is not explicitly set in the options MATPOWER will use
   the default solver, based on a primal-dual interior point method.
   For the AC OPF this is opf.ac.solver = 'MIPS', unless the TSPOPF optional
   package is installed, in which case the default is 'PDIPM'. For the
   DC OPF, the default is opf.dc.solver = 'MIPS'. See MPOPTION for
   more details on the available OPF solvers and other OPF options
   and their default values.

   The solved case is returned either in a single results struct (described
   below) or in the individual data matrices, bus, gen and branch. Also
   returned are the final objective function value (f) and a flag which is
   true if the algorithm was successful in finding a solution (success).
   Additional optional return values are an algorithm specific return status
   (info), elapsed time in seconds (et), the constraint vector (g), the
   Jacobian matrix (jac), and the vector of variables (xr) as well 
   as the constraint multipliers (pimul).

   The single results struct is a MATPOWER case struct (mpc) with the
   usual baseMVA, bus, branch, gen, gencost fields, along with the
   following additional fields:

       .order      see 'help ext2int' for details of this field
       .et         elapsed time in seconds for solving OPF
       .success    1 if solver converged successfully, 0 otherwise
       .om         OPF model object, see 'help opf_model'
       .x          final value of optimization variables (internal order)
       .f          final objective function value
       .mu         shadow prices on ...
           .var
               .l  lower bounds on variables
               .u  upper bounds on variables
           .nln
               .l  lower bounds on nonlinear constraints
               .u  upper bounds on nonlinear constraints
           .lin
               .l  lower bounds on linear constraints
               .u  upper bounds on linear constraints
       .raw        raw solver output in form returned by MINOS, and more
           .xr     final value of optimization variables
           .pimul  constraint multipliers
           .info   solver specific termination code
           .output solver specific output information
              .alg algorithm code of solver used
           .g      (optional) constraint values
           .dg     (optional) constraint 1st derivatives
           .df     (optional) obj fun 1st derivatives (not yet implemented)
           .d2f    (optional) obj fun 2nd derivatives (not yet implemented)
       .var
           .val    optimization variable values, by named block
               .Va     voltage angles
               .Vm     voltage magnitudes (AC only)
               .Pg     real power injections
               .Qg     reactive power injections (AC only)
               .y      constrained cost variable (only if have pwl costs)
               (other) any user defined variable blocks
           .mu     variable bound shadow prices, by named block
               .l  lower bound shadow prices
                   .Va, Vm, Pg, Qg, y, (other)
               .u  upper bound shadow prices
                   .Va, Vm, Pg, Qg, y, (other)
       .nln    (AC only)
           .mu     shadow prices on nonlinear constraints, by named block
               .l  lower bounds
                   .Pmis   real power mismatch equations
                   .Qmis   reactive power mismatch equations
                   .Sf     flow limits at "from" end of branches
                   .St     flow limits at "to" end of branches
               .u  upper bounds
                   .Pmis, Qmis, Sf, St
       .lin
           .mu     shadow prices on linear constraints, by named block
               .l  lower bounds
                   .Pmis   real power mistmatch equations (DC only)
                   .Pf     flow limits at "from" end of branches (DC only)
                   .Pt     flow limits at "to" end of branches (DC only)
                   .PQh    upper portion of gen PQ-capability curve (AC only)
                   .PQl    lower portion of gen PQ-capability curve (AC only)
                   .vl     constant power factor constraint for loads (AC only)
                   .ycon   basin constraints for CCV for pwl costs
                   (other) any user defined constraint blocks
               .u  upper bounds
                   .Pmis, Pf, Pt, PQh, PQl, vl, ycon, (other)
       .cost       user defined cost values, by named block

   See also RUNOPF, DCOPF, UOPF, CASEFORMAT.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [busout, genout, branchout, f, success, info, et, g, jac, xr, pimul] = ...
0002     opf(varargin)
0003 %OPF  Solves an optimal power flow.
0004 %   [RESULTS, SUCCESS] = OPF(MPC, MPOPT)
0005 %
0006 %   Returns either a RESULTS struct and an optional SUCCESS flag, or individual
0007 %   data matrices, the objective function value and a SUCCESS flag. In the
0008 %   latter case, there are additional optional return values. See Examples
0009 %   below for the possible calling syntax options.
0010 %
0011 %   Examples:
0012 %       Output argument options:
0013 %
0014 %       results = opf(...)
0015 %       [results, success] = opf(...)
0016 %       [bus, gen, branch, f, success] = opf(...)
0017 %       [bus, gen, branch, f, success, info, et, g, jac, xr, pimul] = opf(...)
0018 %
0019 %       Input arguments options:
0020 %
0021 %       opf(mpc)
0022 %       opf(mpc, mpopt)
0023 %       opf(mpc, userfcn, mpopt)
0024 %       opf(mpc, A, l, u)
0025 %       opf(mpc, A, l, u, mpopt)
0026 %       opf(mpc, A, l, u, mpopt, N, fparm, H, Cw)
0027 %       opf(mpc, A, l, u, mpopt, N, fparm, H, Cw, z0, zl, zu)
0028 %
0029 %       opf(baseMVA, bus, gen, branch, areas, gencost)
0030 %       opf(baseMVA, bus, gen, branch, areas, gencost, mpopt)
0031 %       opf(baseMVA, bus, gen, branch, areas, gencost, userfcn, mpopt)
0032 %       opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u)
0033 %       opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u, mpopt)
0034 %       opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u, ...
0035 %                                   mpopt, N, fparm, H, Cw)
0036 %       opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u, ...
0037 %                                   mpopt, N, fparm, H, Cw, z0, zl, zu)
0038 %
0039 %   The data for the problem can be specified in one of three ways:
0040 %   (1) a string (mpc) containing the file name of a MATPOWER case
0041 %     which defines the data matrices baseMVA, bus, gen, branch, and
0042 %     gencost (areas is not used at all, it is only included for
0043 %     backward compatibility of the API).
0044 %   (2) a struct (mpc) containing the data matrices as fields.
0045 %   (3) the individual data matrices themselves.
0046 %
0047 %   The optional user parameters for user constraints (A, l, u), user costs
0048 %   (N, fparm, H, Cw), user variable initializer (z0), and user variable
0049 %   limits (zl, zu) can also be specified as fields in a case struct,
0050 %   either passed in directly or defined in a case file referenced by name.
0051 %
0052 %   When specified, A, l, u represent additional linear constraints on the
0053 %   optimization variables, l <= A*[x; z] <= u. If the user specifies an A
0054 %   matrix that has more columns than the number of "x" (OPF) variables,
0055 %   then there are extra linearly constrained "z" variables. For an
0056 %   explanation of the formulation used and instructions for forming the
0057 %   A matrix, see the manual.
0058 %
0059 %   A generalized cost on all variables can be applied if input arguments
0060 %   N, fparm, H and Cw are specified.  First, a linear transformation
0061 %   of the optimization variables is defined by means of r = N * [x; z].
0062 %   Then, to each element of r a function is applied as encoded in the
0063 %   fparm matrix (see manual). If the resulting vector is named w,
0064 %   then H and Cw define a quadratic cost on w: (1/2)*w'*H*w + Cw * w .
0065 %   H and N should be sparse matrices and H should also be symmetric.
0066 %
0067 %   The optional mpopt vector specifies MATPOWER options. If the OPF
0068 %   algorithm is not explicitly set in the options MATPOWER will use
0069 %   the default solver, based on a primal-dual interior point method.
0070 %   For the AC OPF this is opf.ac.solver = 'MIPS', unless the TSPOPF optional
0071 %   package is installed, in which case the default is 'PDIPM'. For the
0072 %   DC OPF, the default is opf.dc.solver = 'MIPS'. See MPOPTION for
0073 %   more details on the available OPF solvers and other OPF options
0074 %   and their default values.
0075 %
0076 %   The solved case is returned either in a single results struct (described
0077 %   below) or in the individual data matrices, bus, gen and branch. Also
0078 %   returned are the final objective function value (f) and a flag which is
0079 %   true if the algorithm was successful in finding a solution (success).
0080 %   Additional optional return values are an algorithm specific return status
0081 %   (info), elapsed time in seconds (et), the constraint vector (g), the
0082 %   Jacobian matrix (jac), and the vector of variables (xr) as well
0083 %   as the constraint multipliers (pimul).
0084 %
0085 %   The single results struct is a MATPOWER case struct (mpc) with the
0086 %   usual baseMVA, bus, branch, gen, gencost fields, along with the
0087 %   following additional fields:
0088 %
0089 %       .order      see 'help ext2int' for details of this field
0090 %       .et         elapsed time in seconds for solving OPF
0091 %       .success    1 if solver converged successfully, 0 otherwise
0092 %       .om         OPF model object, see 'help opf_model'
0093 %       .x          final value of optimization variables (internal order)
0094 %       .f          final objective function value
0095 %       .mu         shadow prices on ...
0096 %           .var
0097 %               .l  lower bounds on variables
0098 %               .u  upper bounds on variables
0099 %           .nln
0100 %               .l  lower bounds on nonlinear constraints
0101 %               .u  upper bounds on nonlinear constraints
0102 %           .lin
0103 %               .l  lower bounds on linear constraints
0104 %               .u  upper bounds on linear constraints
0105 %       .raw        raw solver output in form returned by MINOS, and more
0106 %           .xr     final value of optimization variables
0107 %           .pimul  constraint multipliers
0108 %           .info   solver specific termination code
0109 %           .output solver specific output information
0110 %              .alg algorithm code of solver used
0111 %           .g      (optional) constraint values
0112 %           .dg     (optional) constraint 1st derivatives
0113 %           .df     (optional) obj fun 1st derivatives (not yet implemented)
0114 %           .d2f    (optional) obj fun 2nd derivatives (not yet implemented)
0115 %       .var
0116 %           .val    optimization variable values, by named block
0117 %               .Va     voltage angles
0118 %               .Vm     voltage magnitudes (AC only)
0119 %               .Pg     real power injections
0120 %               .Qg     reactive power injections (AC only)
0121 %               .y      constrained cost variable (only if have pwl costs)
0122 %               (other) any user defined variable blocks
0123 %           .mu     variable bound shadow prices, by named block
0124 %               .l  lower bound shadow prices
0125 %                   .Va, Vm, Pg, Qg, y, (other)
0126 %               .u  upper bound shadow prices
0127 %                   .Va, Vm, Pg, Qg, y, (other)
0128 %       .nln    (AC only)
0129 %           .mu     shadow prices on nonlinear constraints, by named block
0130 %               .l  lower bounds
0131 %                   .Pmis   real power mismatch equations
0132 %                   .Qmis   reactive power mismatch equations
0133 %                   .Sf     flow limits at "from" end of branches
0134 %                   .St     flow limits at "to" end of branches
0135 %               .u  upper bounds
0136 %                   .Pmis, Qmis, Sf, St
0137 %       .lin
0138 %           .mu     shadow prices on linear constraints, by named block
0139 %               .l  lower bounds
0140 %                   .Pmis   real power mistmatch equations (DC only)
0141 %                   .Pf     flow limits at "from" end of branches (DC only)
0142 %                   .Pt     flow limits at "to" end of branches (DC only)
0143 %                   .PQh    upper portion of gen PQ-capability curve (AC only)
0144 %                   .PQl    lower portion of gen PQ-capability curve (AC only)
0145 %                   .vl     constant power factor constraint for loads (AC only)
0146 %                   .ycon   basin constraints for CCV for pwl costs
0147 %                   (other) any user defined constraint blocks
0148 %               .u  upper bounds
0149 %                   .Pmis, Pf, Pt, PQh, PQl, vl, ycon, (other)
0150 %       .cost       user defined cost values, by named block
0151 %
0152 %   See also RUNOPF, DCOPF, UOPF, CASEFORMAT.
0153 
0154 %   MATPOWER
0155 %   $Id: opf.m 2229 2013-12-11 01:28:09Z ray $
0156 %   by Ray Zimmerman, PSERC Cornell
0157 %   and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de Manizales
0158 %   Copyright (c) 1996-2010 by Power System Engineering Research Center (PSERC)
0159 %
0160 %   This file is part of MATPOWER.
0161 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0162 %
0163 %   MATPOWER is free software: you can redistribute it and/or modify
0164 %   it under the terms of the GNU General Public License as published
0165 %   by the Free Software Foundation, either version 3 of the License,
0166 %   or (at your option) any later version.
0167 %
0168 %   MATPOWER is distributed in the hope that it will be useful,
0169 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0170 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
0171 %   GNU General Public License for more details.
0172 %
0173 %   You should have received a copy of the GNU General Public License
0174 %   along with MATPOWER. If not, see <http://www.gnu.org/licenses/>.
0175 %
0176 %   Additional permission under GNU GPL version 3 section 7
0177 %
0178 %   If you modify MATPOWER, or any covered work, to interface with
0179 %   other modules (such as MATLAB code and MEX-files) available in a
0180 %   MATLAB(R) or comparable environment containing parts covered
0181 %   under other licensing terms, the licensors of MATPOWER grant
0182 %   you additional permission to convey the resulting work.
0183 
0184 %%----- initialization -----
0185 t0 = clock;         %% start timer
0186 
0187 %% define named indices into data matrices
0188 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0189     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0190 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0191     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0192     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0193 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0194     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0195     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0196 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0197 
0198 %% process input arguments
0199 [mpc, mpopt] = opf_args(varargin{:});
0200 
0201 %% add zero columns to bus, gen, branch for multipliers, etc if needed
0202 nb   = size(mpc.bus, 1);    %% number of buses
0203 nl   = size(mpc.branch, 1); %% number of branches
0204 ng   = size(mpc.gen, 1);    %% number of dispatchable injections
0205 if size(mpc.bus,2) < MU_VMIN
0206   mpc.bus = [mpc.bus zeros(nb, MU_VMIN-size(mpc.bus,2)) ];
0207 end
0208 if size(mpc.gen,2) < MU_QMIN
0209   mpc.gen = [ mpc.gen zeros(ng, MU_QMIN-size(mpc.gen,2)) ];
0210 end
0211 if size(mpc.branch,2) < MU_ANGMAX
0212   mpc.branch = [ mpc.branch zeros(nl, MU_ANGMAX-size(mpc.branch,2)) ];
0213 end
0214 
0215 %%-----  convert to internal numbering, remove out-of-service stuff  -----
0216 mpc = ext2int(mpc);
0217 
0218 %%-----  construct OPF model object  -----
0219 om = opf_setup(mpc, mpopt);
0220 
0221 %%-----  execute the OPF  -----
0222 if nargout > 7
0223     mpopt.opf.return_raw_der = 1;
0224 end
0225 [results, success, raw] = opf_execute(om, mpopt);
0226 
0227 %%-----  revert to original ordering, including out-of-service stuff  -----
0228 results = int2ext(results);
0229 
0230 %% zero out result fields of out-of-service gens & branches
0231 if ~isempty(results.order.gen.status.off)
0232   results.gen(results.order.gen.status.off, [PG QG MU_PMAX MU_PMIN]) = 0;
0233 end
0234 if ~isempty(results.order.branch.status.off)
0235   results.branch(results.order.branch.status.off, [PF QF PT QT MU_SF MU_ST MU_ANGMIN MU_ANGMAX]) = 0;
0236 end
0237 
0238 %%-----  finish preparing output  -----
0239 et = etime(clock, t0);      %% compute elapsed time
0240 if nargout > 0
0241   if nargout <= 2
0242     results.et = et;
0243     results.success = success;
0244     results.raw = raw;
0245     busout = results;
0246     genout = success;
0247   else
0248     [busout, genout, branchout, f, info, xr, pimul] = deal(results.bus, ...
0249         results.gen, results.branch, results.f, raw.info, raw.xr, raw.pimul);
0250     if isfield(results, 'g')
0251       g = results.g;
0252     end
0253     if isfield(results, 'dg')
0254       jac = results.dg;
0255     end
0256   end
0257 elseif success
0258   results.et = et;
0259   results.success = success;
0260   printpf(results, 1, mpopt);
0261 end

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