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_ALG = 560, unless the TSPOPF optional
package is installed, in which case the default is 540. For the
DC OPF, the default is OPF_ALG_DC = 200. 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, Pf, PQh, PQl, vl, ycon, (other)
.cost user defined cost values, by named block
See also RUNOPF, DCOPF, UOPF, CASEFORMAT.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_ALG = 560, unless the TSPOPF optional 0071 % package is installed, in which case the default is 540. For the 0072 % DC OPF, the default is OPF_ALG_DC = 200. 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, Pf, 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,v 1.73 2010/06/09 14:56:58 ray Exp $ 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(52) = 1; %% RETURN_RAW_DER 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