Description of fmincopf

0001 function [results, success, raw] = fmincopf_solver(om, mpopt)
0002 %FMINCOPF_SOLVER  Solves AC optimal power flow using FMINCON.
0003 %
0004 %   [RESULTS, SUCCESS, RAW] = FMINCOPF_SOLVER(OM, MPOPT)
0005 %
0006 %   Inputs are an OPF model object and a MATPOWER options vector.
0007 %
0008 %   Outputs are a RESULTS struct, SUCCESS flag and RAW output struct.
0009 %
0010 %   RESULTS is a MATPOWER case struct (mpc) with the usual baseMVA, bus
0011 %   branch, gen, gencost fields, along with the following additional
0012 %   fields:
0013 %       .order      see 'help ext2int' for details of this field
0014 %       .x          final value of optimization variables (internal order)
0015 %       .f          final objective function value
0016 %       .mu         shadow prices on ...
0017 %           .var
0018 %               .l  lower bounds on variables
0019 %               .u  upper bounds on variables
0020 %           .nln
0021 %               .l  lower bounds on nonlinear constraints
0022 %               .u  upper bounds on nonlinear constraints
0023 %           .lin
0024 %               .l  lower bounds on linear constraints
0025 %               .u  upper bounds on linear constraints
0026 %
0027 %   SUCCESS     1 if solver converged successfully, 0 otherwise
0028 %
0029 %   RAW         raw output in form returned by MINOS
0030 %       .xr     final value of optimization variables
0031 %       .pimul  constraint multipliers
0032 %       .info   solver specific termination code
0033 %       .output solver specific output information
0034 %
0035 %   See also OPF, FMINCON.
0036 
0037 %   MATPOWER
0038 %   $Id: fmincopf_solver.m,v 1.23 2010/06/09 14:56:58 ray Exp $
0039 %   by Ray Zimmerman, PSERC Cornell
0040 %   and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de Manizales
0041 %   Copyright (c) 2000-2010 by Power System Engineering Research Center (PSERC)
0042 %
0043 %   This file is part of MATPOWER.
0044 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0045 %
0046 %   MATPOWER is free software: you can redistribute it and/or modify
0047 %   it under the terms of the GNU General Public License as published
0048 %   by the Free Software Foundation, either version 3 of the License,
0049 %   or (at your option) any later version.
0050 %
0051 %   MATPOWER is distributed in the hope that it will be useful,
0052 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0053 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
0054 %   GNU General Public License for more details.
0055 %
0056 %   You should have received a copy of the GNU General Public License
0057 %   along with MATPOWER. If not, see <http://www.gnu.org/licenses/>.
0058 %
0059 %   Additional permission under GNU GPL version 3 section 7
0060 %
0061 %   If you modify MATPOWER, or any covered work, to interface with
0062 %   other modules (such as MATLAB code and MEX-files) available in a
0063 %   MATLAB(R) or comparable environment containing parts covered
0064 %   under other licensing terms, the licensors of MATPOWER grant
0065 %   you additional permission to convey the resulting work.
0066 
0067 %%----- initialization -----
0068 %% define named indices into data matrices
0069 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0070     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0071 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0072     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0073     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0074 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0075     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0076     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0077 
0078 %% options
0079 verbose = mpopt(31);    %% VERBOSE
0080 
0081 %% unpack data
0082 mpc = get_mpc(om);
0083 [baseMVA, bus, gen, branch] = ...
0084     deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch);
0085 [vv, ll, nn] = get_idx(om);
0086 
0087 %% problem dimensions
0088 nb = size(bus, 1);          %% number of buses
0089 nl = size(branch, 1);       %% number of branches
0090 ny = getN(om, 'var', 'y');  %% number of piece-wise linear costs
0091 
0092 %% bounds on optimization vars
0093 [x0, LB, UB] = getv(om);
0094 
0095 %% linear constraints
0096 [A, l, u] = linear_constraints(om);
0097 
0098 %% so, can we do anything good about lambda initialization?
0099 if all(bus(:, LAM_P) == 0)
0100   bus(:, LAM_P) = (10)*ones(nb, 1);
0101 end
0102 
0103 %% split l <= A*x <= u into less than, equal to, greater than, and
0104 %% doubly-bounded sets
0105 ieq = find( abs(u-l) <= eps );          %% equality
0106 igt = find( u >=  1e10 & l > -1e10 );   %% greater than, unbounded above
0107 ilt = find( l <= -1e10 & u <  1e10 );   %% less than, unbounded below
0108 ibx = find( (abs(u-l) > eps) & (u < 1e10) & (l > -1e10) );
0109 Af  = [ A(ilt, :); -A(igt, :); A(ibx, :); -A(ibx, :) ];
0110 bf  = [ u(ilt);   -l(igt);     u(ibx);    -l(ibx)];
0111 Afeq = A(ieq, :);
0112 bfeq = u(ieq);
0113 
0114 %% build admittance matrices
0115 [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch);
0116 
0117 %% tolerances
0118 if mpopt(19) == 0           %% CONSTR_MAX_IT
0119   mpopt(19) = 150 + 2*nb;
0120 end
0121 
0122 %% find branches with flow limits
0123 il = find(branch(:, RATE_A) ~= 0 & branch(:, RATE_A) < 1e10);
0124 nl2 = length(il);           %% number of constrained lines
0125 
0126 %% basic optimset options needed for fmincon
0127 fmoptions = optimset('GradObj', 'on', 'GradConstr', 'on', ...
0128             'MaxIter', mpopt(19), 'TolCon', mpopt(16), ...
0129             'TolX', mpopt(17), 'TolFun', mpopt(18) );
0130 fmoptions.MaxFunEvals = 4 * fmoptions.MaxIter;
0131 if verbose == 0,
0132   fmoptions.Display = 'off';
0133 elseif verbose == 1
0134   fmoptions.Display = 'iter';
0135 else
0136   fmoptions.Display = 'testing';
0137 end
0138 
0139 %% select algorithm
0140 otver = ver('optim');
0141 if str2double(otver.Version(1)) < 4
0142   fmoptions = optimset(fmoptions, 'LargeScale', 'off');
0143   Af = full(Af);
0144   Afeq = full(Afeq);
0145 else
0146   if mpopt(55) == 1           %% active-set
0147     fmoptions = optimset(fmoptions, 'Algorithm', 'active-set');
0148     Af = full(Af);
0149     Afeq = full(Afeq);
0150   elseif mpopt(55) == 2       %% interior-point, w/ default 'bfgs' Hessian approx
0151     fmoptions = optimset(fmoptions, 'Algorithm', 'interior-point');
0152   elseif mpopt(55) == 3       %% interior-point, w/ 'lbfgs' Hessian approx
0153     fmoptions = optimset(fmoptions, 'Algorithm', 'interior-point', 'Hessian','lbfgs');
0154   elseif mpopt(55) == 4       %% interior-point, w/ exact user-supplied Hessian
0155     fmc_hessian = @(x, lambda)opf_hessfcn(x, lambda, 1, om, Ybus, Yf(il,:), Yt(il,:), mpopt, il);
0156     fmoptions = optimset(fmoptions, 'Algorithm', 'interior-point', ...
0157         'Hessian', 'user-supplied', 'HessFcn', fmc_hessian);
0158   elseif mpopt(55) == 5       %% interior-point, w/ finite-diff Hessian
0159     fmoptions = optimset(fmoptions, 'Algorithm', 'interior-point', 'Hessian','fin-diff-grads', 'SubProblem', 'cg');
0160   else
0161     error('fmincopf_solver: unknown algorithm specified in FMC_ALG option');
0162   end
0163 end
0164 % fmoptions = optimset(fmoptions, 'DerivativeCheck', 'on', 'FinDiffType', 'central', 'FunValCheck', 'on');
0165 % fmoptions = optimset(fmoptions, 'Diagnostics', 'on');
0166 
0167 %% try to select an interior initial point for interior point solver
0168 if str2double(otver.Version(1)) >= 4 && strcmp(optimget(fmoptions, 'Algorithm'), 'interior-point')
0169   x0 = zeros(getN(om, 'var'), 1);
0170   x0(vv.i1.Va:vv.iN.Va) = 0;
0171   x0(vv.i1.Vm:vv.iN.Vm)   = 1;
0172   x0(vv.i1.Pg:vv.iN.Pg) = (gen(:, PMIN) + gen(:, PMAX)) / 2 / baseMVA;
0173   x0(vv.i1.Qg:vv.iN.Qg) = (gen(:, QMIN) + gen(:, QMAX)) / 2 / baseMVA;
0174 end
0175 
0176 %%-----  run opf  -----
0177 f_fcn = @(x)opf_costfcn(x, om);
0178 gh_fcn = @(x)opf_consfcn(x, om, Ybus, Yf(il,:), Yt(il,:), mpopt, il);
0179 [x, f, info, Output, Lambda] = ...
0180   fmincon(f_fcn, x0, Af, bf, Afeq, bfeq, LB, UB, gh_fcn, fmoptions);
0181 success = (info > 0);
0182 
0183 %% update solution data
0184 Va = x(vv.i1.Va:vv.iN.Va);
0185 Vm = x(vv.i1.Vm:vv.iN.Vm);
0186 Pg = x(vv.i1.Pg:vv.iN.Pg);
0187 Qg = x(vv.i1.Qg:vv.iN.Qg);
0188 V = Vm .* exp(1j*Va);
0189 
0190 %%-----  calculate return values  -----
0191 %% update voltages & generator outputs
0192 bus(:, VA) = Va * 180/pi;
0193 bus(:, VM) = Vm;
0194 gen(:, PG) = Pg * baseMVA;
0195 gen(:, QG) = Qg * baseMVA;
0196 gen(:, VG) = Vm(gen(:, GEN_BUS));
0197 
0198 %% compute branch flows
0199 Sf = V(branch(:, F_BUS)) .* conj(Yf * V);  %% cplx pwr at "from" bus, p.u.
0200 St = V(branch(:, T_BUS)) .* conj(Yt * V);  %% cplx pwr at "to" bus, p.u.
0201 branch(:, PF) = real(Sf) * baseMVA;
0202 branch(:, QF) = imag(Sf) * baseMVA;
0203 branch(:, PT) = real(St) * baseMVA;
0204 branch(:, QT) = imag(St) * baseMVA;
0205 
0206 %% line constraint is actually on square of limit
0207 %% so we must fix multipliers
0208 muSf = zeros(nl, 1);
0209 muSt = zeros(nl, 1);
0210 if ~isempty(il)
0211     muSf(il) = 2 * Lambda.ineqnonlin(1:nl2)       .* branch(il, RATE_A) / baseMVA;
0212     muSt(il) = 2 * Lambda.ineqnonlin((1:nl2)+nl2) .* branch(il, RATE_A) / baseMVA;
0213 end
0214 
0215 %% update Lagrange multipliers
0216 bus(:, MU_VMAX)  = Lambda.upper(vv.i1.Vm:vv.iN.Vm);
0217 bus(:, MU_VMIN)  = Lambda.lower(vv.i1.Vm:vv.iN.Vm);
0218 gen(:, MU_PMAX)  = Lambda.upper(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0219 gen(:, MU_PMIN)  = Lambda.lower(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0220 gen(:, MU_QMAX)  = Lambda.upper(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0221 gen(:, MU_QMIN)  = Lambda.lower(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0222 bus(:, LAM_P)    = Lambda.eqnonlin(nn.i1.Pmis:nn.iN.Pmis) / baseMVA;
0223 bus(:, LAM_Q)    = Lambda.eqnonlin(nn.i1.Qmis:nn.iN.Qmis) / baseMVA;
0224 branch(:, MU_SF) = muSf / baseMVA;
0225 branch(:, MU_ST) = muSt / baseMVA;
0226 
0227 %% package up results
0228 nlnN = getN(om, 'nln');
0229 nlt = length(ilt);
0230 ngt = length(igt);
0231 nbx = length(ibx);
0232 
0233 %% extract multipliers for nonlinear constraints
0234 kl = find(Lambda.eqnonlin < 0);
0235 ku = find(Lambda.eqnonlin > 0);
0236 nl_mu_l = zeros(nlnN, 1);
0237 nl_mu_u = [zeros(2*nb, 1); muSf; muSt];
0238 nl_mu_l(kl) = -Lambda.eqnonlin(kl);
0239 nl_mu_u(ku) =  Lambda.eqnonlin(ku);
0240 
0241 %% extract multipliers for linear constraints
0242 kl = find(Lambda.eqlin < 0);
0243 ku = find(Lambda.eqlin > 0);
0244 
0245 mu_l = zeros(size(u));
0246 mu_l(ieq(kl)) = -Lambda.eqlin(kl);
0247 mu_l(igt) = Lambda.ineqlin(nlt+(1:ngt));
0248 mu_l(ibx) = Lambda.ineqlin(nlt+ngt+nbx+(1:nbx));
0249 
0250 mu_u = zeros(size(u));
0251 mu_u(ieq(ku)) = Lambda.eqlin(ku);
0252 mu_u(ilt) = Lambda.ineqlin(1:nlt);
0253 mu_u(ibx) = Lambda.ineqlin(nlt+ngt+(1:nbx));
0254 
0255 mu = struct( ...
0256   'var', struct('l', Lambda.lower, 'u', Lambda.upper), ...
0257   'nln', struct('l', nl_mu_l, 'u', nl_mu_u), ...
0258   'lin', struct('l', mu_l, 'u', mu_u) );
0259 
0260 results = mpc;
0261 [results.bus, results.branch, results.gen, ...
0262     results.om, results.x, results.mu, results.f] = ...
0263         deal(bus, branch, gen, om, x, mu, f);
0264 
0265 pimul = [ ...
0266   results.mu.nln.l - results.mu.nln.u;
0267   results.mu.lin.l - results.mu.lin.u;
0268   -ones(ny>0, 1);
0269   results.mu.var.l - results.mu.var.u;
0270 ];
0271 raw = struct('xr', x, 'pimul', pimul, 'info', info, 'output', Output);
fmincopf_solver

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SOURCE CODE
