Description of mipsopf

0001 function [results, success, raw] = mipsopf_solver(om, mpopt)
0002 %MIPSOPF_SOLVER  Solves AC optimal power flow using MIPS.
0003 %
0004 %   [RESULTS, SUCCESS, RAW] = MIPSOPF_SOLVER(OM, MPOPT)
0005 %
0006 %   Inputs are an OPF model object and a MATPOWER options struct.
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, MIPS.
0036 
0037 %   MATPOWER
0038 %   $Id: mipsopf_solver.m 2438 2014-12-05 14:32:42Z ray $
0039 %   by Ray Zimmerman, PSERC Cornell
0040 %   and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de Manizales
0041 %   Copyright (c) 2000-2013 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 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0078 
0079 %% options
0080 opt = mpopt.mips;
0081 opt.verbose = mpopt.verbose;
0082 if opt.feastol == 0
0083     opt.feastol = mpopt.opf.violation;  %% = MPOPT.opf.violation by default
0084 end
0085 if ~isfield(opt, 'cost_mult') || isempty(opt.cost_mult)
0086     opt.cost_mult = 1e-4;
0087 end
0088 
0089 %% unpack data
0090 mpc = get_mpc(om);
0091 [baseMVA, bus, gen, branch, gencost] = ...
0092     deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch, mpc.gencost);
0093 [vv, ll, nn] = get_idx(om);
0094 
0095 %% problem dimensions
0096 nb = size(bus, 1);          %% number of buses
0097 nl = size(branch, 1);       %% number of branches
0098 ny = getN(om, 'var', 'y');  %% number of piece-wise linear costs
0099 
0100 %% linear constraints
0101 [A, l, u] = linear_constraints(om);
0102 
0103 %% bounds on optimization vars
0104 [x0, xmin, xmax] = getv(om);
0105 
0106 %% build admittance matrices
0107 [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch);
0108 
0109 %% try to select an interior initial point
0110 if mpopt.opf.init_from_mpc ~= 1
0111     ll = xmin; uu = xmax;
0112     ll(xmin == -Inf) = -1e10;   %% replace Inf with numerical proxies
0113     uu(xmax ==  Inf) =  1e10;
0114     x0 = (ll + uu) / 2;         %% set x0 mid-way between bounds
0115     k = find(xmin == -Inf & xmax < Inf);    %% if only bounded above
0116     x0(k) = xmax(k) - 1;                    %% set just below upper bound
0117     k = find(xmin > -Inf & xmax == Inf);    %% if only bounded below
0118     x0(k) = xmin(k) + 1;                    %% set just above lower bound
0119     Varefs = bus(bus(:, BUS_TYPE) == REF, VA) * (pi/180);
0120     x0(vv.i1.Va:vv.iN.Va) = Varefs(1);  %% angles set to first reference angle
0121     if ny > 0
0122         ipwl = find(gencost(:, MODEL) == PW_LINEAR);
0123     %     PQ = [gen(:, PMAX); gen(:, QMAX)];
0124     %     c = totcost(gencost(ipwl, :), PQ(ipwl));
0125         c = gencost(sub2ind(size(gencost), ipwl, NCOST+2*gencost(ipwl, NCOST)));    %% largest y-value in CCV data
0126         x0(vv.i1.y:vv.iN.y) = max(c) + 0.1 * abs(max(c));
0127     %     x0(vv.i1.y:vv.iN.y) = c + 0.1 * abs(c);
0128     end
0129 end
0130 
0131 %% find branches with flow limits
0132 il = find(branch(:, RATE_A) ~= 0 & branch(:, RATE_A) < 1e10);
0133 nl2 = length(il);           %% number of constrained lines
0134 
0135 %%-----  run opf  -----
0136 f_fcn = @(x)opf_costfcn(x, om);
0137 gh_fcn = @(x)opf_consfcn(x, om, Ybus, Yf(il,:), Yt(il,:), mpopt, il);
0138 hess_fcn = @(x, lambda, cost_mult)opf_hessfcn(x, lambda, cost_mult, om, Ybus, Yf(il,:), Yt(il,:), mpopt, il);
0139 [x, f, info, Output, Lambda] = ...
0140   mips(f_fcn, x0, A, l, u, xmin, xmax, gh_fcn, hess_fcn, opt);
0141 success = (info > 0);
0142 
0143 %% update solution data
0144 Va = x(vv.i1.Va:vv.iN.Va);
0145 Vm = x(vv.i1.Vm:vv.iN.Vm);
0146 Pg = x(vv.i1.Pg:vv.iN.Pg);
0147 Qg = x(vv.i1.Qg:vv.iN.Qg);
0148 V = Vm .* exp(1j*Va);
0149 
0150 %%-----  calculate return values  -----
0151 %% update voltages & generator outputs
0152 bus(:, VA) = Va * 180/pi;
0153 bus(:, VM) = Vm;
0154 gen(:, PG) = Pg * baseMVA;
0155 gen(:, QG) = Qg * baseMVA;
0156 gen(:, VG) = Vm(gen(:, GEN_BUS));
0157 
0158 %% compute branch flows
0159 Sf = V(branch(:, F_BUS)) .* conj(Yf * V);  %% cplx pwr at "from" bus, p.u.
0160 St = V(branch(:, T_BUS)) .* conj(Yt * V);  %% cplx pwr at "to" bus, p.u.
0161 branch(:, PF) = real(Sf) * baseMVA;
0162 branch(:, QF) = imag(Sf) * baseMVA;
0163 branch(:, PT) = real(St) * baseMVA;
0164 branch(:, QT) = imag(St) * baseMVA;
0165 
0166 %% line constraint is actually on square of limit
0167 %% so we must fix multipliers
0168 muSf = zeros(nl, 1);
0169 muSt = zeros(nl, 1);
0170 if ~isempty(il)
0171     muSf(il) = 2 * Lambda.ineqnonlin(1:nl2)       .* branch(il, RATE_A) / baseMVA;
0172     muSt(il) = 2 * Lambda.ineqnonlin((1:nl2)+nl2) .* branch(il, RATE_A) / baseMVA;
0173 end
0174 
0175 %% update Lagrange multipliers
0176 bus(:, MU_VMAX)  = Lambda.upper(vv.i1.Vm:vv.iN.Vm);
0177 bus(:, MU_VMIN)  = Lambda.lower(vv.i1.Vm:vv.iN.Vm);
0178 gen(:, MU_PMAX)  = Lambda.upper(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0179 gen(:, MU_PMIN)  = Lambda.lower(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0180 gen(:, MU_QMAX)  = Lambda.upper(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0181 gen(:, MU_QMIN)  = Lambda.lower(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0182 bus(:, LAM_P)    = Lambda.eqnonlin(nn.i1.Pmis:nn.iN.Pmis) / baseMVA;
0183 bus(:, LAM_Q)    = Lambda.eqnonlin(nn.i1.Qmis:nn.iN.Qmis) / baseMVA;
0184 branch(:, MU_SF) = muSf / baseMVA;
0185 branch(:, MU_ST) = muSt / baseMVA;
0186 
0187 %% package up results
0188 nlnN = getN(om, 'nln');
0189 
0190 %% extract multipliers for nonlinear constraints
0191 kl = find(Lambda.eqnonlin < 0);
0192 ku = find(Lambda.eqnonlin > 0);
0193 nl_mu_l = zeros(nlnN, 1);
0194 nl_mu_u = [zeros(2*nb, 1); muSf; muSt];
0195 nl_mu_l(kl) = -Lambda.eqnonlin(kl);
0196 nl_mu_u(ku) =  Lambda.eqnonlin(ku);
0197 
0198 mu = struct( ...
0199   'var', struct('l', Lambda.lower, 'u', Lambda.upper), ...
0200   'nln', struct('l', nl_mu_l, 'u', nl_mu_u), ...
0201   'lin', struct('l', Lambda.mu_l, 'u', Lambda.mu_u) );
0202 
0203 results = mpc;
0204 [results.bus, results.branch, results.gen, ...
0205     results.om, results.x, results.mu, results.f] = ...
0206         deal(bus, branch, gen, om, x, mu, f);
0207 
0208 pimul = [ ...
0209   results.mu.nln.l - results.mu.nln.u;
0210   results.mu.lin.l - results.mu.lin.u;
0211   -ones(ny>0, 1);
0212   results.mu.var.l - results.mu.var.u;
0213 ];
0214 raw = struct('xr', x, 'pimul', pimul, 'info', info, 'output', Output);
mipsopf_solver

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SOURCE CODE
