Description of ipoptopf

0001 function [results, success, raw] = ipoptopf_solver(om, mpopt)
0002 %IPOPTOPF_SOLVER  Solves AC optimal power flow using MIPS.
0003 %
0004 %   [RESULTS, SUCCESS, RAW] = IPOPTOPF_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, IPOPT.
0036 
0037 %   MATPOWER
0038 %   $Id: ipoptopf_solver.m,v 1.6 2011/06/16 17:45:56 cvs Exp $
0039 %   by Ray Zimmerman, PSERC Cornell
0040 %   and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de Manizales
0041 %   Copyright (c) 2000-2011 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 %% unpack data
0080 mpc = get_mpc(om);
0081 [baseMVA, bus, gen, branch, gencost] = ...
0082     deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch, mpc.gencost);
0083 [vv, ll, nn] = get_idx(om);
0084 
0085 %% problem dimensions
0086 nb = size(bus, 1);          %% number of buses
0087 ng = size(gen, 1);          %% number of gens
0088 nl = size(branch, 1);       %% number of branches
0089 ny = getN(om, 'var', 'y');  %% number of piece-wise linear costs
0090 
0091 %% linear constraints
0092 [A, l, u] = linear_constraints(om);
0093 
0094 %% bounds on optimization vars
0095 [x0, xmin, xmax] = getv(om);
0096 
0097 %% build admittance matrices
0098 [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch);
0099 
0100 %% try to select an interior initial point
0101 ll = xmin; uu = xmax;
0102 ll(xmin == -Inf) = -1e10;   %% replace Inf with numerical proxies
0103 uu(xmax ==  Inf) =  1e10;
0104 x0 = (ll + uu) / 2;
0105 Varefs = bus(bus(:, BUS_TYPE) == REF, VA) * (pi/180);
0106 x0(vv.i1.Va:vv.iN.Va) = Varefs(1);  %% angles set to first reference angle
0107 if ny > 0
0108     ipwl = find(gencost(:, MODEL) == PW_LINEAR);
0109 %     PQ = [gen(:, PMAX); gen(:, QMAX)];
0110 %     c = totcost(gencost(ipwl, :), PQ(ipwl));
0111     c = gencost(sub2ind(size(gencost), ipwl, NCOST+2*gencost(ipwl, NCOST)));    %% largest y-value in CCV data
0112     x0(vv.i1.y:vv.iN.y) = max(c) + 0.1 * abs(max(c));
0113 %     x0(vv.i1.y:vv.iN.y) = c + 0.1 * abs(c);
0114 end
0115 
0116 %% find branches with flow limits
0117 il = find(branch(:, RATE_A) ~= 0 & branch(:, RATE_A) < 1e10);
0118 nl2 = length(il);           %% number of constrained lines
0119 
0120 %%-----  run opf  -----
0121 %% build Jacobian and Hessian structure
0122 nA = size(A, 1);                %% number of original linear constraints
0123 nx = length(x0);
0124 f = branch(:, F_BUS);                           %% list of "from" buses
0125 t = branch(:, T_BUS);                           %% list of "to" buses
0126 Cf = sparse(1:nl, f, ones(nl, 1), nl, nb);      %% connection matrix for line & from buses
0127 Ct = sparse(1:nl, t, ones(nl, 1), nl, nb);      %% connection matrix for line & to buses
0128 Cl = Cf + Ct;
0129 Cb = Cl' * Cl + speye(nb);
0130 Cl2 = Cl(il, :);
0131 Cg = sparse(gen(:, GEN_BUS), (1:ng)', 1, nb, ng);
0132 nz = nx - 2*(nb+ng);
0133 nxtra = nx - 2*nb;
0134 Js = [
0135     Cb      Cb      Cg              sparse(nb,ng)   sparse(nb,nz);
0136     Cb      Cb      sparse(nb,ng)   Cg              sparse(nb,nz);
0137     Cl2     Cl2     sparse(nl2, 2*ng)               sparse(nl2,nz);
0138     Cl2     Cl2     sparse(nl2, 2*ng)               sparse(nl2,nz);
0139     A;
0140 ];
0141 [f, df, d2f] = opf_costfcn(x0, om);
0142 Hs = tril(d2f + [
0143     Cb  Cb  sparse(nb,nxtra);
0144     Cb  Cb  sparse(nb,nxtra);
0145     sparse(nxtra,nx);
0146 ]);
0147 
0148 %% set options struct for IPOPT
0149 options.ipopt = ipopt_options([], mpopt);
0150 
0151 %% extra data to pass to functions
0152 options.auxdata = struct( ...
0153     'om',       om, ...
0154     'Ybus',     Ybus, ...
0155     'Yf',       Yf(il,:), ...
0156     'Yt',       Yt(il,:), ...
0157     'mpopt',    mpopt, ...
0158     'il',       il, ...
0159     'A',        A, ...
0160     'nA',       nA, ...
0161     'neqnln',   2*nb, ...
0162     'niqnln',   2*nl2, ...
0163     'Js',       Js, ...
0164     'Hs',       Hs    );
0165 
0166 % %% check Jacobian and Hessian structure
0167 % xr                  = rand(size(x0));
0168 % lambda              = rand(2*nb+2*nl2, 1);
0169 % options.auxdata.Js  = jacobian(xr, options.auxdata);
0170 % options.auxdata.Hs  = tril(hessian(xr, 1, lambda, options.auxdata));
0171 % Js1 = options.auxdata.Js;
0172 % options.auxdata.Js = Js;
0173 % Hs1 = options.auxdata.Hs;
0174 % [i1, j1, s] = find(Js);
0175 % [i2, j2, s] = find(Js1);
0176 % if length(i1) ~= length(i2) || norm(i1-i2) ~= 0 || norm(j1-j2) ~= 0
0177 %     error('something''s wrong with the Jacobian structure');
0178 % end
0179 % [i1, j1, s] = find(Hs);
0180 % [i2, j2, s] = find(Hs1);
0181 % if length(i1) ~= length(i2) || norm(i1-i2) ~= 0 || norm(j1-j2) ~= 0
0182 %     error('something''s wrong with the Hessian structure');
0183 % end
0184 
0185 %% define variable and constraint bounds
0186 options.lb = xmin;
0187 options.ub = xmax;
0188 options.cl = [zeros(2*nb, 1); -Inf*ones(2*nl2, 1); l];
0189 options.cu = [zeros(2*nb, 1);     zeros(2*nl2, 1); u];
0190 
0191 %% assign function handles
0192 funcs.objective         = @objective;
0193 funcs.gradient          = @gradient;
0194 funcs.constraints       = @constraints;
0195 funcs.jacobian          = @jacobian;
0196 funcs.hessian           = @hessian;
0197 funcs.jacobianstructure = @(d) Js;
0198 funcs.hessianstructure  = @(d) Hs;
0199 %funcs.jacobianstructure = @jacobianstructure;
0200 %funcs.hessianstructure  = @hessianstructure;
0201 
0202 %% run the optimization
0203 [x, info] = ipopt(x0,funcs,options);
0204 
0205 if info.status == 0 || info.status == 1
0206     success = 1;
0207 else
0208     success = 0;
0209 end
0210 if isfield(info, 'iter')
0211     output.iterations = info.iter;
0212 else
0213     output.iterations = [];
0214 end
0215 f = opf_costfcn(x, om);
0216 
0217 %% update solution data
0218 Va = x(vv.i1.Va:vv.iN.Va);
0219 Vm = x(vv.i1.Vm:vv.iN.Vm);
0220 Pg = x(vv.i1.Pg:vv.iN.Pg);
0221 Qg = x(vv.i1.Qg:vv.iN.Qg);
0222 V = Vm .* exp(1j*Va);
0223 
0224 %%-----  calculate return values  -----
0225 %% update voltages & generator outputs
0226 bus(:, VA) = Va * 180/pi;
0227 bus(:, VM) = Vm;
0228 gen(:, PG) = Pg * baseMVA;
0229 gen(:, QG) = Qg * baseMVA;
0230 gen(:, VG) = Vm(gen(:, GEN_BUS));
0231 
0232 %% compute branch flows
0233 Sf = V(branch(:, F_BUS)) .* conj(Yf * V);  %% cplx pwr at "from" bus, p.u.
0234 St = V(branch(:, T_BUS)) .* conj(Yt * V);  %% cplx pwr at "to" bus, p.u.
0235 branch(:, PF) = real(Sf) * baseMVA;
0236 branch(:, QF) = imag(Sf) * baseMVA;
0237 branch(:, PT) = real(St) * baseMVA;
0238 branch(:, QT) = imag(St) * baseMVA;
0239 
0240 %% line constraint is actually on square of limit
0241 %% so we must fix multipliers
0242 muSf = zeros(nl, 1);
0243 muSt = zeros(nl, 1);
0244 if ~isempty(il)
0245     muSf(il) = 2 * info.lambda(2*nb+    (1:nl2)) .* branch(il, RATE_A) / baseMVA;
0246     muSt(il) = 2 * info.lambda(2*nb+nl2+(1:nl2)) .* branch(il, RATE_A) / baseMVA;
0247 end
0248 
0249 %% update Lagrange multipliers
0250 bus(:, MU_VMAX)  = info.zu(vv.i1.Vm:vv.iN.Vm);
0251 bus(:, MU_VMIN)  = info.zl(vv.i1.Vm:vv.iN.Vm);
0252 gen(:, MU_PMAX)  = info.zu(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0253 gen(:, MU_PMIN)  = info.zl(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0254 gen(:, MU_QMAX)  = info.zu(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0255 gen(:, MU_QMIN)  = info.zl(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0256 bus(:, LAM_P)    = info.lambda(nn.i1.Pmis:nn.iN.Pmis) / baseMVA;
0257 bus(:, LAM_Q)    = info.lambda(nn.i1.Qmis:nn.iN.Qmis) / baseMVA;
0258 branch(:, MU_SF) = muSf / baseMVA;
0259 branch(:, MU_ST) = muSt / baseMVA;
0260 
0261 %% package up results
0262 nlnN = getN(om, 'nln');
0263 
0264 %% extract multipliers for nonlinear constraints
0265 kl = find(info.lambda(1:2*nb) < 0);
0266 ku = find(info.lambda(1:2*nb) > 0);
0267 nl_mu_l = zeros(nlnN, 1);
0268 nl_mu_u = [zeros(2*nb, 1); muSf; muSt];
0269 nl_mu_l(kl) = -info.lambda(kl);
0270 nl_mu_u(ku) =  info.lambda(ku);
0271 
0272 %% extract multipliers for linear constraints
0273 lam_lin = info.lambda(2*nb+2*nl2+(1:nA));   %% lambda for linear constraints
0274 kl = find(lam_lin < 0);                     %% lower bound binding
0275 ku = find(lam_lin > 0);                     %% upper bound binding
0276 mu_l = zeros(nA, 1);
0277 mu_l(kl) = -lam_lin(kl);
0278 mu_u = zeros(nA, 1);
0279 mu_u(ku) = lam_lin(ku);
0280 
0281 mu = struct( ...
0282   'var', struct('l', info.zl, 'u', info.zu), ...
0283   'nln', struct('l', nl_mu_l, 'u', nl_mu_u), ...
0284   'lin', struct('l', mu_l, 'u', mu_u) );
0285 
0286 results = mpc;
0287 [results.bus, results.branch, results.gen, ...
0288     results.om, results.x, results.mu, results.f] = ...
0289         deal(bus, branch, gen, om, x, mu, f);
0290 
0291 pimul = [ ...
0292   results.mu.nln.l - results.mu.nln.u;
0293   results.mu.lin.l - results.mu.lin.u;
0294   -ones(ny>0, 1);
0295   results.mu.var.l - results.mu.var.u;
0296 ];
0297 raw = struct('xr', x, 'pimul', pimul, 'info', info.status, 'output', output);
0298 
0299 
0300 %-----  callback functions  -----
0301 function f = objective(x, d)
0302 f = opf_costfcn(x, d.om);
0303 
0304 function df = gradient(x, d)
0305 [f, df] = opf_costfcn(x, d.om);
0306 
0307 function c = constraints(x, d)
0308 [hn, gn] = opf_consfcn(x, d.om, d.Ybus, d.Yf, d.Yt, d.mpopt, d.il);
0309 if isempty(d.A)
0310     c = [gn; hn];
0311 else
0312     c = [gn; hn; d.A*x];
0313 end
0314 
0315 function J = jacobian(x, d)
0316 [hn, gn, dhn, dgn] = opf_consfcn(x, d.om, d.Ybus, d.Yf, d.Yt, d.mpopt, d.il);
0317 J = [dgn'; dhn'; d.A];
0318 
0319 function H = hessian(x, sigma, lambda, d)
0320 lam.eqnonlin   = lambda(1:d.neqnln);
0321 lam.ineqnonlin = lambda(d.neqnln+(1:d.niqnln));
0322 H = tril(opf_hessfcn(x, lam, sigma, d.om, d.Ybus, d.Yf, d.Yt, d.mpopt, d.il));
0323 
0324 % function Js = jacobianstructure(d)
0325 % Js = d.Js;
0326 %
0327 % function Hs = hessianstructure(d)
0328 % Hs = d.Hs;
ipoptopf_solver

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SUBFUNCTIONS

SOURCE CODE
