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, MIPS.
0036 
0037 %   MATPOWER
0038 %   $Id: ipoptopf_solver.m,v 1.4 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 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0078 
0079 %% options
0080 verbose = mpopt(31);    %% VERBOSE
0081 feastol = mpopt(81);    %% PDIPM_FEASTOL
0082 gradtol = mpopt(82);    %% PDIPM_GRADTOL
0083 comptol = mpopt(83);    %% PDIPM_COMPTOL
0084 costtol = mpopt(84);    %% PDIPM_COSTTOL
0085 max_it  = mpopt(85);    %% PDIPM_MAX_IT
0086 max_red = mpopt(86);    %% SCPDIPM_RED_IT
0087 step_control = (mpopt(11) == 565);  %% OPF_ALG == 565, MIPS-sc
0088 if feastol == 0
0089     feastol = mpopt(16);    %% = OPF_VIOLATION by default
0090 end
0091 opt = struct(   'feastol', feastol, ...
0092                 'gradtol', gradtol, ...
0093                 'comptol', comptol, ...
0094                 'costtol', costtol, ...
0095                 'max_it', max_it, ...
0096                 'max_red', max_red, ...
0097                 'step_control', step_control, ...
0098                 'cost_mult', 1e-4, ...
0099                 'verbose', verbose  );
0100 
0101 %% unpack data
0102 mpc = get_mpc(om);
0103 [baseMVA, bus, gen, branch, gencost] = ...
0104     deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch, mpc.gencost);
0105 [vv, ll, nn] = get_idx(om);
0106 
0107 %% problem dimensions
0108 nb = size(bus, 1);          %% number of buses
0109 ng = size(gen, 1);          %% number of buses
0110 nl = size(branch, 1);       %% number of branches
0111 ny = getN(om, 'var', 'y');  %% number of piece-wise linear costs
0112 
0113 %% linear constraints
0114 [A, l, u] = linear_constraints(om);
0115 
0116 %% bounds on optimization vars
0117 [x0, xmin, xmax] = getv(om);
0118 
0119 %% build admittance matrices
0120 [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch);
0121 
0122 %% try to select an interior initial point
0123 ll = xmin; uu = xmax;
0124 ll(xmin == -Inf) = -1e10;   %% replace Inf with numerical proxies
0125 uu(xmax ==  Inf) =  1e10;
0126 x0 = (ll + uu) / 2;
0127 Varefs = bus(bus(:, BUS_TYPE) == REF, VA) * (pi/180);
0128 x0(vv.i1.Va:vv.iN.Va) = Varefs(1);  %% angles set to first reference angle
0129 if ny > 0
0130     ipwl = find(gencost(:, MODEL) == PW_LINEAR);
0131 %     PQ = [gen(:, PMAX); gen(:, QMAX)];
0132 %     c = totcost(gencost(ipwl, :), PQ(ipwl));
0133     c = gencost(sub2ind(size(gencost), ipwl, NCOST+2*gencost(ipwl, NCOST)));    %% largest y-value in CCV data
0134     x0(vv.i1.y:vv.iN.y) = max(c) + 0.1 * abs(max(c));
0135 %     x0(vv.i1.y:vv.iN.y) = c + 0.1 * abs(c);
0136 end
0137 
0138 %% find branches with flow limits
0139 il = find(branch(:, RATE_A) ~= 0 & branch(:, RATE_A) < 1e10);
0140 nl2 = length(il);           %% number of constrained lines
0141 
0142 %%-----  run opf  -----
0143 %% build Jacobian and Hessian structure
0144 nA = size(A, 1);                %% number of original linear constraints
0145 nx = length(x0);
0146 f = branch(:, F_BUS);                           %% list of "from" buses
0147 t = branch(:, T_BUS);                           %% list of "to" buses
0148 Cf = sparse(1:nl, f, ones(nl, 1), nl, nb);      %% connection matrix for line & from buses
0149 Ct = sparse(1:nl, t, ones(nl, 1), nl, nb);      %% connection matrix for line & to buses
0150 Cl = Cf + Ct;
0151 Cb = Cl' * Cl + speye(nb);
0152 Cl2 = Cl(il, :);
0153 Cg = sparse(gen(:, GEN_BUS), (1:ng)', 1, nb, ng);
0154 nz = nx - 2*(nb+ng);
0155 nxtra = nx - 2*nb;
0156 Js = [
0157     Cb      Cb      Cg              sparse(nb,ng)   sparse(nb,nz);
0158     Cb      Cb      sparse(nb,ng)   Cg              sparse(nb,nz);
0159     Cl2     Cl2     sparse(nl2, 2*ng)               sparse(nl2,nz);
0160     Cl2     Cl2     sparse(nl2, 2*ng)               sparse(nl2,nz);
0161     A;
0162 ];
0163 [f, df, d2f] = opf_costfcn(x0, om);
0164 Hs = tril(d2f + [
0165     Cb  Cb  sparse(nb,nxtra);
0166     Cb  Cb  sparse(nb,nxtra);
0167     sparse(nxtra,nx);
0168 ]);
0169 
0170 %% set options struct for IPOPT
0171 options.ipopt = ipopt_options([], mpopt);
0172 
0173 %% extra data to pass to functions
0174 options.auxdata = struct( ...
0175     'om',       om, ...
0176     'Ybus',     Ybus, ...
0177     'Yf',       Yf(il,:), ...
0178     'Yt',       Yt(il,:), ...
0179     'mpopt',    mpopt, ...
0180     'il',       il, ...
0181     'A',        A, ...
0182     'nA',       nA, ...
0183     'neqnln',   2*nb, ...
0184     'niqnln',   2*nl2, ...
0185     'Js',       Js, ...
0186     'Hs',       Hs    );
0187 
0188 % %% check Jacobian and Hessian structure
0189 % xr                  = rand(size(x0));
0190 % lambda              = rand(2*nb+2*nl2, 1);
0191 % options.auxdata.Js  = jacobian(xr, options.auxdata);
0192 % options.auxdata.Hs  = tril(hessian(xr, 1, lambda, options.auxdata));
0193 % Js1 = options.auxdata.Js;
0194 % options.auxdata.Js = Js;
0195 % Hs1 = options.auxdata.Hs;
0196 % [i1, j1, s] = find(Js);
0197 % [i2, j2, s] = find(Js1);
0198 % if length(i1) ~= length(i2) || norm(i1-i2) ~= 0 || norm(j1-j2) ~= 0
0199 %     error('something''s wrong with the Jacobian structure');
0200 % end
0201 % [i1, j1, s] = find(Hs);
0202 % [i2, j2, s] = find(Hs1);
0203 % if length(i1) ~= length(i2) || norm(i1-i2) ~= 0 || norm(j1-j2) ~= 0
0204 %     error('something''s wrong with the Hessian structure');
0205 % end
0206 
0207 %% define variable and constraint bounds
0208 options.lb = xmin;
0209 options.ub = xmax;
0210 options.cl = [zeros(2*nb, 1); -Inf*ones(2*nl2, 1); l];
0211 options.cu = [zeros(2*nb, 1);     zeros(2*nl2, 1); u];
0212 
0213 %% assign function handles
0214 funcs.objective         = @objective;
0215 funcs.gradient          = @gradient;
0216 funcs.constraints       = @constraints;
0217 funcs.jacobian          = @jacobian;
0218 funcs.hessian           = @hessian;
0219 funcs.jacobianstructure = @(d) Js;
0220 funcs.hessianstructure  = @(d) Hs;
0221 %funcs.jacobianstructure = @jacobianstructure;
0222 %funcs.hessianstructure  = @hessianstructure;
0223 
0224 %% run the optimization
0225 [x, info] = ipopt(x0,funcs,options);
0226 
0227 if info.status == 0 || info.status == 1
0228     success = 1;
0229 else
0230     success = 0;
0231 end
0232 if isfield(info, 'iter')
0233     output.iterations = info.iter;
0234 else
0235     output.iterations = [];
0236 end
0237 f = opf_costfcn(x, om);
0238 
0239 %% update solution data
0240 Va = x(vv.i1.Va:vv.iN.Va);
0241 Vm = x(vv.i1.Vm:vv.iN.Vm);
0242 Pg = x(vv.i1.Pg:vv.iN.Pg);
0243 Qg = x(vv.i1.Qg:vv.iN.Qg);
0244 V = Vm .* exp(1j*Va);
0245 
0246 %%-----  calculate return values  -----
0247 %% update voltages & generator outputs
0248 bus(:, VA) = Va * 180/pi;
0249 bus(:, VM) = Vm;
0250 gen(:, PG) = Pg * baseMVA;
0251 gen(:, QG) = Qg * baseMVA;
0252 gen(:, VG) = Vm(gen(:, GEN_BUS));
0253 
0254 %% compute branch flows
0255 Sf = V(branch(:, F_BUS)) .* conj(Yf * V);  %% cplx pwr at "from" bus, p.u.
0256 St = V(branch(:, T_BUS)) .* conj(Yt * V);  %% cplx pwr at "to" bus, p.u.
0257 branch(:, PF) = real(Sf) * baseMVA;
0258 branch(:, QF) = imag(Sf) * baseMVA;
0259 branch(:, PT) = real(St) * baseMVA;
0260 branch(:, QT) = imag(St) * baseMVA;
0261 
0262 %% line constraint is actually on square of limit
0263 %% so we must fix multipliers
0264 muSf = zeros(nl, 1);
0265 muSt = zeros(nl, 1);
0266 if ~isempty(il)
0267     muSf(il) = 2 * info.lambda(2*nb+    (1:nl2)) .* branch(il, RATE_A) / baseMVA;
0268     muSt(il) = 2 * info.lambda(2*nb+nl2+(1:nl2)) .* branch(il, RATE_A) / baseMVA;
0269 end
0270 
0271 %% update Lagrange multipliers
0272 bus(:, MU_VMAX)  = info.zu(vv.i1.Vm:vv.iN.Vm);
0273 bus(:, MU_VMIN)  = info.zl(vv.i1.Vm:vv.iN.Vm);
0274 gen(:, MU_PMAX)  = info.zu(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0275 gen(:, MU_PMIN)  = info.zl(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0276 gen(:, MU_QMAX)  = info.zu(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0277 gen(:, MU_QMIN)  = info.zl(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0278 bus(:, LAM_P)    = info.lambda(nn.i1.Pmis:nn.iN.Pmis) / baseMVA;
0279 bus(:, LAM_Q)    = info.lambda(nn.i1.Qmis:nn.iN.Qmis) / baseMVA;
0280 branch(:, MU_SF) = muSf / baseMVA;
0281 branch(:, MU_ST) = muSt / baseMVA;
0282 
0283 %% package up results
0284 nlnN = getN(om, 'nln');
0285 
0286 %% extract multipliers for nonlinear constraints
0287 kl = find(info.lambda(1:2*nb) < 0);
0288 ku = find(info.lambda(1:2*nb) > 0);
0289 nl_mu_l = zeros(nlnN, 1);
0290 nl_mu_u = [zeros(2*nb, 1); muSf; muSt];
0291 nl_mu_l(kl) = -info.lambda(kl);
0292 nl_mu_u(ku) =  info.lambda(ku);
0293 
0294 %% extract multipliers for linear constraints
0295 lam_lin = info.lambda(2*nb+2*nl2+(1:nA));   %% lambda for linear constraints
0296 kl = find(lam_lin < 0);                     %% lower bound binding
0297 ku = find(lam_lin > 0);                     %% upper bound binding
0298 mu_l = zeros(nA, 1);
0299 mu_l(kl) = -lam_lin(kl);
0300 mu_u = zeros(nA, 1);
0301 mu_u(ku) = lam_lin(ku);
0302 
0303 mu = struct( ...
0304   'var', struct('l', info.zl, 'u', info.zu), ...
0305   'nln', struct('l', nl_mu_l, 'u', nl_mu_u), ...
0306   'lin', struct('l', mu_l, 'u', mu_u) );
0307 
0308 results = mpc;
0309 [results.bus, results.branch, results.gen, ...
0310     results.om, results.x, results.mu, results.f] = ...
0311         deal(bus, branch, gen, om, x, mu, f);
0312 
0313 pimul = [ ...
0314   results.mu.nln.l - results.mu.nln.u;
0315   results.mu.lin.l - results.mu.lin.u;
0316   -ones(ny>0, 1);
0317   results.mu.var.l - results.mu.var.u;
0318 ];
0319 raw = struct('xr', x, 'pimul', pimul, 'info', info.status, 'output', output);
0320 
0321 
0322 %-----  callback functions  -----
0323 function f = objective(x, d)
0324 f = opf_costfcn(x, d.om);
0325 
0326 function df = gradient(x, d)
0327 [f, df] = opf_costfcn(x, d.om);
0328 
0329 function c = constraints(x, d)
0330 [hn, gn] = opf_consfcn(x, d.om, d.Ybus, d.Yf, d.Yt, d.mpopt, d.il);
0331 if isempty(d.A)
0332     c = [gn; hn];
0333 else
0334     c = [gn; hn; d.A*x];
0335 end
0336 
0337 function J = jacobian(x, d)
0338 [hn, gn, dhn, dgn] = opf_consfcn(x, d.om, d.Ybus, d.Yf, d.Yt, d.mpopt, d.il);
0339 J = [dgn'; dhn'; d.A];
0340 
0341 function H = hessian(x, sigma, lambda, d)
0342 lam.eqnonlin   = lambda(1:d.neqnln);
0343 lam.ineqnonlin = lambda(d.neqnln+(1:d.niqnln));
0344 H = tril(opf_hessfcn(x, lam, sigma, d.om, d.Ybus, d.Yf, d.Yt, d.mpopt, d.il));
0345 
0346 % function Js = jacobianstructure(d)
0347 % Js = d.Js;
0348 %
0349 % function Hs = hessianstructure(d)
0350 % Hs = d.Hs;
ipoptopf_solver

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SUBFUNCTIONS

SOURCE CODE
