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 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, IPOPT.
0036 
0037 %   MATPOWER
0038 %   Copyright (c) 2000-2015 by Power System Engineering Research Center (PSERC)
0039 %   by Ray Zimmerman, PSERC Cornell
0040 %   and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de Manizales
0041 %
0042 %   $Id: ipoptopf_solver.m 2644 2015-03-11 19:34:22Z ray $
0043 %
0044 %   This file is part of MATPOWER.
0045 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0046 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0047 
0048 %%----- initialization -----
0049 %% define named indices into data matrices
0050 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0051     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0052 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0053     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0054     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0055 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0056     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0057     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0058 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0059 
0060 %% unpack data
0061 mpc = get_mpc(om);
0062 [baseMVA, bus, gen, branch, gencost] = ...
0063     deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch, mpc.gencost);
0064 [vv, ll, nn] = get_idx(om);
0065 
0066 %% problem dimensions
0067 nb = size(bus, 1);          %% number of buses
0068 ng = size(gen, 1);          %% number of gens
0069 nl = size(branch, 1);       %% number of branches
0070 ny = getN(om, 'var', 'y');  %% number of piece-wise linear costs
0071 
0072 %% linear constraints
0073 [A, l, u] = linear_constraints(om);
0074 
0075 %% bounds on optimization vars
0076 [x0, xmin, xmax] = getv(om);
0077 
0078 %% build admittance matrices
0079 [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch);
0080 
0081 %% try to select an interior initial point
0082 if mpopt.opf.init_from_mpc ~= 1
0083     ll = xmin; uu = xmax;
0084     ll(xmin == -Inf) = -1e10;   %% replace Inf with numerical proxies
0085     uu(xmax ==  Inf) =  1e10;
0086     x0 = (ll + uu) / 2;         %% set x0 mid-way between bounds
0087     k = find(xmin == -Inf & xmax < Inf);    %% if only bounded above
0088     x0(k) = xmax(k) - 1;                    %% set just below upper bound
0089     k = find(xmin > -Inf & xmax == Inf);    %% if only bounded below
0090     x0(k) = xmin(k) + 1;                    %% set just above lower bound
0091     Varefs = bus(bus(:, BUS_TYPE) == REF, VA) * (pi/180);
0092     x0(vv.i1.Va:vv.iN.Va) = Varefs(1);  %% angles set to first reference angle
0093     if ny > 0
0094         ipwl = find(gencost(:, MODEL) == PW_LINEAR);
0095     %     PQ = [gen(:, PMAX); gen(:, QMAX)];
0096     %     c = totcost(gencost(ipwl, :), PQ(ipwl));
0097         c = gencost(sub2ind(size(gencost), ipwl, NCOST+2*gencost(ipwl, NCOST)));    %% largest y-value in CCV data
0098         x0(vv.i1.y:vv.iN.y) = max(c) + 0.1 * abs(max(c));
0099     %     x0(vv.i1.y:vv.iN.y) = c + 0.1 * abs(c);
0100     end
0101 end
0102 
0103 %% find branches with flow limits
0104 il = find(branch(:, RATE_A) ~= 0 & branch(:, RATE_A) < 1e10);
0105 nl2 = length(il);           %% number of constrained lines
0106 
0107 %%-----  run opf  -----
0108 %% build Jacobian and Hessian structure
0109 nA = size(A, 1);                %% number of original linear constraints
0110 nx = length(x0);
0111 f = branch(:, F_BUS);                           %% list of "from" buses
0112 t = branch(:, T_BUS);                           %% list of "to" buses
0113 Cf = sparse(1:nl, f, ones(nl, 1), nl, nb);      %% connection matrix for line & from buses
0114 Ct = sparse(1:nl, t, ones(nl, 1), nl, nb);      %% connection matrix for line & to buses
0115 Cl = Cf + Ct;
0116 Cb = Cl' * Cl + speye(nb);
0117 Cl2 = Cl(il, :);
0118 Cg = sparse(gen(:, GEN_BUS), (1:ng)', 1, nb, ng);
0119 nz = nx - 2*(nb+ng);
0120 nxtra = nx - 2*nb;
0121 Js = [
0122     Cb      Cb      Cg              sparse(nb,ng)   sparse(nb,nz);
0123     Cb      Cb      sparse(nb,ng)   Cg              sparse(nb,nz);
0124     Cl2     Cl2     sparse(nl2, 2*ng)               sparse(nl2,nz);
0125     Cl2     Cl2     sparse(nl2, 2*ng)               sparse(nl2,nz);
0126     A;
0127 ];
0128 [f, df, d2f] = opf_costfcn(x0, om);
0129 Hs = tril(d2f + [
0130     Cb  Cb  sparse(nb,nxtra);
0131     Cb  Cb  sparse(nb,nxtra);
0132     sparse(nxtra,nx);
0133 ]);
0134 
0135 %% set options struct for IPOPT
0136 options.ipopt = ipopt_options([], mpopt);
0137 
0138 %% extra data to pass to functions
0139 options.auxdata = struct( ...
0140     'om',       om, ...
0141     'Ybus',     Ybus, ...
0142     'Yf',       Yf(il,:), ...
0143     'Yt',       Yt(il,:), ...
0144     'mpopt',    mpopt, ...
0145     'il',       il, ...
0146     'A',        A, ...
0147     'nA',       nA, ...
0148     'neqnln',   2*nb, ...
0149     'niqnln',   2*nl2, ...
0150     'Js',       Js, ...
0151     'Hs',       Hs    );
0152 
0153 % %% check Jacobian and Hessian structure
0154 % xr                  = rand(size(x0));
0155 % lambda              = rand(2*nb+2*nl2, 1);
0156 % options.auxdata.Js  = jacobian(xr, options.auxdata);
0157 % options.auxdata.Hs  = tril(hessian(xr, 1, lambda, options.auxdata));
0158 % Js1 = options.auxdata.Js;
0159 % options.auxdata.Js = Js;
0160 % Hs1 = options.auxdata.Hs;
0161 % [i1, j1, s] = find(Js);
0162 % [i2, j2, s] = find(Js1);
0163 % if length(i1) ~= length(i2) || norm(i1-i2) ~= 0 || norm(j1-j2) ~= 0
0164 %     error('something''s wrong with the Jacobian structure');
0165 % end
0166 % [i1, j1, s] = find(Hs);
0167 % [i2, j2, s] = find(Hs1);
0168 % if length(i1) ~= length(i2) || norm(i1-i2) ~= 0 || norm(j1-j2) ~= 0
0169 %     error('something''s wrong with the Hessian structure');
0170 % end
0171 
0172 %% define variable and constraint bounds
0173 options.lb = xmin;
0174 options.ub = xmax;
0175 options.cl = [zeros(2*nb, 1);  -Inf(2*nl2, 1); l];
0176 options.cu = [zeros(2*nb, 1); zeros(2*nl2, 1); u];
0177 
0178 %% assign function handles
0179 funcs.objective         = @objective;
0180 funcs.gradient          = @gradient;
0181 funcs.constraints       = @constraints;
0182 funcs.jacobian          = @jacobian;
0183 funcs.hessian           = @hessian;
0184 funcs.jacobianstructure = @(d) Js;
0185 funcs.hessianstructure  = @(d) Hs;
0186 %funcs.jacobianstructure = @jacobianstructure;
0187 %funcs.hessianstructure  = @hessianstructure;
0188 
0189 %% run the optimization
0190 if have_fcn('ipopt_auxdata')
0191     [x, info] = ipopt_auxdata(x0,funcs,options);
0192 else
0193     [x, info] = ipopt(x0,funcs,options);
0194 end
0195 
0196 if info.status == 0 || info.status == 1
0197     success = 1;
0198 else
0199     success = 0;
0200 end
0201 if isfield(info, 'iter')
0202     output.iterations = info.iter;
0203 else
0204     output.iterations = [];
0205 end
0206 f = opf_costfcn(x, om);
0207 
0208 %% update solution data
0209 Va = x(vv.i1.Va:vv.iN.Va);
0210 Vm = x(vv.i1.Vm:vv.iN.Vm);
0211 Pg = x(vv.i1.Pg:vv.iN.Pg);
0212 Qg = x(vv.i1.Qg:vv.iN.Qg);
0213 V = Vm .* exp(1j*Va);
0214 
0215 %%-----  calculate return values  -----
0216 %% update voltages & generator outputs
0217 bus(:, VA) = Va * 180/pi;
0218 bus(:, VM) = Vm;
0219 gen(:, PG) = Pg * baseMVA;
0220 gen(:, QG) = Qg * baseMVA;
0221 gen(:, VG) = Vm(gen(:, GEN_BUS));
0222 
0223 %% compute branch flows
0224 Sf = V(branch(:, F_BUS)) .* conj(Yf * V);  %% cplx pwr at "from" bus, p.u.
0225 St = V(branch(:, T_BUS)) .* conj(Yt * V);  %% cplx pwr at "to" bus, p.u.
0226 branch(:, PF) = real(Sf) * baseMVA;
0227 branch(:, QF) = imag(Sf) * baseMVA;
0228 branch(:, PT) = real(St) * baseMVA;
0229 branch(:, QT) = imag(St) * baseMVA;
0230 
0231 %% line constraint is actually on square of limit
0232 %% so we must fix multipliers
0233 muSf = zeros(nl, 1);
0234 muSt = zeros(nl, 1);
0235 if ~isempty(il)
0236     muSf(il) = 2 * info.lambda(2*nb+    (1:nl2)) .* branch(il, RATE_A) / baseMVA;
0237     muSt(il) = 2 * info.lambda(2*nb+nl2+(1:nl2)) .* branch(il, RATE_A) / baseMVA;
0238 end
0239 
0240 %% update Lagrange multipliers
0241 bus(:, MU_VMAX)  = info.zu(vv.i1.Vm:vv.iN.Vm);
0242 bus(:, MU_VMIN)  = info.zl(vv.i1.Vm:vv.iN.Vm);
0243 gen(:, MU_PMAX)  = info.zu(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0244 gen(:, MU_PMIN)  = info.zl(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0245 gen(:, MU_QMAX)  = info.zu(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0246 gen(:, MU_QMIN)  = info.zl(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0247 bus(:, LAM_P)    = info.lambda(nn.i1.Pmis:nn.iN.Pmis) / baseMVA;
0248 bus(:, LAM_Q)    = info.lambda(nn.i1.Qmis:nn.iN.Qmis) / baseMVA;
0249 branch(:, MU_SF) = muSf / baseMVA;
0250 branch(:, MU_ST) = muSt / baseMVA;
0251 
0252 %% package up results
0253 nlnN = getN(om, 'nln');
0254 
0255 %% extract multipliers for nonlinear constraints
0256 kl = find(info.lambda(1:2*nb) < 0);
0257 ku = find(info.lambda(1:2*nb) > 0);
0258 nl_mu_l = zeros(nlnN, 1);
0259 nl_mu_u = [zeros(2*nb, 1); muSf; muSt];
0260 nl_mu_l(kl) = -info.lambda(kl);
0261 nl_mu_u(ku) =  info.lambda(ku);
0262 
0263 %% extract multipliers for linear constraints
0264 lam_lin = info.lambda(2*nb+2*nl2+(1:nA));   %% lambda for linear constraints
0265 kl = find(lam_lin < 0);                     %% lower bound binding
0266 ku = find(lam_lin > 0);                     %% upper bound binding
0267 mu_l = zeros(nA, 1);
0268 mu_l(kl) = -lam_lin(kl);
0269 mu_u = zeros(nA, 1);
0270 mu_u(ku) = lam_lin(ku);
0271 
0272 mu = struct( ...
0273   'var', struct('l', info.zl, 'u', info.zu), ...
0274   'nln', struct('l', nl_mu_l, 'u', nl_mu_u), ...
0275   'lin', struct('l', mu_l, 'u', mu_u) );
0276 
0277 results = mpc;
0278 [results.bus, results.branch, results.gen, ...
0279     results.om, results.x, results.mu, results.f] = ...
0280         deal(bus, branch, gen, om, x, mu, f);
0281 
0282 pimul = [ ...
0283   results.mu.nln.l - results.mu.nln.u;
0284   results.mu.lin.l - results.mu.lin.u;
0285   -ones(ny>0, 1);
0286   results.mu.var.l - results.mu.var.u;
0287 ];
0288 raw = struct('xr', x, 'pimul', pimul, 'info', info.status, 'output', output);
0289 
0290 
0291 %-----  callback functions  -----
0292 function f = objective(x, d)
0293 f = opf_costfcn(x, d.om);
0294 
0295 function df = gradient(x, d)
0296 [f, df] = opf_costfcn(x, d.om);
0297 
0298 function c = constraints(x, d)
0299 [hn, gn] = opf_consfcn(x, d.om, d.Ybus, d.Yf, d.Yt, d.mpopt, d.il);
0300 if isempty(d.A)
0301     c = [gn; hn];
0302 else
0303     c = [gn; hn; d.A*x];
0304 end
0305 
0306 function J = jacobian(x, d)
0307 [hn, gn, dhn, dgn] = opf_consfcn(x, d.om, d.Ybus, d.Yf, d.Yt, d.mpopt, d.il);
0308 J = [dgn'; dhn'; d.A];
0309 
0310 function H = hessian(x, sigma, lambda, d)
0311 lam.eqnonlin   = lambda(1:d.neqnln);
0312 lam.ineqnonlin = lambda(d.neqnln+(1:d.niqnln));
0313 H = tril(opf_hessfcn(x, lam, sigma, d.om, d.Ybus, d.Yf, d.Yt, d.mpopt, d.il));
0314 
0315 % function Js = jacobianstructure(d)
0316 % Js = d.Js;
0317 %
0318 % function Hs = hessianstructure(d)
0319 % Hs = d.Hs;
ipoptopf_solver

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SUBFUNCTIONS

SOURCE CODE
