Description of ktropf

0001 function [results, success, raw] = ktropf_solver(om, mpopt)
0002 %KTROPF_SOLVER  Solves AC optimal power flow using KNITRO.
0003 %
0004 %   [RESULTS, SUCCESS, RAW] = KTROPF_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, KTRLINK.
0036 
0037 %   MATPOWER
0038 %   Copyright (c) 2000-2016, Power Systems Engineering Research Center (PSERC)
0039 %   by Ray Zimmerman, PSERC Cornell
0040 %   and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Nacional de Colombia
0041 %
0042 %   This file is part of MATPOWER.
0043 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0044 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0045 
0046 %%----- initialization -----
0047 %% define named indices into data matrices
0048 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0049     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0050 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0051     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0052     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0053 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0054     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0055     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0056 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0057 
0058 %% options
0059 use_ktropts_file = 1;       %% use a KNITRO options file to pass options
0060 create_ktropts_file = 0;    %% generate a KNITRO options file on the fly
0061 
0062 %% unpack data
0063 mpc = get_mpc(om);
0064 [baseMVA, bus, gen, branch, gencost] = ...
0065     deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch, mpc.gencost);
0066 [vv, ll, nn] = get_idx(om);
0067 
0068 %% problem dimensions
0069 nb = size(bus, 1);          %% number of buses
0070 ng = size(gen, 1);          %% number of gens
0071 nl = size(branch, 1);       %% number of branches
0072 ny = getN(om, 'var', 'y');  %% number of piece-wise linear costs
0073 
0074 %% bounds on optimization vars
0075 [x0, xmin, xmax] = getv(om);
0076 
0077 %% linear constraints
0078 [A, l, u] = linear_constraints(om);
0079 
0080 %% split l <= A*x <= u into less than, equal to, greater than, and
0081 %% doubly-bounded sets
0082 ieq = find( abs(u-l) <= eps );          %% equality
0083 igt = find( u >=  1e10 & l > -1e10 );   %% greater than, unbounded above
0084 ilt = find( l <= -1e10 & u <  1e10 );   %% less than, unbounded below
0085 ibx = find( (abs(u-l) > eps) & (u < 1e10) & (l > -1e10) );
0086 Af  = [ A(ilt, :); -A(igt, :); A(ibx, :); -A(ibx, :) ];
0087 bf  = [ u(ilt);   -l(igt);     u(ibx);    -l(ibx)];
0088 Afeq = A(ieq, :);
0089 bfeq = u(ieq);
0090 
0091 %% build admittance matrices
0092 [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch);
0093 
0094 %% try to select an interior initial point
0095 if mpopt.opf.init_from_mpc ~= 1
0096     ll = xmin; uu = xmax;
0097     ll(xmin == -Inf) = -1e10;   %% replace Inf with numerical proxies
0098     uu(xmax ==  Inf) =  1e10;
0099     x0 = (ll + uu) / 2;         %% set x0 mid-way between bounds
0100     k = find(xmin == -Inf & xmax < Inf);    %% if only bounded above
0101     x0(k) = xmax(k) - 1;                    %% set just below upper bound
0102     k = find(xmin > -Inf & xmax == Inf);    %% if only bounded below
0103     x0(k) = xmin(k) + 1;                    %% set just above lower bound
0104     Varefs = bus(bus(:, BUS_TYPE) == REF, VA) * (pi/180);
0105     x0(vv.i1.Va:vv.iN.Va) = Varefs(1);  %% angles set to first reference angle
0106     if ny > 0
0107         ipwl = find(gencost(:, MODEL) == PW_LINEAR);
0108     %     PQ = [gen(:, PMAX); gen(:, QMAX)];
0109     %     c = totcost(gencost(ipwl, :), PQ(ipwl));
0110         c = gencost(sub2ind(size(gencost), ipwl, NCOST+2*gencost(ipwl, NCOST)));    %% largest y-value in CCV data
0111         x0(vv.i1.y:vv.iN.y) = max(c) + 0.1 * abs(max(c));
0112     %     x0(vv.i1.y:vv.iN.y) = c + 0.1 * abs(c);
0113     end
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 %% build Jacobian and Hessian structure
0121 nA = size(A, 1);                %% number of original linear constraints
0122 nx = length(x0);
0123 f = branch(:, F_BUS);                           %% list of "from" buses
0124 t = branch(:, T_BUS);                           %% list of "to" buses
0125 Cf = sparse(1:nl, f, ones(nl, 1), nl, nb);      %% connection matrix for line & from buses
0126 Ct = sparse(1:nl, t, ones(nl, 1), nl, nb);      %% connection matrix for line & to buses
0127 Cl = Cf + Ct;
0128 Cb = Cl' * Cl + speye(nb);
0129 Cl2 = Cl(il, :);
0130 Cg = sparse(gen(:, GEN_BUS), (1:ng)', 1, nb, ng);
0131 nz = nx - 2*(nb+ng);
0132 nxtra = nx - 2*nb;
0133 Js = [
0134     Cl2     Cl2     sparse(nl2, 2*ng)               sparse(nl2,nz);
0135     Cl2     Cl2     sparse(nl2, 2*ng)               sparse(nl2,nz);
0136     Cb      Cb      Cg              sparse(nb,ng)   sparse(nb,nz);
0137     Cb      Cb      sparse(nb,ng)   Cg              sparse(nb,nz);
0138 ];
0139 [f, df, d2f] = opf_costfcn(x0, om);
0140 Hs = d2f + [
0141     Cb  Cb  sparse(nb,nxtra);
0142     Cb  Cb  sparse(nb,nxtra);
0143     sparse(nxtra,nx);
0144 ];
0145 
0146 %% basic optimset options needed for ktrlink
0147 hess_fcn = @(x, lambda)opf_hessfcn(x, lambda, 1, om, Ybus, Yf(il,:), Yt(il,:), mpopt, il);
0148 fmoptions = optimset('GradObj', 'on', 'GradConstr', 'on', ...
0149                 'Hessian', 'user-supplied', 'HessFcn', hess_fcn, ...
0150                 'JacobPattern', Js, 'HessPattern', Hs );
0151 if use_ktropts_file
0152     if ~isempty(mpopt.knitro.opt_fname)
0153         opt_fname = mpopt.knitro.opt_fname;
0154     elseif mpopt.knitro.opt
0155         opt_fname = sprintf('knitro_user_options_%d.txt', mpopt.knitro.opt);
0156     else
0157         %% create ktropts file
0158         ktropts.algorithm           = 1;
0159         ktropts.outlev              = mpopt.verbose;
0160         ktropts.feastol             = mpopt.opf.violation;
0161         ktropts.xtol                = mpopt.knitro.tol_x;
0162         ktropts.opttol              = mpopt.knitro.tol_f;
0163         if mpopt.fmincon.max_it ~= 0
0164             ktropts.maxit           = mpopt.fmincon.max_it;
0165         end
0166         ktropts.bar_directinterval  = 0;
0167         opt_fname = write_ktropts(ktropts);
0168         create_ktropts_file = 1;    %% make a note that I created it
0169     end
0170 else
0171     fmoptions = optimset(fmoptions, 'Algorithm', 'interior-point', ...
0172         'TolCon', mpopt.opf.violation, 'TolX', mpopt.knitro.tol_x, ...
0173         'TolFun', mpopt.knitro.tol_f );
0174     if mpopt.fmincon.max_it ~= 0
0175         fmoptions = optimset(fmoptions, 'MaxIter', mpopt.fmincon.max_it, ...
0176                     'MaxFunEvals', 4 * mpopt.fmincon.max_it);
0177     end
0178     if mpopt.verbose == 0,
0179       fmoptions.Display = 'off';
0180     elseif mpopt.verbose == 1
0181       fmoptions.Display = 'iter';
0182     else
0183       fmoptions.Display = 'testing';
0184     end
0185     opt_fname = [];
0186 end
0187 
0188 %%-----  run opf  -----
0189 f_fcn = @(x)opf_costfcn(x, om);
0190 gh_fcn = @(x)opf_consfcn(x, om, Ybus, Yf(il,:), Yt(il,:), mpopt, il);
0191 if have_fcn('knitromatlab')
0192     [x, f, info, Output, Lambda] = knitromatlab(f_fcn, x0, Af, bf, Afeq, bfeq, ...
0193                                     xmin, xmax, gh_fcn, [], fmoptions, opt_fname);
0194 else
0195     [x, f, info, Output, Lambda] = ktrlink(f_fcn, x0, Af, bf, Afeq, bfeq, ...
0196                                     xmin, xmax, gh_fcn, fmoptions, opt_fname);
0197 end
0198 success = (info == 0);
0199 
0200 %% delete ktropts file
0201 if create_ktropts_file  %% ... but only if I created it
0202     delete(opt_fname);
0203 end
0204 
0205 %% update solution data
0206 Va = x(vv.i1.Va:vv.iN.Va);
0207 Vm = x(vv.i1.Vm:vv.iN.Vm);
0208 Pg = x(vv.i1.Pg:vv.iN.Pg);
0209 Qg = x(vv.i1.Qg:vv.iN.Qg);
0210 V = Vm .* exp(1j*Va);
0211 
0212 %%-----  calculate return values  -----
0213 %% update voltages & generator outputs
0214 bus(:, VA) = Va * 180/pi;
0215 bus(:, VM) = Vm;
0216 gen(:, PG) = Pg * baseMVA;
0217 gen(:, QG) = Qg * baseMVA;
0218 gen(:, VG) = Vm(gen(:, GEN_BUS));
0219 
0220 %% compute branch flows
0221 Sf = V(branch(:, F_BUS)) .* conj(Yf * V);  %% cplx pwr at "from" bus, p.u.
0222 St = V(branch(:, T_BUS)) .* conj(Yt * V);  %% cplx pwr at "to" bus, p.u.
0223 branch(:, PF) = real(Sf) * baseMVA;
0224 branch(:, QF) = imag(Sf) * baseMVA;
0225 branch(:, PT) = real(St) * baseMVA;
0226 branch(:, QT) = imag(St) * baseMVA;
0227 
0228 %% line constraint is actually on square of limit
0229 %% so we must fix multipliers
0230 muSf = zeros(nl, 1);
0231 muSt = zeros(nl, 1);
0232 if ~isempty(il)
0233     muSf(il) = 2 * Lambda.ineqnonlin(1:nl2)       .* branch(il, RATE_A) / baseMVA;
0234     muSt(il) = 2 * Lambda.ineqnonlin((1:nl2)+nl2) .* branch(il, RATE_A) / baseMVA;
0235 end
0236 
0237 %% fix Lambdas
0238 %% (shadow prices on equality variable bounds can come back on wrong limit)
0239 kl = find(Lambda.lower > 0 & Lambda.upper == 0);
0240 Lambda.upper(kl) = Lambda.lower(kl);
0241 Lambda.lower(kl) = 0;
0242 ku = find(Lambda.upper < 0 & Lambda.lower == 0);
0243 Lambda.lower(ku) = Lambda.upper(ku);
0244 Lambda.upper(ku) = 0;
0245 
0246 %% update Lagrange multipliers
0247 bus(:, MU_VMAX)  = Lambda.upper(vv.i1.Vm:vv.iN.Vm);
0248 bus(:, MU_VMIN)  = -Lambda.lower(vv.i1.Vm:vv.iN.Vm);
0249 gen(:, MU_PMAX)  = Lambda.upper(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0250 gen(:, MU_PMIN)  = -Lambda.lower(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0251 gen(:, MU_QMAX)  = Lambda.upper(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0252 gen(:, MU_QMIN)  = -Lambda.lower(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0253 bus(:, LAM_P)    = Lambda.eqnonlin(nn.i1.Pmis:nn.iN.Pmis) / baseMVA;
0254 bus(:, LAM_Q)    = Lambda.eqnonlin(nn.i1.Qmis:nn.iN.Qmis) / baseMVA;
0255 branch(:, MU_SF) = muSf / baseMVA;
0256 branch(:, MU_ST) = muSt / baseMVA;
0257 
0258 %% package up results
0259 nlnN = getN(om, 'nln');
0260 nlt = length(ilt);
0261 ngt = length(igt);
0262 nbx = length(ibx);
0263 
0264 %% extract multipliers for nonlinear constraints
0265 kl = find(Lambda.eqnonlin < 0);
0266 ku = find(Lambda.eqnonlin > 0);
0267 nl_mu_l = zeros(nlnN, 1);
0268 nl_mu_u = [zeros(2*nb, 1); muSf; muSt];
0269 nl_mu_l(kl) = -Lambda.eqnonlin(kl);
0270 nl_mu_u(ku) =  Lambda.eqnonlin(ku);
0271 
0272 %% extract multipliers for linear constraints
0273 kl = find(Lambda.eqlin < 0);
0274 ku = find(Lambda.eqlin > 0);
0275 
0276 mu_l = zeros(size(u));
0277 mu_l(ieq(kl)) = -Lambda.eqlin(kl);
0278 mu_l(igt) = Lambda.ineqlin(nlt+(1:ngt));
0279 mu_l(ibx) = Lambda.ineqlin(nlt+ngt+nbx+(1:nbx));
0280 
0281 mu_u = zeros(size(u));
0282 mu_u(ieq(ku)) = Lambda.eqlin(ku);
0283 mu_u(ilt) = Lambda.ineqlin(1:nlt);
0284 mu_u(ibx) = Lambda.ineqlin(nlt+ngt+(1:nbx));
0285 
0286 mu = struct( ...
0287   'var', struct('l', -Lambda.lower, 'u', Lambda.upper), ...
0288   'nln', struct('l', nl_mu_l, 'u', nl_mu_u), ...
0289   'lin', struct('l', mu_l, 'u', mu_u) );
0290 
0291 results = mpc;
0292 [results.bus, results.branch, results.gen, ...
0293     results.om, results.x, results.mu, results.f] = ...
0294         deal(bus, branch, gen, om, x, mu, f);
0295 
0296 pimul = [ ...
0297   results.mu.nln.l - results.mu.nln.u;
0298   results.mu.lin.l - results.mu.lin.u;
0299   -ones(ny>0, 1);
0300   results.mu.var.l - results.mu.var.u;
0301 ];
0302 raw = struct('xr', x, 'pimul', pimul, 'info', info, 'output', Output);
0303 
0304 
0305 %%-----  write_ktropts  -----
0306 function fname = write_ktropts(ktropts)
0307 
0308 %% generate file name
0309 fname = sprintf('ktropts_%06d.txt', fix(1e6*rand));
0310 
0311 %% open file
0312 [fd, msg] = fopen(fname, 'wt');     %% write options file
0313 if fd == -1
0314     error('could not create %d : %s', fname, msg);
0315 end
0316 
0317 %% write options
0318 fields = fieldnames(ktropts);
0319 for k = 1:length(fields)
0320     fprintf(fd, '%s %g\n', fields{k}, ktropts.(fields{k}));
0321 end
0322 
0323 %% close file
0324 if fd ~= 1
0325     fclose(fd);
0326 end
ktropf_solver

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SUBFUNCTIONS

SOURCE CODE
