t_opf_ipopt

T_OPF_IPOPT  Tests for IPOPT-based AC optimal power flow.

0001 function t_opf_ipopt(quiet)
0002 %T_OPF_IPOPT  Tests for IPOPT-based AC optimal power flow.
0003 
0004 %   MATPOWER
0005 %   Copyright (c) 2004-2016, Power Systems Engineering Research Center (PSERC)
0006 %   by Ray Zimmerman, PSERC Cornell
0007 %
0008 %   This file is part of MATPOWER.
0009 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0010 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0011 
0012 if nargin < 1
0013     quiet = 0;
0014 end
0015 
0016 num_tests = 125;
0017 
0018 t_begin(num_tests, quiet);
0019 
0020 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0021     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0022 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0023     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0024     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0025 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0026     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0027     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0028 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0029 
0030 casefile = 't_case9_opf';
0031 if quiet
0032     verbose = 0;
0033 else
0034     verbose = 0;
0035 end
0036 if have_fcn('octave')
0037     if have_fcn('octave', 'vnum') >= 4
0038         file_in_path_warn_id = 'Octave:data-file-in-path';
0039     else
0040         file_in_path_warn_id = 'Octave:load-file-in-path';
0041     end
0042     s1 = warning('query', file_in_path_warn_id);
0043     warning('off', file_in_path_warn_id);
0044 end
0045 
0046 t0 = 'IPOPT : ';
0047 mpopt = mpoption('opf.violation', 1e-6);
0048 mpopt = mpoption(mpopt, 'out.all', 0, 'verbose', verbose, 'opf.ac.solver', 'IPOPT');
0049 
0050 if have_fcn('ipopt')
0051     %% set up indices
0052     ib_data     = [1:BUS_AREA BASE_KV:VMIN];
0053     ib_voltage  = [VM VA];
0054     ib_lam      = [LAM_P LAM_Q];
0055     ib_mu       = [MU_VMAX MU_VMIN];
0056     ig_data     = [GEN_BUS QMAX QMIN MBASE:APF];
0057     ig_disp     = [PG QG VG];
0058     ig_mu       = (MU_PMAX:MU_QMIN);
0059     ibr_data    = (1:ANGMAX);
0060     ibr_flow    = (PF:QT);
0061     ibr_mu      = [MU_SF MU_ST];
0062     ibr_angmu   = [MU_ANGMIN MU_ANGMAX];
0063 
0064     %% get solved AC OPF case from MAT-file
0065     load soln9_opf;     %% defines bus_soln, gen_soln, branch_soln, f_soln
0066 
0067     %% run OPF
0068     t = t0;
0069     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(casefile, mpopt);
0070     t_ok(success, [t 'success']);
0071     t_is(f, f_soln, 3, [t 'f']);
0072     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0073     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0074     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0075     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0076     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0077     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0078     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0079     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0080     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0081     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0082 
0083     %% run with automatic conversion of single-block pwl to linear costs
0084     t = [t0 '(single-block PWL) : '];
0085     mpc = loadcase(casefile);
0086     mpc.gencost(3, NCOST) = 2;
0087     [r, success] = runopf(mpc, mpopt);
0088     [f, bus, gen, branch] = deal(r.f, r.bus, r.gen, r.branch);
0089     t_ok(success, [t 'success']);
0090     t_is(f, f_soln, 3, [t 'f']);
0091     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0092     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0093     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0094     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0095     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0096     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0097     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0098     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0099     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0100     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0101     xr = [r.var.val.Va;r.var.val.Vm;r.var.val.Pg;r.var.val.Qg;0;r.var.val.y];
0102     t_is(r.x, xr, 8, [t 'check on raw x returned from OPF']);
0103 
0104     %% get solved AC OPF case from MAT-file
0105     load soln9_opf_Plim;       %% defines bus_soln, gen_soln, branch_soln, f_soln
0106 
0107     %% run OPF with active power line limits
0108     t = [t0 '(P line lim) : '];
0109     mpopt1 = mpoption(mpopt, 'opf.flow_lim', 'P');
0110     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(casefile, mpopt1);
0111     t_ok(success, [t 'success']);
0112     t_is(f, f_soln, 3, [t 'f']);
0113     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0114     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0115     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0116     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0117     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0118     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0119     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0120     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0121     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0122     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0123 
0124     %%-----  test OPF with quadratic gen costs moved to generalized costs  -----
0125     mpc = loadcase(casefile);
0126     mpc.gencost = [
0127         2   1500    0   3   0.11    5   0;
0128         2   2000    0   3   0.085   1.2 0;
0129         2   3000    0   3   0.1225  1   0;
0130     ];
0131     [baseMVA, bus_soln, gen_soln, gencost, branch_soln, f_soln, success, et] = runopf(mpc, mpopt);
0132     branch_soln = branch_soln(:,1:MU_ST);
0133 
0134     A = sparse(0,0);
0135     l = [];
0136     u = [];
0137     nb = size(mpc.bus, 1);      % number of buses
0138     ng = size(mpc.gen, 1);      % number of gens
0139     thbas = 1;                thend    = thbas+nb-1;
0140     vbas     = thend+1;       vend     = vbas+nb-1;
0141     pgbas    = vend+1;        pgend    = pgbas+ng-1;
0142     qgbas    = pgend+1;       qgend    = qgbas+ng-1;
0143     nxyz = 2*nb + 2*ng;
0144     N = sparse((1:ng)', (pgbas:pgend)', mpc.baseMVA * ones(ng,1), ng, nxyz);
0145     fparm = ones(ng,1) * [ 1 0 0 1 ];
0146     [junk, ix] = sort(mpc.gen(:, 1));
0147     H = 2 * spdiags(mpc.gencost(ix, 5), 0, ng, ng);
0148     Cw = mpc.gencost(ix, 6);
0149     mpc.gencost(:, 5:7) = 0;
0150 
0151     %% run OPF with quadratic gen costs moved to generalized costs
0152     t = [t0 'w/quadratic generalized gen cost : '];
0153     [r, success] = opf(mpc, A, l, u, mpopt, N, fparm, H, Cw);
0154     [f, bus, gen, branch] = deal(r.f, r.bus, r.gen, r.branch);
0155     t_ok(success, [t 'success']);
0156     t_is(f, f_soln, 3, [t 'f']);
0157     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0158     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0159     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0160     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0161     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0162     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0163     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0164     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0165     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0166     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0167     t_is(r.cost.usr, f, 12, [t 'user cost']);
0168 
0169     %%-----  run OPF with extra linear user constraints & costs  -----
0170     %% single new z variable constrained to be greater than or equal to
0171     %% deviation from 1 pu voltage at bus 1, linear cost on this z
0172     %% get solved AC OPF case from MAT-file
0173     load soln9_opf_extras1;   %% defines bus_soln, gen_soln, branch_soln, f_soln
0174     A = sparse([1;1;2;2],[10;25;10;25],[-1;1;1;1],2,25);
0175     u = [Inf; Inf];
0176     l = [-1; 1];
0177 
0178     N = sparse(1, 25, 1, 1, 25);    %% new z variable only
0179     fparm = [1 0 0 1];              %% w = r = z
0180     H = sparse(1,1);                %% no quadratic term
0181     Cw = 100;
0182 
0183     t = [t0 'w/extra constraints & costs 1 : '];
0184     [r, success] = opf(casefile, A, l, u, mpopt, N, fparm, H, Cw);
0185     [f, bus, gen, branch] = deal(r.f, r.bus, r.gen, r.branch);
0186     t_ok(success, [t 'success']);
0187     t_is(f, f_soln, 3, [t 'f']);
0188     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0189     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0190     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0191     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0192     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0193     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0194     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0195     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0196     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0197     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0198     t_is(r.var.val.z, 0.025419, 6, [t 'user variable']);
0199     t_is(r.cost.usr, 2.5419, 4, [t 'user cost']);
0200 
0201     %%-----  test OPF with capability curves  -----
0202     mpc = loadcase('t_case9_opfv2');
0203     %% remove angle diff limits
0204     mpc.branch(1, ANGMAX) = 360;
0205     mpc.branch(9, ANGMIN) = -360;
0206 
0207     %% get solved AC OPF case from MAT-file
0208     load soln9_opf_PQcap;   %% defines bus_soln, gen_soln, branch_soln, f_soln
0209     
0210     %% run OPF with capability curves
0211     t = [t0 'w/capability curves : '];
0212     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(mpc, mpopt);
0213     t_ok(success, [t 'success']);
0214     t_is(f, f_soln, 3, [t 'f']);
0215     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0216     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0217     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0218     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0219     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0220     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0221     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0222     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0223     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0224     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0225 
0226     %%-----  test OPF with angle difference limits  -----
0227     mpc = loadcase('t_case9_opfv2');
0228     %% remove capability curves
0229     mpc.gen(2:3, [PC1, PC2, QC1MIN, QC1MAX, QC2MIN, QC2MAX]) = zeros(2,6);
0230 
0231     %% get solved AC OPF case from MAT-file
0232     load soln9_opf_ang;   %% defines bus_soln, gen_soln, branch_soln, f_soln
0233     
0234     %% run OPF with angle difference limits
0235     t = [t0 'w/angle difference limits : '];
0236     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(mpc, mpopt);
0237     t_ok(success, [t 'success']);
0238     t_is(f, f_soln, 3, [t 'f']);
0239     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0240     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0241     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0242     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  1, [t 'bus mu']);
0243     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0244     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0245     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0246     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0247     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0248     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0249     t_is(branch(:,ibr_angmu ), branch_soln(:,ibr_angmu ),  2, [t 'branch angle mu']);
0250 
0251     %%-----  test OPF with ignored angle difference limits  -----
0252     %% get solved AC OPF case from MAT-file
0253     load soln9_opf;   %% defines bus_soln, gen_soln, branch_soln, f_soln
0254 
0255     %% run OPF with ignored angle difference limits
0256     t = [t0 'w/ignored angle difference limits : '];
0257     mpopt1 = mpoption(mpopt, 'opf.ignore_angle_lim', 1);
0258     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(mpc, mpopt1);
0259     %% ang limits are not in this solution data, so let's remove them
0260     branch(1, ANGMAX) = 360;
0261     branch(9, ANGMIN) = -360;
0262     t_ok(success, [t 'success']);
0263     t_is(f, f_soln, 3, [t 'f']);
0264     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0265     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0266     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0267     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0268     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0269     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0270     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0271     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0272     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0273     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0274 
0275     %%-----  test OPF with opf.use_vg  -----
0276     %% get solved AC OPF case from MAT-file
0277     load soln9_opf_vg;  %% defines bus_soln, gen_soln, branch_soln, f_soln
0278                         %%    and bus_soln1, gen_soln1, branch_soln1, f_soln1
0279     
0280     %% run with opf.use_vg = 1
0281     t = [t0 'w/opf.use_vg = 1 : '];
0282     mpc = loadcase(casefile);
0283     mpc.gen = mpc.gen([1 2 1 3], :);
0284     mpc.gencost = mpc.gencost([1 2 1 3], :);
0285     mpc.gen([1 3], [PMAX PMIN]) = mpc.gen([1 3], [PMAX PMIN]) / 2;
0286     mpc.gen(3, [QMIN, QMAX]) = 0;   %% no reactive capability for gen 3
0287     mpc.gencost([1 3], COST:end) = mpc.gencost([1 3], COST:end) / 2;
0288     mpc.gen(1, VG) = 1.05;
0289     mpc.gen(3, VG) = 1.06;
0290     mpopt1 = mpoption(mpopt, 'opf.use_vg', 1);
0291     r = runopf(mpc, mpopt1);
0292     t_ok(r.success, [t 'success']);
0293     t_is(r.f, f_soln, 3, [t 'f']);
0294     t_is(   r.bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0295     t_is(   r.bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0296     t_is(   r.bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0297     t_is(   r.bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0298     t_is(   r.gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0299     t_is(   r.gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0300     t_is(   r.gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0301     t_is(r.branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0302     t_is(r.branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0303     t_is(r.branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0304 
0305     %% run with opf.use_vg = 0.9
0306     t = [t0 'w/opf.use_vg = 0.9 : '];
0307     mpopt1 = mpoption(mpopt, 'opf.use_vg', 0.9);
0308     r = runopf(mpc, mpopt1);
0309     t_ok(r.success, [t 'success']);
0310     t_is(r.f, f_soln1, 3, [t 'f']);
0311     t_is(   r.bus(:,ib_data   ),    bus_soln1(:,ib_data   ), 10, [t 'bus data']);
0312     t_is(   r.bus(:,ib_voltage),    bus_soln1(:,ib_voltage),  3, [t 'bus voltage']);
0313     t_is(   r.bus(:,ib_lam    ),    bus_soln1(:,ib_lam    ),  3, [t 'bus lambda']);
0314     t_is(   r.bus(:,ib_mu     ),    bus_soln1(:,ib_mu     ),  2, [t 'bus mu']);
0315     t_is(   r.gen(:,ig_data   ),    gen_soln1(:,ig_data   ), 10, [t 'gen data']);
0316     t_is(   r.gen(:,ig_disp   ),    gen_soln1(:,ig_disp   ),  3, [t 'gen dispatch']);
0317     t_is(   r.gen(:,ig_mu     ),    gen_soln1(:,ig_mu     ),  3, [t 'gen mu']);
0318     t_is(r.branch(:,ibr_data  ), branch_soln1(:,ibr_data  ), 10, [t 'branch data']);
0319     t_is(r.branch(:,ibr_flow  ), branch_soln1(:,ibr_flow  ),  3, [t 'branch flow']);
0320     t_is(r.branch(:,ibr_mu    ), branch_soln1(:,ibr_mu    ),  2, [t 'branch mu']);
0321 else
0322     t_skip(num_tests, 'IPOPT not available');
0323 end
0324 
0325 if have_fcn('octave')
0326     warning(s1.state, file_in_path_warn_id);
0327 end
0328 
0329 t_end;