t_opf_fmincon

T_OPF_FMINCON  Tests for FMINCON-based optimal power flow.

0001 function t_opf_fmincon(quiet)
0002 %T_OPF_FMINCON  Tests for FMINCON-based optimal power flow.
0003 
0004 %   MATPOWER
0005 %   Copyright (c) 2004-2017, 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 https://matpower.org for more info.
0011 
0012 if nargin < 1
0013     quiet = 0;
0014 end
0015 
0016 %% current mismatch, cartesian V
0017 options = {
0018     {0, 0},
0019     {0, 1},
0020     {1, 0},
0021     {1, 1},
0022 };
0023 
0024 num_tests = 216;
0025 
0026 t_begin(length(options)*num_tests, quiet);
0027 
0028 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0029     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0030 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0031     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0032     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0033 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0034     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0035     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0036 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0037 
0038 casefile = 't_case9_opf';
0039 if quiet
0040     verbose = 0;
0041 else
0042     verbose = 0;
0043 end
0044 
0045 mpopt = mpoption('opf.violation', 1e-6);
0046 mpopt = mpoption(mpopt, 'out.all', 0, 'verbose', verbose, 'opf.ac.solver', 'FMINCON');
0047 mpopt = mpoption(mpopt, 'fmincon.tol_x', 1e-7, 'fmincon.tol_f', 1e-9);
0048 
0049 %% use active-set method for MATLAB 7.6-7.9 (R2008a-R2009b)
0050 vstr = have_fcn('matlab', 'vstr');
0051 if strcmp(vstr, '7.6') || strcmp(vstr, '7.7') || ...
0052         strcmp(vstr, '7.8') || strcmp(vstr, '7.9')
0053     mpopt = mpoption(mpopt, 'fmincon.alg', 1);
0054 end
0055 
0056 for k = 1:length(options)
0057     if options{k}{1}, bal = 'I';  else, bal = 'S'; end  %% nodal balance
0058     if options{k}{2}, crd = 'c';  else, crd = 'p'; end  %% V coordinates
0059     t0 = sprintf('fmincon OPF (%s,%s) : ', bal, crd);
0060 
0061     if ~have_fcn('fmincon')
0062         t_skip(num_tests, 'fmincon not available');
0063         continue;
0064     end
0065 
0066     mpopt = mpoption(mpopt, 'opf.current_balance',  options{k}{1}, ...
0067                             'opf.v_cartesian',      options{k}{2} );
0068 
0069     %% set up indices
0070     ib_data     = [1:BUS_AREA BASE_KV:VMIN];
0071     ib_voltage  = [VM VA];
0072     ib_lam      = [LAM_P LAM_Q];
0073     ib_mu       = [MU_VMAX MU_VMIN];
0074     ig_data     = [GEN_BUS QMAX QMIN MBASE:APF];
0075     ig_disp     = [PG QG VG];
0076     ig_mu       = (MU_PMAX:MU_QMIN);
0077     ibr_data    = (1:ANGMAX);
0078     ibr_flow    = (PF:QT);
0079     ibr_mu      = [MU_SF MU_ST];
0080     ibr_angmu   = [MU_ANGMIN MU_ANGMAX];
0081 
0082     %% get solved AC OPF case from MAT-file
0083     load soln9_opf;     %% defines bus_soln, gen_soln, branch_soln, f_soln
0084 
0085     %% run OPF
0086     for s = 0:3
0087         mpopt = mpoption(mpopt, 'opf.start', s);
0088         t = sprintf('%s(start=%d): ', t0, s);
0089         [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(casefile, mpopt);
0090         t_ok(success, [t 'success']);
0091         t_is(f, f_soln, 3, [t 'f']);
0092         t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0093         t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0094         t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0095         t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0096         t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0097         t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0098         t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0099         t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0100         t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0101         t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0102     end
0103     mpopt = mpoption(mpopt, 'opf.start', 0);    %% set 'opf.start' back to default
0104 
0105     %% run with automatic conversion of single-block pwl to linear costs
0106     t = [t0 '(single-block PWL) : '];
0107     mpc = loadcase(casefile);
0108     mpc.gencost(2, NCOST) = 2;
0109     [r, success] = runopf(mpc, mpopt);
0110     [f, bus, gen, branch] = deal(r.f, r.bus, r.gen, r.branch);
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     if mpopt.opf.v_cartesian
0124         xr = [r.var.val.Vr;r.var.val.Vi;r.var.val.Pg;r.var.val.Qg;0;r.var.val.y];
0125     else
0126         xr = [r.var.val.Va;r.var.val.Vm;r.var.val.Pg;r.var.val.Qg;0;r.var.val.y];
0127     end
0128     t_is(r.x, xr, 8, [t 'raw x returned from OPF']);
0129 
0130     %% get solved AC OPF case from MAT-file
0131     load soln9_opf_Plim;       %% defines bus_soln, gen_soln, branch_soln, f_soln
0132 
0133     %% run OPF with active power line limits
0134     t = [t0 '(P line lim) : '];
0135     mpopt1 = mpoption(mpopt, 'opf.flow_lim', 'P');
0136     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(casefile, mpopt1);
0137     t_ok(success, [t 'success']);
0138     t_is(f, f_soln, 3, [t 'f']);
0139     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0140     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0141     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0142     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0143     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0144     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0145     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0146     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0147     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0148     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0149 
0150     t = [t0 '(P^2 line lim) : '];
0151     mpopt1 = mpoption(mpopt, 'opf.flow_lim', '2');
0152     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(casefile, mpopt1);
0153     t_ok(success, [t 'success']);
0154     t_is(f, f_soln, 3, [t 'f']);
0155     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0156     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0157     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0158     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0159     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0160     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0161     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0162     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0163     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0164     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0165 
0166     %%-----  test OPF with quadratic gen costs moved to generalized costs  -----
0167     mpc = loadcase(casefile);
0168     mpc.gencost = [
0169         2   1500    0   3   0.11    5   0;
0170         2   2000    0   3   0.085   1.2 0;
0171         2   3000    0   3   0.1225  1   0;
0172     ];
0173     [baseMVA, bus_soln, gen_soln, gencost, branch_soln, f_soln, success, et] = runopf(mpc, mpopt);
0174     branch_soln = branch_soln(:,1:MU_ST);
0175 
0176     A = sparse(0,0);
0177     l = [];
0178     u = [];
0179     nb = size(mpc.bus, 1);      % number of buses
0180     ng = size(mpc.gen, 1);      % number of gens
0181     thbas = 1;                thend    = thbas+nb-1;
0182     vbas     = thend+1;       vend     = vbas+nb-1;
0183     pgbas    = vend+1;        pgend    = pgbas+ng-1;
0184     qgbas    = pgend+1;       qgend    = qgbas+ng-1;
0185     nxyz = 2*nb + 2*ng;
0186     N = sparse((1:ng)', (pgbas:pgend)', mpc.baseMVA * ones(ng,1), ng, nxyz);
0187     fparm = [ 1    0   0 1;
0188               1 -100 100 1;
0189               1  -10  10 1 ];
0190     H = 2 * spdiags(mpc.gencost(:, 5), 0, ng, ng);
0191     Cw = mpc.gencost(:, 6);
0192     mpc.gencost(:, 5:7) = 0;
0193 
0194     %% run OPF with quadratic gen costs moved to generalized costs
0195     t = [t0 'w/quadratic generalized gen cost : '];
0196     [r, success] = opf(mpc, A, l, u, mpopt, N, fparm, H, Cw);
0197     [f, bus, gen, branch] = deal(r.f, r.bus, r.gen, r.branch);
0198     t_ok(success, [t 'success']);
0199     t_is(f, f_soln, 3, [t 'f']);
0200     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0201     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0202     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0203     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0204     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0205     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0206     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0207     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0208     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0209     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0210     t_is(r.cost.usr, f, 12, [t 'user cost']);
0211 
0212     %%-----  run OPF with legacy costs and deadzone  -----
0213     if mpopt.opf.v_cartesian
0214         t_skip(17, 'legacy cost example n/a to cartesian V case')
0215     else
0216         load soln9_opf;
0217         mpc = loadcase(casefile);
0218         mpc.N = sparse((1:nb)', (vbas:vend)', ones(nb,1), nb, nxyz);
0219         mpc.fparm = ones(nb,1) * [ 2 1.08 0.02 1e8 ];
0220         mpc.Cw = ones(nb, 1);
0221         t = [t0 'w/legacy cost, in deadzone : '];
0222         r = runopf(mpc, mpopt);
0223         [f, bus, gen, branch] = deal(r.f, r.bus, r.gen, r.branch);
0224         t_ok(r.success, [t 'success']);
0225         t_is(f, f_soln, 3, [t 'f']);
0226         t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0227         t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0228         t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0229         t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0230         t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0231         t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0232         t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0233         t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0234         t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0235         t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0236         t_is(r.cost.usr, 0, 12, [t 'user cost']);
0237 
0238         t = [t0 'w/legacy cost, not in deadzone : '];
0239         mpc.fparm = ones(nb,1) * [ 2 1.08 0.01 1e8 ];
0240         r = runopf(mpc, mpopt);
0241         [f, bus, gen, branch] = deal(r.f, r.bus, r.gen, r.branch);
0242         t_ok(r.success, [t 'success']);
0243         t_is(f, 9009.0890, 3, [t 'f']);
0244         t_is([min(bus(:, VM)) mean(bus(:, VM)) max(bus(:, VM))], ...
0245             [1.066624, 1.083980, 1.091698], 5, [t 'bus voltage']);
0246         t_is(r.cost.usr, 1673.065465, 4, [t 'user cost']);
0247     end
0248 
0249     %%-----  run OPF with extra linear user constraints & costs  -----
0250     %% single new z variable constrained to be greater than or equal to
0251     %% deviation from 1 pu voltage at bus 1, linear cost on this z
0252     %% get solved AC OPF case from MAT-file
0253     if mpopt.opf.v_cartesian
0254         t_skip(14, 'lin constraint/cost example n/a to cartesian V case')
0255     else
0256         load soln9_opf_extras1;   %% defines bus_soln, gen_soln, branch_soln, f_soln
0257         A = sparse([1;1;2;2],[10;25;10;25],[-1;1;1;1],2,25);
0258         u = [Inf; Inf];
0259         l = [-1; 1];
0260 
0261         N = sparse(1, 25, 1, 1, 25);    %% new z variable only
0262         fparm = [1 0 0 1];              %% w = r = z
0263         H = sparse(1,1);                %% no quadratic term
0264         Cw = 100;
0265 
0266         t = [t0 'w/extra constraints & costs 1 : '];
0267         [r, success] = opf(casefile, A, l, u, mpopt, N, fparm, H, Cw);
0268         [f, bus, gen, branch] = deal(r.f, r.bus, r.gen, r.branch);
0269         t_ok(success, [t 'success']);
0270         t_is(f, f_soln, 3, [t 'f']);
0271         t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0272         t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0273         t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  2, [t 'bus lambda']);
0274         t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0275         t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0276         t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0277         t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0278         t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0279         t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0280         t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0281         t_is(r.var.val.z, 0.025419, 6, [t 'user variable']);
0282         t_is(r.cost.usr, 2.5419, 4, [t 'user cost']);
0283     end
0284 
0285     %%-----  test OPF with capability curves  -----
0286     mpc = loadcase('t_case9_opfv2');
0287     %% remove angle diff limits
0288     mpc.branch(1, ANGMAX) = 360;
0289     mpc.branch(9, ANGMIN) = -360;
0290 
0291     %% get solved AC OPF case from MAT-file
0292     load soln9_opf_PQcap;   %% defines bus_soln, gen_soln, branch_soln, f_soln
0293     
0294     %% run OPF with capability curves
0295     t = [t0 'w/capability curves : '];
0296     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(mpc, mpopt);
0297     t_ok(success, [t 'success']);
0298     t_is(f, f_soln, 3, [t 'f']);
0299     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0300     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0301     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0302     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0303     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0304     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0305     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0306     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0307     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0308     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0309 
0310     %%-----  test OPF with angle difference limits  -----
0311     mpc = loadcase('t_case9_opfv2');
0312     %% remove capability curves
0313     mpc.gen(2:3, [PC1, PC2, QC1MIN, QC1MAX, QC2MIN, QC2MAX]) = zeros(2,6);
0314 
0315     %% get solved AC OPF case from MAT-file
0316     load soln9_opf_ang;   %% defines bus_soln, gen_soln, branch_soln, f_soln
0317     
0318     %% run OPF with angle difference limits
0319     t = [t0 'w/angle difference limits : '];
0320     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(mpc, mpopt);
0321     t_ok(success, [t 'success']);
0322     t_is(f, f_soln, 3, [t 'f']);
0323     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0324     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0325     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0326     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  1, [t 'bus mu']);
0327     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0328     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0329     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0330     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0331     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0332     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0333     t_is(branch(:,ibr_angmu ), branch_soln(:,ibr_angmu ),  2, [t 'branch angle mu']);
0334 
0335     %%-----  test OPF with ignored angle difference limits  -----
0336     %% get solved AC OPF case from MAT-file
0337     load soln9_opf;   %% defines bus_soln, gen_soln, branch_soln, f_soln
0338 
0339     %% run OPF with ignored angle difference limits
0340     t = [t0 'w/ignored angle difference limits : '];
0341     mpopt1 = mpoption(mpopt, 'opf.ignore_angle_lim', 1);
0342     [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(mpc, mpopt1);
0343     %% ang limits are not in this solution data, so let's remove them
0344     branch(1, ANGMAX) = 360;
0345     branch(9, ANGMIN) = -360;
0346     t_ok(success, [t 'success']);
0347     t_is(f, f_soln, 3, [t 'f']);
0348     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0349     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0350     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0351     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0352     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0353     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0354     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0355     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0356     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0357     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0358 
0359     %% angle bounded above by 0, unbounded below
0360     %% for issue/18
0361     t = [t0 'w/angle difference limit = 0 : '];
0362     mpc = loadcase(casefile);
0363     b = 5;
0364     mpc.branch(b, ANGMAX) = 0;
0365     r = runopf(mpc, mpopt);
0366     t_ok(success, [t 'success']);
0367     diff = r.bus(r.branch(b, F_BUS), VA) - r.bus(r.branch(b, T_BUS), VA);
0368     t_is(diff, 0, 5, [t 'angle diff']);
0369 
0370     %%-----  OPF with ref bus not = bus 1, ref angle not = 0  -----
0371     t = [t0 'ref bus ~= 1, ref ang ~= 0 : '];
0372     mpc = loadcase(casefile);
0373     mpc.bus([1;3], BUS_TYPE) = [PV; REF];   %% swap bus types
0374     bus_soln([1;3], BUS_TYPE) = bus_soln([3;1], BUS_TYPE);   %% swap bus types
0375     mpc.bus(3, VA) = 3.3014277;
0376     r = runopf(mpc, mpopt);
0377     [success, f, bus, gen, branch] = deal(r.success, r.f, r.bus, r.gen, r.branch);
0378     t_ok(success, [t 'success']);
0379     t_is(f, f_soln, 3, [t 'f']);
0380     t_is(   bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0381     t_is(   bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0382     t_is(   bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0383     t_is(   bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0384     t_is(   gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0385     t_is(   gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0386     t_is(   gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0387     t_is(branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0388     t_is(branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0389     t_is(branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0390 
0391     %%-----  test OPF with opf.use_vg  -----
0392     %% get solved AC OPF case from MAT-file
0393     load soln9_opf_vg;  %% defines bus_soln, gen_soln, branch_soln, f_soln
0394                         %%    and bus_soln1, gen_soln1, branch_soln1, f_soln1
0395     
0396     %% run with opf.use_vg = 1
0397     t = [t0 'w/opf.use_vg = 1 : '];
0398     mpc = loadcase(casefile);
0399     mpc.gen = mpc.gen([1 2 1 3], :);
0400     mpc.gencost = mpc.gencost([1 2 1 3], :);
0401     mpc.gen([1 3], [PMAX PMIN]) = mpc.gen([1 3], [PMAX PMIN]) / 2;
0402     mpc.gen(3, [QMIN, QMAX]) = 0;   %% no reactive capability for gen 3
0403     mpc.gencost([1 3], COST:end) = mpc.gencost([1 3], COST:end) / 2;
0404     mpc.gen(1, VG) = 1.05;
0405     mpc.gen(3, VG) = 1.06;
0406     mpopt1 = mpoption(mpopt, 'opf.use_vg', 1);
0407     r = runopf(mpc, mpopt1);
0408     t_ok(r.success, [t 'success']);
0409     t_is(r.f, f_soln, 3, [t 'f']);
0410     t_is(   r.bus(:,ib_data   ),    bus_soln(:,ib_data   ), 10, [t 'bus data']);
0411     t_is(   r.bus(:,ib_voltage),    bus_soln(:,ib_voltage),  3, [t 'bus voltage']);
0412     t_is(   r.bus(:,ib_lam    ),    bus_soln(:,ib_lam    ),  3, [t 'bus lambda']);
0413     t_is(   r.bus(:,ib_mu     ),    bus_soln(:,ib_mu     ),  2, [t 'bus mu']);
0414     t_is(   r.gen(:,ig_data   ),    gen_soln(:,ig_data   ), 10, [t 'gen data']);
0415     t_is(   r.gen(:,ig_disp   ),    gen_soln(:,ig_disp   ),  3, [t 'gen dispatch']);
0416     t_is(   r.gen(:,ig_mu     ),    gen_soln(:,ig_mu     ),  3, [t 'gen mu']);
0417     t_is(r.branch(:,ibr_data  ), branch_soln(:,ibr_data  ), 10, [t 'branch data']);
0418     t_is(r.branch(:,ibr_flow  ), branch_soln(:,ibr_flow  ),  3, [t 'branch flow']);
0419     t_is(r.branch(:,ibr_mu    ), branch_soln(:,ibr_mu    ),  2, [t 'branch mu']);
0420 
0421     %% run with opf.use_vg = 0.9
0422     t = [t0 'w/opf.use_vg = 0.9 : '];
0423     mpopt1 = mpoption(mpopt, 'opf.use_vg', 0.9);
0424     r = runopf(mpc, mpopt1);
0425     t_ok(r.success, [t 'success']);
0426     t_is(r.f, f_soln1, 3, [t 'f']);
0427     t_is(   r.bus(:,ib_data   ),    bus_soln1(:,ib_data   ), 10, [t 'bus data']);
0428     t_is(   r.bus(:,ib_voltage),    bus_soln1(:,ib_voltage),  3, [t 'bus voltage']);
0429     t_is(   r.bus(:,ib_lam    ),    bus_soln1(:,ib_lam    ),  3, [t 'bus lambda']);
0430     t_is(   r.bus(:,ib_mu     ),    bus_soln1(:,ib_mu     ),  2, [t 'bus mu']);
0431     t_is(   r.gen(:,ig_data   ),    gen_soln1(:,ig_data   ), 10, [t 'gen data']);
0432     t_is(   r.gen(:,ig_disp   ),    gen_soln1(:,ig_disp   ),  3, [t 'gen dispatch']);
0433     t_is(   r.gen(:,ig_mu     ),    gen_soln1(:,ig_mu     ),  3, [t 'gen mu']);
0434     t_is(r.branch(:,ibr_data  ), branch_soln1(:,ibr_data  ), 10, [t 'branch data']);
0435     t_is(r.branch(:,ibr_flow  ), branch_soln1(:,ibr_flow  ),  3, [t 'branch flow']);
0436     t_is(r.branch(:,ibr_mu    ), branch_soln1(:,ibr_mu    ),  2, [t 'branch mu']);
0437 
0438     t = [t0 'hi-deg polynomial costs : '];
0439     mpc = loadcase(casefile);
0440     mpc.gencost = [
0441         2   1500    0   6   1e-6/5  0   0   0   0   0;
0442         2   3000    0   5   1e-4/4  0   0   0   0   0;
0443         2   2000    0   3   1/2     0   0   0   0   0;
0444     ];
0445     r = runopf(mpc, mpopt);
0446     [f, bus, gen, branch] = deal(r.f, r.bus, r.gen, r.branch);
0447     t_ok(r.success, [t 'success']);
0448     t_is(f, 11899.4652, 4, [t 'f']);
0449     t_is(gen(:, PG), [100.703628; 88.719864; 128.679485], 5, [t 'Pg']);
0450     t_is([min(bus(:, VM)) mean(bus(:, VM)) max(bus(:, VM))], ...
0451         [1.059191 1.079404 1.1], 5, [t 'bus voltage']);
0452 
0453     %% OPF with user-defined nonlinear constraints
0454     t = [t0 'w/nonlin eq constraint : '];
0455     mpc = loadcase('case30');
0456     mpc.user_constraints.nle = {
0457         {'Pg_usr', 1, 'opf_nle_fcn1', 'opf_nle_hess1', {'Pg'}, {}}
0458     };
0459     r = runopf(mpc, mpopt);
0460     t_ok(r.success, [t 'success']);
0461     t_is(r.gen(1, PG) * r.gen(2, PG) / 100, r.gen(6, PG), 8, t);
0462     t_is(r.gen(6, PG), 20.751163, 5, t);
0463 
0464     %% OPF with all buses isolated
0465     t = [t0 'all buses isolated : '];
0466     mpc.bus(:, BUS_TYPE) = NONE;
0467     try
0468         r = runopf(mpc, mpopt);
0469         t_is(r.success, 0, 12, [t 'success = 0']);
0470     catch
0471         t_ok(0, [t 'unexpected fatal error']);
0472     end
0473 
0474     %% OPF with no branch limits
0475     t = [t0 'w/no branch limits : '];
0476     mpc = loadcase(casefile);
0477     mpc.branch(:, RATE_A) = 0;
0478     r = runopf(mpc, mpopt);
0479     t_ok(r.success, [t 'success']);
0480     t_is(r.f, 5496.128635, 4, [t 'f']);
0481     t_is(r.gen(:, PG), [90; 220.463932; 10], 5, [t 'Pg']);
0482     t_is([min(r.bus(:, VM)) mean(r.bus(:, VM)) max(r.bus(:, VM))], ...
0483         [1.070692 1.090449 1.1], 5, [t 'bus voltage']);
0484 end
0485 
0486 t_end;