t_most_uc

T_MOST_UC  Tests of deteministic unit commitment optimizations

   T_MOST_UC(QUIET, CREATE_PLOTS, CREATE_PDFS, SAVEPATH)
   Can generate summary plots and save them as PDFs in a directory of
   your choice.
   E.g. t_most_uc(0, 1, 1, '~/Downloads/uc_plots')

0001 function t_most_uc(quiet, create_plots, create_pdfs, savepath)
0002 %T_MOST_UC  Tests of deteministic unit commitment optimizations
0003 %
0004 %   T_MOST_UC(QUIET, CREATE_PLOTS, CREATE_PDFS, SAVEPATH)
0005 %   Can generate summary plots and save them as PDFs in a directory of
0006 %   your choice.
0007 %   E.g. t_most_uc(0, 1, 1, '~/Downloads/uc_plots')
0008 
0009 %   MOST
0010 %   Copyright (c) 2015-2016, Power Systems Engineering Research Center (PSERC)
0011 %   by Ray Zimmerman, PSERC Cornell
0012 %
0013 %   This file is part of MOST.
0014 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0015 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0016 
0017 if nargin < 4
0018     savepath = '.';             %% save in current working directory by default
0019     if nargin < 3
0020         create_pdfs = 0;        %% do NOT save plots to PDF files
0021         if nargin < 2
0022             create_plots = 0;   %% do NOT create summary plots of results
0023             if nargin < 1
0024                 quiet = 0;      %% verbose by default
0025             end
0026         end
0027     end
0028 end
0029 if create_plots
0030     if create_pdfs
0031         fname = 'uc-ex';
0032     else
0033         fname = '';
0034     end
0035     pp = 0;     %% plot counter
0036 end
0037 
0038 solvers = {'CPLEX', 'GLPK', 'GUROBI', 'MOSEK', 'OT'};
0039 fcn = {'cplex', 'glpk', 'gurobi', 'mosek', 'intlinprog'};
0040 % solvers = {'OT'};
0041 % fcn = {'intlinprog'};
0042 % solvers = {'GUROBI'};
0043 % fcn = {'gurobi'};
0044 ntests = 52;
0045 t_begin(ntests*length(solvers), quiet);
0046 
0047 if quiet
0048     verbose = 0;
0049 else
0050     verbose = 0;
0051 end
0052 % verbose = 2;
0053 
0054 if have_fcn('octave')
0055     if have_fcn('octave', 'vnum') >= 4
0056         file_in_path_warn_id = 'Octave:data-file-in-path';
0057     else
0058         file_in_path_warn_id = 'Octave:load-file-in-path';
0059     end
0060     s1 = warning('query', file_in_path_warn_id);
0061     warning('off', file_in_path_warn_id);
0062 end
0063 
0064 casefile = 'ex_case3b';
0065 solnfile =  't_most_uc_soln';
0066 soln = load(solnfile);
0067 mpopt = mpoption;
0068 mpopt = mpoption(mpopt, 'out.gen', 1);
0069 mpopt = mpoption(mpopt, 'verbose', verbose);
0070 % mpopt = mpoption(mpopt, 'opf.violation', 1e-6, 'mips.gradtol', 1e-8, ...
0071 %         'mips.comptol', 1e-8, 'mips.costtol', 1e-8);
0072 mpopt = mpoption(mpopt, 'model', 'DC');
0073 mpopt = mpoption(mpopt, 'most.price_stage_warn_tol', 1e1);
0074 
0075 %% solver options
0076 if have_fcn('cplex')
0077     %mpopt = mpoption(mpopt, 'cplex.lpmethod', 0);       %% automatic
0078     %mpopt = mpoption(mpopt, 'cplex.lpmethod', 1);       %% primal simplex
0079     mpopt = mpoption(mpopt, 'cplex.lpmethod', 2);       %% dual simplex
0080     %mpopt = mpoption(mpopt, 'cplex.lpmethod', 3);       %% network simplex
0081     %mpopt = mpoption(mpopt, 'cplex.lpmethod', 4);       %% barrier
0082     mpopt = mpoption(mpopt, 'cplex.opts.mip.tolerances.mipgap', 0);
0083     mpopt = mpoption(mpopt, 'cplex.opts.mip.tolerances.absmipgap', 0);
0084     mpopt = mpoption(mpopt, 'cplex.opts.threads', 2);
0085 end
0086 if have_fcn('glpk')
0087     mpopt = mpoption(mpopt, 'glpk.opts.mipgap', 0);
0088     mpopt = mpoption(mpopt, 'glpk.opts.tolint', 1e-10);
0089     mpopt = mpoption(mpopt, 'glpk.opts.tolobj', 1e-10);
0090 end
0091 if have_fcn('gurobi')
0092     %mpopt = mpoption(mpopt, 'gurobi.method', -1);       %% automatic
0093     %mpopt = mpoption(mpopt, 'gurobi.method', 0);        %% primal simplex
0094     mpopt = mpoption(mpopt, 'gurobi.method', 1);        %% dual simplex
0095     %mpopt = mpoption(mpopt, 'gurobi.method', 2);        %% barrier
0096     mpopt = mpoption(mpopt, 'gurobi.threads', 2);
0097     mpopt = mpoption(mpopt, 'gurobi.opts.MIPGap', 0);
0098     mpopt = mpoption(mpopt, 'gurobi.opts.MIPGapAbs', 0);
0099 end
0100 if have_fcn('mosek')
0101     sc = mosek_symbcon;
0102     %mpopt = mpoption(mpopt, 'mosek.lp_alg', sc.MSK_OPTIMIZER_FREE);            %% default
0103     %mpopt = mpoption(mpopt, 'mosek.lp_alg', sc.MSK_OPTIMIZER_INTPNT);          %% interior point
0104     %mpopt = mpoption(mpopt, 'mosek.lp_alg', sc.MSK_OPTIMIZER_PRIMAL_SIMPLEX);  %% primal simplex
0105     mpopt = mpoption(mpopt, 'mosek.lp_alg', sc.MSK_OPTIMIZER_DUAL_SIMPLEX);     %% dual simplex
0106     %mpopt = mpoption(mpopt, 'mosek.lp_alg', sc.MSK_OPTIMIZER_FREE_SIMPLEX);    %% automatic simplex
0107     %mpopt = mpoption(mpopt, 'mosek.opts.MSK_DPAR_MIO_TOL_X', 0);
0108     mpopt = mpoption(mpopt, 'mosek.opts.MSK_IPAR_MIO_NODE_OPTIMIZER', sc.MSK_OPTIMIZER_DUAL_SIMPLEX);
0109     mpopt = mpoption(mpopt, 'mosek.opts.MSK_IPAR_MIO_ROOT_OPTIMIZER', sc.MSK_OPTIMIZER_DUAL_SIMPLEX);
0110     mpopt = mpoption(mpopt, 'mosek.opts.MSK_DPAR_MIO_TOL_ABS_RELAX_INT', 1e-9);
0111     %mpopt = mpoption(mpopt, 'mosek.opts.MSK_DPAR_MIO_TOL_REL_RELAX_INT', 0);
0112     mpopt = mpoption(mpopt, 'mosek.opts.MSK_DPAR_MIO_TOL_REL_GAP', 0);
0113     mpopt = mpoption(mpopt, 'mosek.opts.MSK_DPAR_MIO_TOL_ABS_GAP', 0);
0114 end
0115 if have_fcn('intlinprog')
0116     %mpopt = mpoption(mpopt, 'linprog.Algorithm', 'interior-point');
0117     %mpopt = mpoption(mpopt, 'linprog.Algorithm', 'active-set');
0118     %mpopt = mpoption(mpopt, 'linprog.Algorithm', 'simplex');
0119     mpopt = mpoption(mpopt, 'linprog.Algorithm', 'dual-simplex');
0120     %mpopt = mpoption(mpopt, 'intlinprog.RootLPAlgorithm', 'primal-simplex');
0121     mpopt = mpoption(mpopt, 'intlinprog.RootLPAlgorithm', 'dual-simplex');
0122     mpopt = mpoption(mpopt, 'intlinprog.TolCon', 1e-9);
0123     mpopt = mpoption(mpopt, 'intlinprog.TolGapAbs', 0);
0124     mpopt = mpoption(mpopt, 'intlinprog.TolGapRel', 0);
0125     mpopt = mpoption(mpopt, 'intlinprog.TolInteger', 1e-6);
0126     %% next line is to work around a bug in intlinprog
0127     % (Technical Support Case #01841662)
0128     % (except actually in this case it triggers it rather than working
0129     %  around it, so we comment it out)
0130     %mpopt = mpoption(mpopt, 'intlinprog.LPPreprocess', 'none');
0131 end
0132 if ~verbose
0133     mpopt = mpoption(mpopt, 'out.all', 0);
0134 end
0135 % mpopt = mpoption(mpopt, 'out.all', -1);
0136 
0137 %% define named indices into data matrices
0138 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0139     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0140 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0141     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0142     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0143 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0144     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0145     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0146 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0147 [CT_LABEL, CT_PROB, CT_TABLE, CT_TBUS, CT_TGEN, CT_TBRCH, CT_TAREABUS, ...
0148     CT_TAREAGEN, CT_TAREABRCH, CT_ROW, CT_COL, CT_CHGTYPE, CT_REP, ...
0149     CT_REL, CT_ADD, CT_NEWVAL, CT_TLOAD, CT_TAREALOAD, CT_LOAD_ALL_PQ, ...
0150     CT_LOAD_FIX_PQ, CT_LOAD_DIS_PQ, CT_LOAD_ALL_P, CT_LOAD_FIX_P, ...
0151     CT_LOAD_DIS_P, CT_TGENCOST, CT_TAREAGENCOST, CT_MODCOST_F, ...
0152     CT_MODCOST_X] = idx_ct;
0153 
0154 %% load base case file
0155 mpc = loadcase(casefile);
0156 
0157 nb = size(mpc.bus, 1);
0158 nl = size(mpc.branch, 1);
0159 ng = size(mpc.gen, 1);
0160 
0161 xgd = loadxgendata('ex_xgd_uc', mpc);
0162 [iwind, mpc, xgd] = addwind('ex_wind_uc', mpc, xgd);
0163 profiles = getprofiles('ex_wind_profile_d', iwind);
0164 profiles = getprofiles('ex_load_profile', profiles);
0165 nt = size(profiles(1).values, 1);
0166 
0167 mpc_full = mpc;
0168 xgd_full = xgd;
0169 
0170 mpc.gencost(:, [STARTUP SHUTDOWN]) = 0; % remove startup/shutdown costs
0171 xgd.MinUp(2) = 1;                       % remove min up-time constraint
0172 xgd.PositiveLoadFollowReserveQuantity(3) = 250; % remove ramp reserve
0173 xgd.PositiveLoadFollowReservePrice(3) = 1e-6;   % constraint and costs
0174 xgd.NegativeLoadFollowReservePrice(3) = 1e-6;
0175 mpc0 = mpc;
0176 xgd0 = xgd;
0177 
0178 for s = 1:length(solvers)
0179     if ~have_fcn(fcn{s})     %% check if we have the solver
0180         t_skip(ntests, sprintf('%s not installed', solvers{s}));
0181     else
0182         mpopt = mpoption(mpopt, 'opf.dc.solver', solvers{s});
0183         mpopt = mpoption(mpopt, 'most.solver', mpopt.opf.dc.solver);
0184         mpopt = mpoption(mpopt, 'most.storage.cyclic', 1);
0185 
0186         t = sprintf('%s : base (econ disp, no network) : ', solvers{s});
0187         mpc = mpc0;
0188         xgd = xgd0;
0189         mpopt = mpoption(mpopt, 'most.dc_model', 0);
0190         mdi = loadmd(mpc, nt, xgd, [], [], profiles);
0191         mdo = most(mdi, mpopt);
0192         ms = most_summary(mdo);
0193         t_ok(mdo.QP.exitflag > 0, [t 'success']);
0194         ex = soln.ed;
0195         t_is(ms.f, ex.f, 8, [t 'f']);
0196         t_is(ms.Pg, ex.Pg, 8, [t 'Pg']);
0197         t_is(ms.Rup, ex.Rup, 8, [t 'Rup']);
0198         t_is(ms.Rdn, ex.Rdn, 8, [t 'Rdn']);
0199         t_is(ms.Pf, ex.Pf, 8, [t 'Pf']);
0200         t_is(ms.u, ex.u, 8, [t 'u']);
0201         t_is(ms.lamP, ex.lamP, 5, [t 'lamP']);
0202         t_is(ms.muF, ex.muF, 8, [t 'muF']);
0203         % ed = most_summary(mdo);
0204         if create_plots
0205             pp = pp + 1;
0206             plot_case('Base : No Network', mdo, ms, 500, 100, savepath, pp, fname);
0207         end
0208         % keyboard;
0209 
0210         t = sprintf('%s : + DC OPF constraints : ', solvers{s});
0211         mpc = mpc0;
0212         % mpc.gen(iwind, PMAX) = 50;
0213         mpopt = mpoption(mpopt, 'most.dc_model', 1);
0214         mdi = loadmd(mpc, nt, xgd, [], [], profiles);
0215         mdo = most(mdi, mpopt);
0216         ms = most_summary(mdo);
0217         t_ok(mdo.QP.exitflag > 0, [t 'success']);
0218         ex = soln.dcopf;
0219         t_is(ms.f, ex.f, 8, [t 'f']);
0220         t_is(ms.Pg, ex.Pg, 8, [t 'Pg']);
0221         t_is(ms.Rup, ex.Rup, 8, [t 'Rup']);
0222         t_is(ms.Rdn, ex.Rdn, 8, [t 'Rdn']);
0223         t_is(ms.Pf, ex.Pf, 8, [t 'Pf']);
0224         t_is(ms.u, ex.u, 8, [t 'u']);
0225         t_is(ms.lamP, ex.lamP, 5, [t 'lamP']);
0226         t_is(ms.muF, ex.muF, 8, [t 'muF']);
0227         % dcopf = most_summary(mdo);
0228         if create_plots
0229             pp = pp + 1;
0230             plot_case('+ DC Network', mdo, ms, 500, 100, savepath, pp, fname);
0231         end
0232         % keyboard;
0233 
0234         t = sprintf('%s : + startup/shutdown costs : ', solvers{s});
0235         if mpopt.out.all
0236             fprintf('Add STARTUP and SHUTDOWN costs\n');
0237         end
0238         mpc = mpc_full;
0239         % mpc.gencost(3, STARTUP)  = 3524.9944997;    %% CPLEX, GLPK
0240         % mpc.gencost(3, SHUTDOWN) = 3524.9944997;
0241         % mpc.gencost(3, STARTUP)  = 3524.99499778;    %% Gurobi
0242         % mpc.gencost(3, SHUTDOWN) = 3524.9949978;
0243         % mpc.gencost(3, STARTUP)  = 3524.9949988;    %% MOSEK
0244         % mpc.gencost(3, SHUTDOWN)  = 3524.9949986;    %% MOSEK
0245         mdi = loadmd(mpc, nt, xgd, [], [], profiles);
0246         mdo = most(mdi, mpopt);
0247         ms = most_summary(mdo);
0248         t_ok(mdo.QP.exitflag > 0, [t 'success']);
0249         ex = soln.wstart;
0250         t_is(ms.f, ex.f, 8, [t 'f']);
0251         t_is(ms.Pg, ex.Pg, 8, [t 'Pg']);
0252         t_is(ms.Rup, ex.Rup, 8, [t 'Rup']);
0253         t_is(ms.Rdn, ex.Rdn, 8, [t 'Rdn']);
0254         t_is(ms.Pf, ex.Pf, 8, [t 'Pf']);
0255         t_is(ms.u, ex.u, 8, [t 'u']);
0256         t_is(ms.lamP, ex.lamP, 8, [t 'lamP']);
0257         t_is(ms.muF, ex.muF, 8, [t 'muF']);
0258         % wstart = most_summary(mdo);
0259         if create_plots
0260             pp = pp + 1;
0261             plot_case('+ Startup/Shutdown Costs', mdo, ms, 500, 100, savepath, pp, fname);
0262         end
0263         % keyboard;
0264 
0265         t = sprintf('%s : + min up/down time constraints : ', solvers{s});
0266         if mpopt.out.all
0267             fprintf('Add MinUp time\n');
0268         end
0269         xgd.MinUp(2) = 3;
0270         mdi = loadmd(mpc, nt, xgd, [], [], profiles);
0271         mdo = most(mdi, mpopt);
0272         ms = most_summary(mdo);
0273         t_ok(mdo.QP.exitflag > 0, [t 'success']);
0274         ex = soln.wminup;
0275         t_is(ms.f, ex.f, 8, [t 'f']);
0276         t_is(ms.Pg, ex.Pg, 8, [t 'Pg']);
0277         t_is(ms.Rup, ex.Rup, 8, [t 'Rup']);
0278         t_is(ms.Rdn, ex.Rdn, 8, [t 'Rdn']);
0279         t_is(ms.Pf, ex.Pf, 8, [t 'Pf']);
0280         t_is(ms.u, ex.u, 8, [t 'u']);
0281         t_is(ms.lamP, ex.lamP, 8, [t 'lamP']);
0282         t_is(ms.muF, ex.muF, 8, [t 'muF']);
0283         % wminup = most_summary(mdo);
0284         if create_plots
0285             pp = pp + 1;
0286             plot_case('+ Min Up/Down Time Constraints', mdo, ms, 500, 100, savepath, pp, fname);
0287         end
0288         % keyboard;
0289 
0290         t = sprintf('%s : + ramp constraint/ramp res cost : ', solvers{s});
0291         if mpopt.out.all
0292             fprintf('Restrict ramping and add ramp reserve costs\n');
0293         end
0294         xgd = xgd_full;
0295         mdi = loadmd(mpc, nt, xgd, [], [], profiles);
0296         mdo = most(mdi, mpopt);
0297         ms = most_summary(mdo);
0298         t_ok(mdo.QP.exitflag > 0, [t 'success']);
0299         ex = soln.wramp;
0300         t_is(ms.f, ex.f, 8, [t 'f']);
0301         t_is(ms.Pg, ex.Pg, 8, [t 'Pg']);
0302         t_is(ms.Rup, ex.Rup, 8, [t 'Rup']);
0303         t_is(ms.Rdn, ex.Rdn, 8, [t 'Rdn']);
0304         t_is(ms.Pf, ex.Pf, 8, [t 'Pf']);
0305         t_is(ms.u, ex.u, 8, [t 'u']);
0306         t_is(ms.lamP, ex.lamP, 8, [t 'lamP']);
0307         t_is(ms.muF, ex.muF, 8, [t 'muF']);
0308         % wramp = most_summary(mdo);
0309         if create_plots
0310             pp = pp + 1;
0311             plot_case('+ Ramping Constraints/Ramp Reserve Costs', mdo, ms, 500, 100, savepath, pp, fname);
0312         end
0313         % keyboard;
0314 
0315         t = sprintf('%s : + storage : ', solvers{s});
0316         if mpopt.out.all
0317             fprintf('Add storage\n');
0318         end
0319         [iess, mpc, xgd, sd] = addstorage('ex_storage', mpc, xgd);
0320         mdi = loadmd(mpc, nt, xgd, sd, [], profiles);
0321         mdo = most(mdi, mpopt);
0322         ms = most_summary(mdo);
0323         t_ok(mdo.QP.exitflag > 0, [t 'success']);
0324         ex = soln.wstorage;
0325         t_is(ms.f, ex.f, 8, [t 'f']);
0326         t_is(ms.Pg, ex.Pg, 8, [t 'Pg']);
0327         t_is(ms.Rup, ex.Rup, 8, [t 'Rup']);
0328         t_is(ms.Rdn, ex.Rdn, 8, [t 'Rdn']);
0329         t_is(ms.Pf, ex.Pf, 8, [t 'Pf']);
0330         t_is(ms.u, ex.u, 8, [t 'u']);
0331         % t_is(ms.lamP, ex.lamP, 5, [t 'lamP']);
0332         % t_is(ms.muF, ex.muF, 5, [t 'muF']);
0333         % wstorage = most_summary(mdo);
0334         if create_plots
0335             pp = pp + 1;
0336             plot_case('+ Storage', mdo, ms, 500, 100, savepath, pp, fname);
0337             create_plots = 0;   %% don't do them again
0338         end
0339         % keyboard;
0340     end
0341 end
0342 
0343 if have_fcn('octave')
0344     warning(s1.state, file_in_path_warn_id);
0345 end
0346 
0347 t_end;
0348 
0349 % save t_most_uc_soln ed dcopf wstart wminup wramp wstorage
0350 
0351 function h = plot_case(label, md, ms, maxq, maxp, mypath, pp, fname)
0352 
0353 if nargin < 8
0354     fname = '';
0355 end
0356 
0357 %% colors:  blue     red               yellow           purple            green
0358 cc = {[0 0.45 0.74], [0.85 0.33 0.1], [0.93 0.69 0.13], [0.49 0.18 0.56], [0.47 0.67 0.19]};
0359 
0360 ig = (1:3)';
0361 id = 4;
0362 iw = 5;
0363 is = 6;
0364 
0365 subplot(3, 1, 1);
0366 md.mpc = rmfield(md.mpc, 'genfuel');
0367 plot_uc(md, [], 'title', label);
0368 ylabel('Unit Commitment', 'FontSize', 16);
0369 ah = gca;
0370 ah.YAxisLocation = 'left';
0371 
0372 subplot(3, 1, 2);
0373 x = (1:ms.nt)';
0374 y1 = ms.Pg(ig, :)';
0375 if ms.ng == 6
0376     y1 = [y1 max(-ms.Pg(is, :), 0)' max(ms.Pg(is, :), 0)'];
0377 end
0378 y2 = -sum(ms.Pg([id; iw], :), 1)';
0379 [ah1, h1, h2] = plotyy(x, y1, x, y2);
0380 axis(ah1(1), [0.5 12.5 0 maxq]);
0381 axis(ah1(2), [0.5 12.5 0 maxq]);
0382 % ah1(1).XLim = [0.5 12.5];
0383 % ah1(2).XLim = [0.5 12.5];
0384 % ah1(1).YLim = [0 300];
0385 % ah1(2).YLim = [0 450];
0386 ah1(1).YTickMode = 'auto';
0387 ah1(2).YTickMode = 'auto';
0388 ah1(1).XTick = 1:12;
0389 nn = 3;
0390 for j = 1:3
0391     h1(j).LineWidth = 2;
0392     h1(j).Color = cc{j};
0393 end
0394 if ms.ng == 6
0395     h1(4).LineWidth = 2;
0396     h1(4).Color = cc{5};
0397     h1(4).LineStyle = ':';
0398     h1(5).LineWidth = 2;
0399     h1(5).Color = cc{5};
0400 end
0401 h2.LineWidth = 2;
0402 h2.Color = cc{4};
0403 h2.LineStyle = ':';
0404 ah1(2).YColor = cc{4};
0405 %title('Generation & Net Load', 'FontSize', 16);
0406 ylabel(ah1(1), 'Generation, MW', 'FontSize', 16);
0407 ylabel(ah1(2), 'Net Load, MW', 'FontSize', 16);
0408 xlabel('Period', 'FontSize', 16);
0409 set(ah1(1), 'FontSize', 14);
0410 set(ah1(2), 'FontSize', 14);
0411 if ms.ng == 6
0412     legend('Gen 1', 'Gen 2', 'Gen 3', 'Storage Charge', 'Storage Discharge', 'Location', [0.7 0.6 0 0]);
0413 else
0414     legend('Gen 1', 'Gen 2', 'Gen 3', 'Location', [0.7 0.58 0 0]);
0415 end
0416 
0417 subplot(3, 1, 3);
0418 y1 = ms.lamP';
0419 plot(x, y1, 'LineWidth', 2);
0420 % title('Nodal Price', 'FontSize', 16);
0421 ylabel('Nodal Price, $/MWh', 'FontSize', 16);
0422 xlabel('Period', 'FontSize', 16);
0423 axis([0.5 12.5 0 maxp]);
0424 ah = gca;
0425 set(ah, 'FontSize', 14);
0426 ah.XTick = 1:12;
0427 legend('Bus 1', 'Bus 2', 'Bus 3', 'Location', [0.7 0.28 0 0]);
0428 
0429 if nargin > 7 && ~isempty(fname)
0430     h = gcf;
0431     set(h, 'PaperSize', [11 8.5]);
0432     set(h, 'PaperPosition', [0.25 0.25 10.5 8]);
0433     print('-dpdf', fullfile(mypath, sprintf('%s-%d', fname, pp)));
0434 end