Description of toggle

0001 function mpc = toggle_reserves(mpc, on_off)
0002 %TOGGLE_RESERVES Enable or disable fixed reserve requirements.
0003 %   MPC = TOGGLE_RESERVES(MPC, 'on')
0004 %   MPC = TOGGLE_RESERVES(MPC, 'off')
0005 %
0006 %   Enables or disables a set of OPF userfcn callbacks to implement
0007 %   co-optimization of reserves with fixed zonal reserve requirements.
0008 %
0009 %   These callbacks expect to find a 'reserves' field in the input MPC,
0010 %   where MPC.reserves is a struct with the following fields:
0011 %       zones   nrz x ng, zone(i, j) = 1, if gen j belongs to zone i
0012 %                                      0, otherwise
0013 %       req     nrz x 1, zonal reserve requirement in MW
0014 %       cost    (ng or ngr) x 1, cost of reserves in $/MW
0015 %       qty     (ng or ngr) x 1, max quantity of reserves in MW (optional)
0016 %   where nrz is the number of reserve zones and ngr is the number of
0017 %   generators belonging to at least one reserve zone and ng is the total
0018 %   number of generators.
0019 %
0020 %   The 'int2ext' callback also packages up results and stores them in
0021 %   the following output fields of results.reserves:
0022 %       R       - ng x 1, reserves provided by each gen in MW
0023 %       Rmin    - ng x 1, lower limit on reserves provided by each gen, (MW)
0024 %       Rmax    - ng x 1, upper limit on reserves provided by each gen, (MW)
0025 %       mu.l    - ng x 1, shadow price on reserve lower limit, ($/MW)
0026 %       mu.u    - ng x 1, shadow price on reserve upper limit, ($/MW)
0027 %       mu.Pmax - ng x 1, shadow price on Pg + R <= Pmax constraint, ($/MW)
0028 %       prc     - ng x 1, reserve price for each gen equal to maximum of the
0029 %                         shadow prices on the zonal requirement constraint
0030 %                         for each zone the generator belongs to
0031 %
0032 %   See also RUNOPF_W_RES, ADD_USERFCN, REMOVE_USERFCN, RUN_USERFCN,
0033 %   T_CASE30_USERFCNS.
0034 
0035 %   MATPOWER
0036 %   $Id: toggle_reserves.m,v 1.15 2010/04/26 19:45:26 ray Exp $
0037 %   by Ray Zimmerman, PSERC Cornell
0038 %   Copyright (c) 2009-2010 by Power System Engineering Research Center (PSERC)
0039 %
0040 %   This file is part of MATPOWER.
0041 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0042 %
0043 %   MATPOWER is free software: you can redistribute it and/or modify
0044 %   it under the terms of the GNU General Public License as published
0045 %   by the Free Software Foundation, either version 3 of the License,
0046 %   or (at your option) any later version.
0047 %
0048 %   MATPOWER is distributed in the hope that it will be useful,
0049 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0050 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
0051 %   GNU General Public License for more details.
0052 %
0053 %   You should have received a copy of the GNU General Public License
0054 %   along with MATPOWER. If not, see <http://www.gnu.org/licenses/>.
0055 %
0056 %   Additional permission under GNU GPL version 3 section 7
0057 %
0058 %   If you modify MATPOWER, or any covered work, to interface with
0059 %   other modules (such as MATLAB code and MEX-files) available in a
0060 %   MATLAB(R) or comparable environment containing parts covered
0061 %   under other licensing terms, the licensors of MATPOWER grant
0062 %   you additional permission to convey the resulting work.
0063 
0064 if strcmp(on_off, 'on')
0065     %% check for proper reserve inputs
0066     if ~isfield(mpc, 'reserves') || ~isstruct(mpc.reserves) || ...
0067             ~isfield(mpc.reserves, 'zones') || ...
0068             ~isfield(mpc.reserves, 'req') || ...
0069             ~isfield(mpc.reserves, 'cost')
0070         error('toggle_reserves: case must contain a ''reserves'' field, a struct defining ''zones'', ''req'' and ''cost''');
0071     end
0072     
0073     %% add callback functions
0074     %% note: assumes all necessary data included in 1st arg (mpc, om, results)
0075     %%       so, no additional explicit args are needed
0076     mpc = add_userfcn(mpc, 'ext2int', @userfcn_reserves_ext2int);
0077     mpc = add_userfcn(mpc, 'formulation', @userfcn_reserves_formulation);
0078     mpc = add_userfcn(mpc, 'int2ext', @userfcn_reserves_int2ext);
0079     mpc = add_userfcn(mpc, 'printpf', @userfcn_reserves_printpf);
0080     mpc = add_userfcn(mpc, 'savecase', @userfcn_reserves_savecase);
0081 elseif strcmp(on_off, 'off')
0082     mpc = remove_userfcn(mpc, 'savecase', @userfcn_reserves_savecase);
0083     mpc = remove_userfcn(mpc, 'printpf', @userfcn_reserves_printpf);
0084     mpc = remove_userfcn(mpc, 'int2ext', @userfcn_reserves_int2ext);
0085     mpc = remove_userfcn(mpc, 'formulation', @userfcn_reserves_formulation);
0086     mpc = remove_userfcn(mpc, 'ext2int', @userfcn_reserves_ext2int);
0087 else
0088     error('toggle_reserves: 2nd argument must be either ''on'' or ''off''');
0089 end
0090 
0091 
0092 %%-----  ext2int  ------------------------------------------------------
0093 function mpc = userfcn_reserves_ext2int(mpc, args)
0094 %
0095 %   mpc = userfcn_reserves_ext2int(mpc, args)
0096 %
0097 %   This is the 'ext2int' stage userfcn callback that prepares the input
0098 %   data for the formulation stage. It expects to find a 'reserves' field
0099 %   in mpc as described above. The optional args are not currently used.
0100 
0101 %% initialize some things
0102 r = mpc.reserves;
0103 o = mpc.order;
0104 ng0 = size(o.ext.gen, 1);   %% number of original gens (+ disp loads)
0105 nrz = size(r.req, 1);       %% number of reserve zones
0106 if nrz > 1
0107     mpc.reserves.rgens = any(r.zones);  %% mask of gens available to provide reserves
0108 else
0109     mpc.reserves.rgens = r.zones;
0110 end
0111 igr = find(mpc.reserves.rgens); %% indices of gens available to provide reserves
0112 ngr = length(igr);              %% number of gens available to provide reserves
0113 
0114 %% check data for consistent dimensions
0115 if size(r.zones, 1) ~= nrz
0116     error('userfcn_reserves_ext2int: the number of rows in mpc.reserves.req (%d) and mpc.reserves.zones (%d) must match', nrz, size(r.zones, 1));
0117 end
0118 if size(r.cost, 1) ~= ng0 && size(r.cost, 1) ~= ngr
0119     error('userfcn_reserves_ext2int: the number of rows in mpc.reserves.cost (%d) must equal the total number of generators (%d) or the number of generators able to provide reserves (%d)', size(r.cost, 1), ng0, ngr);
0120 end
0121 if isfield(r, 'qty') && size(r.qty, 1) ~= size(r.cost, 1)
0122     error('userfcn_reserves_ext2int: mpc.reserves.cost (%d x 1) and mpc.reserves.qty (%d x 1) must be the same dimension', size(r.cost, 1), size(r.qty, 1));
0123 end
0124 
0125 %% convert both cost and qty from ngr x 1 to full ng x 1 vectors if necessary
0126 if size(r.cost, 1) < ng0
0127     mpc.reserves.original.cost = r.cost;    %% save original
0128     cost = zeros(ng0, 1);
0129     cost(igr) = r.cost;
0130     mpc.reserves.cost = cost;
0131     if isfield(r, 'qty')
0132         mpc.reserves.original.qty = r.qty;  %% save original
0133         qty = zeros(ng0, 1);
0134         qty(igr) = r.qty;
0135         mpc.reserves.qty = qty;
0136     end
0137 end
0138 
0139 %%-----  convert stuff to internal indexing  -----
0140 %% convert all reserve parameters (zones, costs, qty, rgens)
0141 if isfield(r, 'qty')
0142     mpc = ext2int(mpc, {'reserves', 'qty'}, 'gen');
0143 end
0144 mpc = ext2int(mpc, {'reserves', 'cost'}, 'gen');
0145 mpc = ext2int(mpc, {'reserves', 'zones'}, 'gen', 2);
0146 mpc = ext2int(mpc, {'reserves', 'rgens'}, 'gen', 2);
0147 
0148 %% save indices of gens available to provide reserves
0149 mpc.order.ext.reserves.igr = igr;               %% external indexing
0150 mpc.reserves.igr = find(mpc.reserves.rgens);    %% internal indexing
0151 
0152 
0153 %%-----  formulation  --------------------------------------------------
0154 function om = userfcn_reserves_formulation(om, args)
0155 %
0156 %   om = userfcn_reserves_formulation(om, args)
0157 %
0158 %   This is the 'formulation' stage userfcn callback that defines the
0159 %   user costs and constraints for fixed reserves. It expects to find
0160 %   a 'reserves' field in the mpc stored in om, as described above.
0161 %   By the time it is passed to this callback, mpc.reserves should
0162 %   have two additional fields:
0163 %       igr     1 x ngr, indices of generators available for reserves
0164 %       rgens   1 x ng, 1 if gen avaiable for reserves, 0 otherwise
0165 %   It is also assumed that if cost or qty were ngr x 1, they have been
0166 %   expanded to ng x 1 and that everything has been converted to
0167 %   internal indexing, i.e. all gens are on-line (by the 'ext2int'
0168 %   callback). The optional args are not currently used.
0169 
0170 %% define named indices into data matrices
0171 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0172     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0173     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0174 
0175 %% initialize some things
0176 mpc = get_mpc(om);
0177 r = mpc.reserves;
0178 igr = r.igr;                %% indices of gens available to provide reserves
0179 ngr = length(igr);          %% number of gens available to provide reserves
0180 ng  = size(mpc.gen, 1);     %% number of on-line gens (+ disp loads)
0181 
0182 %% variable bounds
0183 Rmin = zeros(ngr, 1);               %% bound below by 0
0184 Rmax = Inf * ones(ngr, 1);          %% bound above by ...
0185 k = find(mpc.gen(igr, RAMP_10));
0186 Rmax(k) = mpc.gen(igr(k), RAMP_10); %% ... ramp rate and ...
0187 if isfield(r, 'qty')
0188     k = find(r.qty(igr) < Rmax);
0189     Rmax(k) = r.qty(igr(k));        %% ... stated max reserve qty
0190 end
0191 Rmax = Rmax / mpc.baseMVA;
0192 
0193 %% constraints
0194 I = speye(ngr);                     %% identity matrix
0195 Ar = [sparse(1:ngr, igr, 1, ngr, ng) I];
0196 ur = mpc.gen(igr, PMAX) / mpc.baseMVA;
0197 lreq = r.req / mpc.baseMVA;
0198 
0199 %% cost
0200 Cw = r.cost(igr) * mpc.baseMVA;     %% per unit cost coefficients
0201 
0202 %% add them to the model
0203 om = add_vars(om, 'R', ngr, [], Rmin, Rmax);
0204 om = add_constraints(om, 'Pg_plus_R', Ar, [], ur, {'Pg', 'R'});
0205 om = add_constraints(om, 'Rreq', r.zones(:, igr), lreq, [], {'R'});
0206 om = add_costs(om, 'Rcost', struct('N', I, 'Cw', Cw), {'R'});
0207 
0208 
0209 %%-----  int2ext  ------------------------------------------------------
0210 function results = userfcn_reserves_int2ext(results, args)
0211 %
0212 %   results = userfcn_reserves_int2ext(results, args)
0213 %
0214 %   This is the 'int2ext' stage userfcn callback that converts everything
0215 %   back to external indexing and packages up the results. It expects to
0216 %   find a 'reserves' field in the results struct as described for mpc
0217 %   above, including the two additional fields 'igr' and 'rgens'. It also
0218 %   expects the results to contain a variable 'R' and linear constraints
0219 %   'Pg_plus_R' and 'Rreq' which are used to populate output fields in
0220 %   results.reserves. The optional args are not currently used.
0221 
0222 %% initialize some things
0223 r = results.reserves;
0224 
0225 %% grab some info in internal indexing order
0226 igr = r.igr;                %% indices of gens available to provide reserves
0227 ng  = size(results.gen, 1); %% number of on-line gens (+ disp loads)
0228 
0229 %%-----  convert stuff back to external indexing  -----
0230 %% convert all reserve parameters (zones, costs, qty, rgens)
0231 if isfield(r, 'qty')
0232     results = int2ext(results, {'reserves', 'qty'}, 'gen');
0233 end
0234 results = int2ext(results, {'reserves', 'cost'}, 'gen');
0235 results = int2ext(results, {'reserves', 'zones'}, 'gen', 2);
0236 results = int2ext(results, {'reserves', 'rgens'}, 'gen', 2);
0237 results.order.int.reserves.igr = results.reserves.igr;  %% save internal version
0238 results.reserves.igr = results.order.ext.reserves.igr;  %% use external version
0239 r = results.reserves;       %% update
0240 o = results.order;          %% update
0241 
0242 %% grab same info in external indexing order
0243 igr0 = r.igr;               %% indices of gens available to provide reserves
0244 ng0  = size(o.ext.gen, 1);  %% number of gens (+ disp loads)
0245 
0246 %%-----  results post-processing  -----
0247 %% get the results (per gen reserves, multipliers) with internal gen indexing
0248 %% and convert from p.u. to per MW units
0249 [R0, Rl, Ru] = getv(results.om, 'R');
0250 R       = zeros(ng, 1);
0251 Rmin    = zeros(ng, 1);
0252 Rmax    = zeros(ng, 1);
0253 mu_l    = zeros(ng, 1);
0254 mu_u    = zeros(ng, 1);
0255 mu_Pmax = zeros(ng, 1);
0256 R(igr)       = results.var.val.R * results.baseMVA;
0257 Rmin(igr)    = Rl * results.baseMVA;
0258 Rmax(igr)    = Ru * results.baseMVA;
0259 mu_l(igr)    = results.var.mu.l.R / results.baseMVA;
0260 mu_u(igr)    = results.var.mu.u.R / results.baseMVA;
0261 mu_Pmax(igr) = results.lin.mu.u.Pg_plus_R / results.baseMVA;
0262 
0263 %% store in results in results struct
0264 z = zeros(ng0, 1);
0265 results.reserves.R       = int2ext(results, R, z, 'gen');
0266 results.reserves.Rmin    = int2ext(results, Rmin, z, 'gen');
0267 results.reserves.Rmax    = int2ext(results, Rmax, z, 'gen');
0268 results.reserves.mu.l    = int2ext(results, mu_l, z, 'gen');
0269 results.reserves.mu.u    = int2ext(results, mu_u, z, 'gen');
0270 results.reserves.mu.Pmax = int2ext(results, mu_Pmax, z, 'gen');
0271 results.reserves.prc     = z;
0272 for k = igr0
0273     iz = find(r.zones(:, k));
0274     results.reserves.prc(k) = max(results.lin.mu.l.Rreq(iz)) / results.baseMVA;
0275 end
0276 results.reserves.totalcost = results.cost.Rcost;
0277 
0278 %% replace ng x 1 cost, qty with ngr x 1 originals
0279 if isfield(r, 'original')
0280     if isfield(r, 'qty')
0281         results.reserves.qty = r.original.qty;
0282     end
0283     results.reserves.cost = r.original.cost;
0284     results.reserves = rmfield(results.reserves, 'original');
0285 end
0286 
0287 
0288 %%-----  printpf  ------------------------------------------------------
0289 function results = userfcn_reserves_printpf(results, fd, mpopt, args)
0290 %
0291 %   results = userfcn_reserves_printpf(results, fd, mpopt, args)
0292 %
0293 %   This is the 'printpf' stage userfcn callback that pretty-prints the
0294 %   results. It expects a results struct, a file descriptor and a MATPOWER
0295 %   options vector. The optional args are not currently used.
0296 
0297 %% define named indices into data matrices
0298 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0299     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0300     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0301 
0302 %%-----  print results  -----
0303 r = results.reserves;
0304 nrz = size(r.req, 1);
0305 OUT_ALL = mpopt(32);
0306 if OUT_ALL ~= 0
0307     fprintf(fd, '\n================================================================================');
0308     fprintf(fd, '\n|     Reserves                                                                 |');
0309     fprintf(fd, '\n================================================================================');
0310     fprintf(fd, '\n Gen   Bus   Status  Reserves   Price');
0311     fprintf(fd, '\n  #     #              (MW)     ($/MW)     Included in Zones ...');
0312     fprintf(fd, '\n----  -----  ------  --------  --------   ------------------------');
0313     for k = r.igr
0314         iz = find(r.zones(:, k));
0315         fprintf(fd, '\n%3d %6d     %2d ', k, results.gen(k, GEN_BUS), results.gen(k, GEN_STATUS));
0316         if results.gen(k, GEN_STATUS) > 0 && abs(results.reserves.R(k)) > 1e-6
0317             fprintf(fd, '%10.2f', results.reserves.R(k));
0318         else
0319             fprintf(fd, '       -  ');
0320         end
0321         fprintf(fd, '%10.2f     ', results.reserves.prc(k));
0322         for i = 1:length(iz)
0323             if i ~= 1
0324                 fprintf(fd, ', ');
0325             end
0326             fprintf(fd, '%d', iz(i));
0327         end
0328     end
0329     fprintf(fd, '\n                     --------');
0330     fprintf(fd, '\n            Total:%10.2f              Total Cost: $%.2f', ...
0331         sum(results.reserves.R(r.igr)), results.reserves.totalcost);
0332     fprintf(fd, '\n');
0333     
0334     fprintf(fd, '\nZone  Reserves   Price  ');
0335     fprintf(fd, '\n  #     (MW)     ($/MW) ');
0336     fprintf(fd, '\n----  --------  --------');
0337     for k = 1:nrz
0338         iz = find(r.zones(k, :));     %% gens in zone k
0339         fprintf(fd, '\n%3d%10.2f%10.2f', k, sum(results.reserves.R(iz)), ...
0340                     results.lin.mu.l.Rreq(k) / results.baseMVA);
0341     end
0342     fprintf(fd, '\n');
0343     
0344     fprintf(fd, '\n================================================================================');
0345     fprintf(fd, '\n|     Reserve Limits                                                           |');
0346     fprintf(fd, '\n================================================================================');
0347     fprintf(fd, '\n Gen   Bus   Status  Rmin mu     Rmin    Reserves    Rmax    Rmax mu   Pmax mu ');
0348     fprintf(fd, '\n  #     #             ($/MW)     (MW)      (MW)      (MW)     ($/MW)    ($/MW) ');
0349     fprintf(fd, '\n----  -----  ------  --------  --------  --------  --------  --------  --------');
0350     for k = r.igr
0351         fprintf(fd, '\n%3d %6d     %2d ', k, results.gen(k, GEN_BUS), results.gen(k, GEN_STATUS));
0352         if results.gen(k, GEN_STATUS) > 0 && results.reserves.mu.l(k) > 1e-6
0353             fprintf(fd, '%10.2f', results.reserves.mu.l(k));
0354         else
0355             fprintf(fd, '       -  ');
0356         end
0357         fprintf(fd, '%10.2f', results.reserves.Rmin(k));
0358         if results.gen(k, GEN_STATUS) > 0 && abs(results.reserves.R(k)) > 1e-6
0359             fprintf(fd, '%10.2f', results.reserves.R(k));
0360         else
0361             fprintf(fd, '       -  ');
0362         end
0363         fprintf(fd, '%10.2f', results.reserves.Rmax(k));
0364         if results.gen(k, GEN_STATUS) > 0 && results.reserves.mu.u(k) > 1e-6
0365             fprintf(fd, '%10.2f', results.reserves.mu.u(k));
0366         else
0367             fprintf(fd, '       -  ');
0368         end
0369         if results.gen(k, GEN_STATUS) > 0 && results.reserves.mu.Pmax(k) > 1e-6
0370             fprintf(fd, '%10.2f', results.reserves.mu.Pmax(k));
0371         else
0372             fprintf(fd, '       -  ');
0373         end
0374     end
0375     fprintf(fd, '\n                                         --------');
0376     fprintf(fd, '\n                                Total:%10.2f', sum(results.reserves.R(r.igr)));
0377     fprintf(fd, '\n');
0378 end
0379 
0380 
0381 %%-----  savecase  -----------------------------------------------------
0382 function mpc = userfcn_reserves_savecase(mpc, fd, prefix, args)
0383 %
0384 %   mpc = userfcn_reserves_savecase(mpc, fd, mpopt, args)
0385 %
0386 %   This is the 'savecase' stage userfcn callback that prints the M-file
0387 %   code to save the 'reserves' field in the case file. It expects a
0388 %   MATPOWER case struct (mpc), a file descriptor and variable prefix
0389 %   (usually 'mpc.'). The optional args are not currently used.
0390 
0391 r = mpc.reserves;
0392 
0393 fprintf(fd, '\n%%%%-----  Reserve Data  -----%%%%\n');
0394 fprintf(fd, '%%%% reserve zones, element i, j is 1 if gen j is in zone i, 0 otherwise\n');
0395 fprintf(fd, '%sreserves.zones = [\n', prefix);
0396 template = '';
0397 for i = 1:size(r.zones, 2)
0398     template = [template, '\t%d'];
0399 end
0400 template = [template, ';\n'];
0401 fprintf(fd, template, r.zones.');
0402 fprintf(fd, '];\n');
0403 
0404 fprintf(fd, '\n%%%% reserve requirements for each zone in MW\n');
0405 fprintf(fd, '%sreserves.req = [\t%g', prefix, r.req(1));
0406 if length(r.req) > 1
0407     fprintf(fd, ';\t%g', r.req(2:end));
0408 end
0409 fprintf(fd, '\t];\n');
0410 
0411 fprintf(fd, '\n%%%% reserve costs in $/MW for each gen that belongs to at least 1 zone\n');
0412 fprintf(fd, '%%%% (same order as gens, but skipping any gen that does not belong to any zone)\n');
0413 fprintf(fd, '%sreserves.cost = [\t%g', prefix, r.cost(1));
0414 if length(r.cost) > 1
0415     fprintf(fd, ';\t%g', r.cost(2:end));
0416 end
0417 fprintf(fd, '\t];\n');
0418 
0419 if isfield(r, 'qty')
0420     fprintf(fd, '\n%%%% OPTIONAL max reserve quantities for each gen that belongs to at least 1 zone\n');
0421     fprintf(fd, '%%%% (same order as gens, but skipping any gen that does not belong to any zone)\n');
0422     fprintf(fd, '%sreserves.qty = [\t%g', prefix, r.qty(1));
0423     if length(r.qty) > 1
0424         fprintf(fd, ';\t%g', r.qty(2:end));
0425     end
0426     fprintf(fd, '\t];\n');
0427 end
0428 
0429 %% save output fields for solved case
0430 if isfield(r, 'R')
0431     if exist('serialize', 'file') == 2
0432         fprintf(fd, '\n%%%% solved values\n');
0433         fprintf(fd, '%sreserves.R = %s\n', prefix, serialize(r.R));
0434         fprintf(fd, '%sreserves.Rmin = %s\n', prefix, serialize(r.Rmin));
0435         fprintf(fd, '%sreserves.Rmax = %s\n', prefix, serialize(r.Rmax));
0436         fprintf(fd, '%sreserves.mu.l = %s\n', prefix, serialize(r.mu.l));
0437         fprintf(fd, '%sreserves.mu.u = %s\n', prefix, serialize(r.mu.u));
0438         fprintf(fd, '%sreserves.prc = %s\n', prefix, serialize(r.prc));
0439         fprintf(fd, '%sreserves.totalcost = %s\n', prefix, serialize(r.totalcost));
0440     else
0441         url = 'http://www.mathworks.com/matlabcentral/fileexchange/12063';
0442         warning('MATPOWER:serialize', ...
0443             'userfcn_reserves_savecase: Cannot save the ''reserves'' output fields without the ''serialize'' function, which is available as a free download from:\n<%s>\n\n', url);
0444     end
0445 end
toggle_reserves

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SUBFUNCTIONS

SOURCE CODE
