Function Opf Matpower

function [MVAbase, bus, gen, gencost, branch, f, success, et] = ... runopf(casedata, mpopt, fname, solvedcase) %RUNOPF Runs an optimal power flow. % [RESULTS, SUCCESS] = RUNOPF(CASEDATA, MPOPT, FNAME, SOLVEDCASE) % % Runs an optimal power flow (AC OPF by default), optionally returning % a RESULTS struct and SUCCESS flag. % % Inputs (all are optional): % CASEDATA : either a MATPOWER case struct or a string containing % the name of the file with the case data (default is 'case9') % (see also CASEFORMAT and LOADCASE) % MPOPT : MATPOWER options struct to override default options % can be used to specify the solution algorithm, output options % termination tolerances, and more (see also MPOPTION). % FNAME : name of a file to which the pretty-printed output will % be appended % SOLVEDCASE : name of file to which the solved case will be saved % in MATPOWER case format (M-file will be assumed unless the % specified name ends with '.mat') % % Outputs (all are optional): % RESULTS : results struct, with the following fields: % (all fields from the input MATPOWER case, i.e. bus, branch, % gen, etc., but with solved voltages, power flows, etc.) % order - info used in external internal data conversion % et - elapsed time in seconds % success - success flag, 1 = succeeded, 0 = failed % (additional OPF fields, see OPF for details) % SUCCESS : the success flag can additionally be returned as % a second output argument % % Calling syntax options: % results = runopf; % results = runopf(casedata); % results = runopf(casedata, mpopt); % results = runopf(casedata, mpopt, fname); % results = runopf(casedata, mpopt, fname, solvedcase); % [results, success] = runopf(...); % % Alternatively, for compatibility with previous versions of MATPOWER, % some of the results can be returned as individual output arguments: % % [baseMVA, bus, gen, gencost, branch, f, success, et] = runopf(...); % % Example: % results = runopf('case30'); % % See also RUNDCOPF, RUNUOPF.

% MATPOWER % $Id: runopf.m 2411 2014-11-04 20:13:56Z ray $ % by Ray Zimmerman, PSERC Cornell % Copyright (c) 1996-2010 by Power System Engineering Research Center

(PSERC) % % This file is part of MATPOWER.

% See http://www.pserc.cornell.edu/matpower/ for more info. % % MATPOWER is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published % by the Free Software Foundation, either version 3 of the License, % or (at your option) any later version. % % MATPOWER is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with MATPOWER. If not, see . % % Additional permission under GNU GPL version 3 section 7 % % If you modify MATPOWER, or any covered work, to interface with % other modules (such as MATLAB code and MEX-files) available in a % MATLAB(R) or comparable environment containing parts covered % under other licensing terms, the licensors of MATPOWER grant % you additional permission to convey the resulting work.

%%----- initialize ----- %% default arguments if nargin < 4 solvedcase = ''; %% don't save solved case if nargin < 3 fname = ''; %% don't print results to a file if nargin < 2 mpopt = mpoption; %% use default options if nargin < 1 casedata = 'case9'; %% default data file is 'case9.m' end end end end

%%----- run the optimal power flow ----- [r, success] = opf(casedata, mpopt);

%%----- output results ----- if fname [fd, msg] = fopen(fname, 'at'); if fd == -1 error(msg); else if mpopt.out.all == 0 printpf(r, fd, mpoption(mpopt, 'out.all', -1)); else printpf(r, fd, mpopt); end fclose(fd); end end printpf(r, 1, mpopt);

%% save solved case if solvedcase savecase(solvedcase, r); end

if nargout == 1 || nargout == 2 MVAbase = r; bus = success; elseif nargout > 2 [MVAbase, bus, gen, gencost, branch, f, et] = ... deal(r.baseMVA, r.bus, r.gen, r.gencost, r.branch, r.f, r.et); % else %% don't define MVAbase, so it doesn't print anything end

function [busout, genout, branchout, f, success, info, et, g, jac, xr, pimul]

= ... opf(varargin) %OPF Solves an optimal power flow. % [RESULTS, SUCCESS] = OPF(MPC, MPOPT) % % Returns either a RESULTS struct and an optional SUCCESS flag, or

individual % data matrices, the objective function value and a SUCCESS flag. In the % latter case, there are additional optional return values. See Examples % below for the possible calling syntax options. % % Examples: % Output argument options: % % results = opf(...) % [results, success] = opf(...) % [bus, gen, branch, f, success] = opf(...) % [bus, gen, branch, f, success, info, et, g, jac, xr, pimul] =

opf(...) % % Input arguments options: % % opf(mpc) % opf(mpc, mpopt) % opf(mpc, userfcn, mpopt) % opf(mpc, A, l, u) % opf(mpc, A, l, u, mpopt) % opf(mpc, A, l, u, mpopt, N, fparm, H, Cw) % opf(mpc, A, l, u, mpopt, N, fparm, H, Cw, z0, zl, zu) % % opf(baseMVA, bus, gen, branch, areas, gencost) % opf(baseMVA, bus, gen, branch, areas, gencost, mpopt) % opf(baseMVA, bus, gen, branch, areas, gencost, userfcn, mpopt) % opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u) % opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u, mpopt) % opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u, ... % mpopt, N, fparm, H, Cw) % opf(baseMVA, bus, gen, branch, areas, gencost, A, l, u, ... % mpopt, N, fparm, H, Cw, z0, zl, zu) % % The data for the problem can be specified in one of three ways: % (1) a string (mpc) containing the file name of a MATPOWER case % which defines the data matrices baseMVA, bus, gen, branch, and % gencost (areas is not used at all, it is only included for % backward compatibility of the API). % (2) a struct (mpc) containing the data matrices as fields. % (3) the individual data matrices themselves. % % The optional user parameters for user constraints (A, l, u), user costs % (N, fparm, H, Cw), user variable initializer (z0), and user variable % limits (zl, zu) can also be specified as fields in a case struct, % either passed in directly or defined in a case file referenced by name. % % When specified, A, l, u represent additional linear constraints on the % optimization variables, l

% then there are extra linearly constrained "z" variables. For an % explanation of the formulation used and instructions for forming the % A matrix, see the manual. % % A generalized cost on all variables can be applied if input arguments % N, fparm, H and Cw are specified. First, a linear transformation % of the optimization variables is defined by means of r = N * [x; z]. % Then, to each element of r a function is applied as encoded in the % fparm matrix (see manual). If the resulting vector is named w, % then H and Cw define a quadratic cost on w: (1/2)*w'*H*w + Cw * w . % H and N should be sparse matrices and H should also be symmetric. % % The optional mpopt vector specifies MATPOWER options. If the OPF % algorithm is not explicitly set in the options MATPOWER will use % the default solver, based on a primal-dual interior point method. % For the AC OPF this is opf.ac.solver = 'MIPS', unless the TSPOPF optional % package is installed, in which case the default is 'PDIPM'. For the % DC OPF, the default is opf.dc.solver = 'MIPS'. See MPOPTION for % more details on the available OPF solvers and other OPF options % and their default values. % % The solved case is returned either in a single results struct (described % below) or in the individual data matrices, bus, gen and branch. Also % returned are the final objective function value (f) and a flag which is % true if the algorithm was successful in finding a solution (success). % Additional optional return values are an algorithm specific return status % (info), elapsed time in seconds (et), the constraint vector (g), the % Jacobian matrix (jac), and the vector of variables (xr) as well % as the constraint multipliers (pimul). % % The single results struct is a MATPOWER case struct (mpc) with the % usual baseMVA, bus, branch, gen, gencost fields, along with the % following additional fields: % % .order see 'help ext2int' for details of this field % .et elapsed time in seconds for solving OPF % .success 1 if solver converged successfully, 0 otherwise % .om OPF model object, see 'help opf_model' % .x final value of optimization variables (internal order) % .f final objective function value % .mu shadow prices on ... % .var % .l lower bounds on variables % .u upper bounds on variables % .nln % .l lower bounds on nonlinear constraints % .u upper bounds on nonlinear constraints % .lin % .l lower bounds on linear constraints % .u upper bounds on linear constraints % .raw raw solver output in form returned by MINOS, and more % .xr final value of optimization variables % .pimul constraint multipliers % .info solver specific termination code % .output solver specific output information % .alg algorithm code of solver used % .g (optional) constraint values

% .dg (optional) constraint 1st derivatives % .df (optional) obj fun 1st derivatives (not yet implemented) % .d2f (optional) obj fun 2nd derivatives (not yet implemented) % .var % .val optimization variable values, by named block % .Va voltage angles % .Vm voltage magnitudes (AC only) % .Pg real power injections % .Qg reactive power injections (AC only) % .y constrained cost variable (only if have pwl costs) % (other) any user defined variable blocks % .mu variable bound shadow prices, by named block % .l lower bound shadow prices % .Va, Vm, Pg, Qg, y, (other) % .u upper bound shadow prices % .Va, Vm, Pg, Qg, y, (other) % .nln (AC only) % .mu shadow prices on nonlinear constraints, by named block % .l lower bounds % .Pmis real power mismatch equations % .Qmis reactive power mismatch equations % .Sf flow limits at "from" end of branches % .St flow limits at "to" end of branches % .u upper bounds % .Pmis, Qmis, Sf, St % .lin % .mu shadow prices on linear constraints, by named block % .l lower bounds % .Pmis real power mistmatch equations (DC only) % .Pf flow limits at "from" end of branches (DC only) % .Pt flow limits at "to" end of branches (DC only) % .PQh upper portion of gen PQ-capability curve (AC

only) % .PQl lower portion of gen PQ-capability curve (AC

only) % .vl constant power factor constraint for loads (AC

only) % .ycon basin constraints for CCV for pwl costs % (other) any user defined constraint blocks % .u upper bounds % .Pmis, Pf, Pt, PQh, PQl, vl, ycon, (other) % .cost user defined cost values, by named block % % See also RUNOPF, DCOPF, UOPF, CASEFORMAT.

% MATPOWER % $Id: opf.m 2229 2013-12-11 01:28:09Z ray $ % by Ray Zimmerman, PSERC Cornell % and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de

Manizales % Copyright (c) 1996-2010 by Power System Engineering Research Center

(PSERC) % % This file is part of MATPOWER. % See http://www.pserc.cornell.edu/matpower/ for more info. % % MATPOWER is free software: you can redistribute it and/or modify

% it under the terms of the GNU General Public License as published % by the Free Software Foundation, either version 3 of the License, % or (at your option) any later version. % % MATPOWER is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with MATPOWER. If not, see . % % Additional permission under GNU GPL version 3 section 7 % % If you modify MATPOWER, or any covered work, to interface with % other modules (such as MATLAB code and MEX-files) available in a % MATLAB(R) or comparable environment containing parts covered % under other licensing terms, the licensors of MATPOWER grant % you additional permission to convey the resulting work.

%%----- initialization ----- t0 = clock; %% start timer

%% define named indices into data matrices [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ... VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus; [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ... MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ... QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen; [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ... TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ... ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch; [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;

%% process input arguments [mpc, mpopt] = opf_args(varargin{:});

%% add zero columns to bus, gen, branch for multipliers, etc if needed nb = size(mpc.bus, 1); %% number of buses nl = size(mpc.branch, 1); %% number of branches ng = size(mpc.gen, 1); %% number of dispatchable injections if size(mpc.bus,2) < MU_VMIN mpc.bus = [mpc.bus zeros(nb, MU_VMIN-size(mpc.bus,2)) ]; end if size(mpc.gen,2) < MU_QMIN mpc.gen = [ mpc.gen zeros(ng, MU_QMIN-size(mpc.gen,2)) ]; end if size(mpc.branch,2) < MU_ANGMAX mpc.branch = [ mpc.branch zeros(nl, MU_ANGMAX-size(mpc.branch,2)) ]; end

%%----- convert to internal numbering, remove out-of-service stuff ----- mpc = ext2int(mpc);

%%----- construct OPF model object ----- om = opf_setup(mpc, mpopt);

%%----- execute the OPF ----- if nargout > 7 mpopt.opf.return_raw_der = 1; end [results, success, raw] = opf_execute(om, mpopt);

%%----- revert to original ordering, including out-of-service stuff ----- results = int2ext(results);

%% zero out result fields of out-of-service gens & branches if ~isempty(results.order.gen.status.off) results.gen(results.order.gen.status.off, [PG QG MU_PMAX MU_PMIN]) = 0; end if ~isempty(results.order.branch.status.off) results.branch(results.order.branch.status.off, [PF QF PT QT MU_SF MU_ST

MU_ANGMIN MU_ANGMAX]) = 0; end

%%----- finish preparing output ----- et = etime(clock, t0); %% compute elapsed time if nargout > 0 if nargout

function [baseMVA, bus, gen, branch, gencost, Au, lbu, ubu, ... mpopt, N, fparm, H, Cw, z0, zl, zu, userfcn] = ... opf_args(baseMVA, bus, gen, branch, areas, gencost, Au, lbu, ubu, ... mpopt, N, fparm, H, Cw, z0, zl, zu) %OPF_ARGS Parses and initializes OPF input arguments. % [MPC, MPOPT] = OPF_ARGS( ... ) % [BASEMVA, BUS, GEN, BRANCH, GENCOST, A, L, U, MPOPT, ... % N, FPARM, H, CW, Z0, ZL, ZU, USERFCN] = OPF_ARGS( ... ) % Returns the full set of initialized OPF input arguments, filling in % default values for missing arguments. See Examples below for the % possible calling syntax options. % % Examples: % Output argument options: % % [mpc, mpopt] = opf_args( ... ) % [baseMVA, bus, gen, branch, gencost, A, l, u, mpopt, ... % N, fparm, H, Cw, z0, zl, zu, userfcn] = opf_args( ... ) % % Input arguments options: % % opf_args(mpc) % opf_args(mpc, mpopt) % opf_args(mpc, userfcn, mpopt) % opf_args(mpc, A, l, u) % opf_args(mpc, A, l, u, mpopt) % opf_args(mpc, A, l, u, mpopt, N, fparm, H, Cw) % opf_args(mpc, A, l, u, mpopt, N, fparm, H, Cw, z0, zl, zu) % % opf_args(baseMVA, bus, gen, branch, areas, gencost) % opf_args(baseMVA, bus, gen, branch, areas, gencost, mpopt) % opf_args(baseMVA, bus, gen, branch, areas, gencost, userfcn, mpopt) % opf_args(baseMVA, bus, gen, branch, areas, gencost, A, l, u) % opf_args(baseMVA, bus, gen, branch, areas, gencost, A, l, u, mpopt) % opf_args(baseMVA, bus, gen, branch, areas, gencost, A, l, u, ... % mpopt, N, fparm, H, Cw) % opf_args(baseMVA, bus, gen, branch, areas, gencost, A, l, u, ... % mpopt, N, fparm, H, Cw, z0, zl, zu) % % The data for the problem can be specified in one of three ways: % (1) a string (mpc) containing the file name of a MATPOWER case % which defines the data matrices baseMVA, bus, gen, branch, and % gencost (areas is not used at all, it is only included for % backward compatibility of the API). % (2) a struct (mpc) containing the data matrices as fields. % (3) the individual data matrices themselves. % % The optional user parameters for user constraints (A, l, u), user costs % (N, fparm, H, Cw), user variable initializer (z0), and user variable % limits (zl, zu) can also be specified as fields in a case struct, % either passed in directly or defined in a case file referenced by name. % % When specified, A, l, u represent additional linear constraints on the % optimization variables, l

% A matrix, see the manual. % % A generalized cost on all variables can be applied if input arguments % N, fparm, H and Cw are specified. First, a linear transformation % of the optimization variables is defined by means of r = N * [x; z]. % Then, to each element of r a function is applied as encoded in the % fparm matrix (see manual). If the resulting vector is named w, % then H and Cw define a quadratic cost on w: (1/2)*w'*H*w + Cw * w . % H and N should be sparse matrices and H should also be symmetric. % % The optional mpopt vector specifies MATPOWER options. See MPOPTION % for details and default values.

% MATPOWER % $Id: opf_args.m 2409 2014-10-22 20:59:54Z ray $ % by Ray Zimmerman, PSERC Cornell % and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de


(PSERC) % % This file is part of MATPOWER. % See http://www.pserc.cornell.edu/matpower/ for more info. % % MATPOWER is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published % by the Free Software Foundation, either version 3 of the License, % or (at your option) any later version. % % MATPOWER is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with MATPOWER. If not, see . % % Additional permission under GNU GPL version 3 section 7 % % If you modify MATPOWER, or any covered work, to interface with % other modules (such as MATLAB code and MEX-files) available in a % MATLAB(R) or comparable environment containing parts covered % under other licensing terms, the licensors of MATPOWER grant % you additional permission to convey the resulting work.

if nargout == 2 want_mpc = 1; else want_mpc = 0; end userfcn = []; if ischar(baseMVA) || isstruct(baseMVA) %% passing filename or struct %---- opf(baseMVA, bus, gen, branch, areas, gencost, Au, lbu, ubu,

mpopt, N, fparm, H, Cw, z0, zl, zu) % 12 opf(casefile, Au, lbu, ubu, mpopt, N, fparm, H, Cw,

z0, zl, zu)

% 9 opf(casefile, Au, lbu, ubu, mpopt, N, fparm, H, Cw) % 5 opf(casefile, Au, lbu, ubu, mpopt) % 4 opf(casefile, Au, lbu, ubu) % 3 opf(casefile, userfcn, mpopt) % 2 opf(casefile, mpopt) % 1 opf(casefile) if any(nargin == [1, 2, 3, 4, 5, 9, 12]) casefile = baseMVA; if nargin == 12 zu = fparm; zl = N; z0 = mpopt; Cw = ubu; H = lbu; fparm = Au; N = gencost; mpopt = areas; ubu = branch; lbu = gen; Au = bus; elseif nargin == 9 zu = []; zl = []; z0 = []; Cw = ubu; H = lbu; fparm = Au; N = gencost; mpopt = areas; ubu = branch; lbu = gen; Au = bus; elseif nargin == 5 zu = []; zl = []; z0 = []; Cw = []; H = sparse(0,0); fparm = []; N = sparse(0,0); mpopt = areas; ubu = branch; lbu = gen; Au = bus; elseif nargin == 4 zu = []; zl = []; z0 = []; Cw = []; H = sparse(0,0); fparm = []; N = sparse(0,0); mpopt = mpoption; ubu = branch; lbu = gen; Au = bus; elseif nargin == 3

userfcn = bus; zu = []; zl = []; z0 = []; Cw = []; H = sparse(0,0); fparm = []; N = sparse(0,0); mpopt = gen; ubu = []; lbu = []; Au = sparse(0,0); elseif nargin == 2 zu = []; zl = []; z0 = []; Cw = []; H = sparse(0,0); fparm = []; N = sparse(0,0); mpopt = bus; ubu = []; lbu = []; Au = sparse(0,0); elseif nargin == 1 zu = []; zl = []; z0 = []; Cw = []; H = sparse(0,0); fparm = []; N = sparse(0,0); mpopt = mpoption; ubu = []; lbu = []; Au = sparse(0,0); end else error('opf_args.m: Incorrect input parameter order, number or type'); end mpc = loadcase(casefile); [baseMVA, bus, gen, branch, gencost] = ... deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch, mpc.gencost); if isfield(mpc, 'areas') areas = mpc.areas; else areas = []; end if isempty(Au) && isfield(mpc, 'A') [Au, lbu, ubu] = deal(mpc.A, mpc.l, mpc.u); end if isempty(N) && isfield(mpc, 'N') %% these two must go

together [N, Cw] = deal(mpc.N, mpc.Cw); end if isempty(H) && isfield(mpc, 'H') %% will default to zeros H = mpc.H;

end if isempty(fparm) && isfield(mpc, 'fparm') %% will default to [1 0 0 1] fparm = mpc.fparm; end if isempty(z0) && isfield(mpc, 'z0') z0 = mpc.z0; end if isempty(zl) && isfield(mpc, 'zl') zl = mpc.zl; end if isempty(zu) && isfield(mpc, 'zu') zu = mpc.zu; end if isempty(userfcn) && isfield(mpc, 'userfcn') userfcn = mpc.userfcn; end else %% passing individual data matrices %---- opf(baseMVA, bus, gen, branch, areas, gencost, Au, lbu, ubu,

mpopt, N, fparm, H, Cw, z0, zl, zu) % 17 opf(baseMVA, bus, gen, branch, areas, gencost, Au, lbu, ubu,

mpopt, N, fparm, H, Cw, z0, zl, zu) % 14 opf(baseMVA, bus, gen, branch, areas, gencost, Au, lbu, ubu,

mpopt, N, fparm, H, Cw) % 10 opf(baseMVA, bus, gen, branch, areas, gencost, Au, lbu, ubu,

mpopt) % 9 opf(baseMVA, bus, gen, branch, areas, gencost, Au, lbu, ubu) % 8 opf(baseMVA, bus, gen, branch, areas, gencost, userfcn, mpopt) % 7 opf(baseMVA, bus, gen, branch, areas, gencost, mpopt) % 6 opf(baseMVA, bus, gen, branch, areas, gencost) if any(nargin == [6, 7, 8, 9, 10, 14, 17]) if nargin == 14 zu = []; zl = []; z0 = []; elseif nargin == 10 zu = []; zl = []; z0 = []; Cw = []; H = sparse(0,0); fparm = []; N = sparse(0,0); elseif nargin == 9 zu = []; zl = []; z0 = []; Cw = []; H = sparse(0,0); fparm = []; N = sparse(0,0); mpopt = mpoption; elseif nargin == 8 userfcn = Au; zu = []; zl = []; z0 = []; Cw = [];

H = sparse(0,0); fparm = []; N = sparse(0,0); mpopt = lbu; ubu = []; lbu = []; Au = sparse(0,0); elseif nargin == 7 zu = []; zl = []; z0 = []; Cw = []; H = sparse(0,0); fparm = []; N = sparse(0,0); mpopt = Au; ubu = []; lbu = []; Au = sparse(0,0); elseif nargin == 6 zu = []; zl = []; z0 = []; Cw = []; H = sparse(0,0); fparm = []; N = sparse(0,0); mpopt = mpoption; ubu = []; lbu = []; Au = sparse(0,0); end else error('opf_args.m: Incorrect input parameter order, number or type'); end if want_mpc mpc = struct( ... 'baseMVA', baseMVA, ... 'bus', bus, ... 'gen', gen, ... 'branch', branch, ... 'gencost', gencost ... ); end end nw = size(N, 1); if nw if size(Cw, 1) ~= nw error('opf_args.m: dimension mismatch between N and Cw in generalized

cost parameters'); end if ~isempty(fparm) && size(fparm, 1) ~= nw error('opf_args.m: dimension mismatch between N and fparm in generalized

cost parameters'); end if ~isempty(H) && (size(H, 1) ~= nw || size(H, 2) ~= nw)

error('opf_args.m: dimension mismatch between N and H in generalized cost

parameters'); end if size(Au, 1) > 0 && size(N, 2) ~= size(Au, 2) error('opf_args.m: A and N must have the same number of columns'); end %% make sure N and H are sparse if ~issparse(N) error('opf_args.m: N must be sparse in generalized cost parameters'); end if ~issparse(H) error('opf_args.m: H must be sparse in generalized cost parameters'); end end if ~issparse(Au) error('opf_args.m: Au must be sparse'); end if isempty(mpopt) mpopt = mpoption; end if want_mpc if ~isempty(areas) mpc.areas = areas; end if ~isempty(Au) [mpc.A, mpc.l, mpc.u] = deal(Au, lbu, ubu); end if ~isempty(N) [mpc.N, mpc.Cw ] = deal(N, Cw); if ~isempty(fparm) mpc.fparm = fparm; end if ~isempty(H) mpc.H = H; end end if ~isempty(z0) mpc.z0 = z0; end if ~isempty(zl) mpc.zl = zl; end if ~isempty(zu) mpc.zu = zu; end if ~isempty(userfcn) mpc.userfcn = userfcn; end baseMVA = mpc; bus = mpopt; end

function om = opf_setup(mpc, mpopt) %OPF Constructs an OPF model object from a MATPOWER case struct. % OM = OPF_SETUP(MPC, MPOPT) % % Assumes that MPC is a MATPOWER case struct with internal indexing, % all equipment in-service, etc. % % See also OPF, EXT2INT, OPF_EXECUTE.

% MATPOWER % $Id: opf_setup.m 2435 2014-12-03 20:55:02Z ray $ % by Ray Zimmerman, PSERC Cornell % and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de



%% options dc = strcmp(upper(mpopt.model), 'DC'); alg = upper(mpopt.opf.ac.solver);

%% define named indices into data matrices [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ... VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus; [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ... MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ... QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen; [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ... TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ... ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch; [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;

%% data dimensions nb = size(mpc.bus, 1); %% number of buses nl = size(mpc.branch, 1); %% number of branches ng = size(mpc.gen, 1); %% number of dispatchable injections if isfield(mpc, 'A') nusr = size(mpc.A, 1); %% number of linear user constraints else nusr = 0; end if isfield(mpc, 'N') nw = size(mpc.N, 1); %% number of general cost vars, w else nw = 0; end

if dc %% ignore reactive costs for DC mpc.gencost = pqcost(mpc.gencost, ng);

%% reduce A and/or N from AC dimensions to DC dimensions, if needed if nusr || nw acc = [nb+(1:nb) 2*nb+ng+(1:ng)]; %% Vm and Qg columns if nusr && size(mpc.A, 2) >= 2*nb + 2*ng %% make sure there aren't any constraints on Vm or Qg if any(any(mpc.A(:, acc))) error('opf_setup: attempting to solve DC OPF with user constraints on

Vm or Qg'); end mpc.A(:, acc) = []; %% delete Vm and Qg columns end if nw && size(mpc.N, 2) >= 2*nb + 2*ng %% make sure there aren't any costs on Vm or Qg if any(any(mpc.N(:, acc))) [ii, jj] = find(mpc.N(:, acc)); ii = unique(ii); %% indices of w with potential non-zero cost

terms from Vm or Qg if any(mpc.Cw(ii)) || (isfield(mpc, 'H') && ~isempty(mpc.H) && ... any(any(mpc.H(:, ii)))) error('opf_setup: attempting to solve DC OPF with user costs on Vm

or Qg'); end end mpc.N(:, acc) = []; %% delete Vm and Qg columns end end end

%% convert single-block piecewise-linear costs into linear polynomial cost pwl1 = find(mpc.gencost(:, MODEL) == PW_LINEAR & mpc.gencost(:, NCOST) == 2); % p1 = []; if ~isempty(pwl1) x0 = mpc.gencost(pwl1, COST); y0 = mpc.gencost(pwl1, COST+1); x1 = mpc.gencost(pwl1, COST+2); y1 = mpc.gencost(pwl1, COST+3); m = (y1 - y0) ./ (x1 - x0);

b = y0 - m .* x0; mpc.gencost(pwl1, MODEL) = POLYNOMIAL; mpc.gencost(pwl1, NCOST) = 2; mpc.gencost(pwl1, COST:COST+1) = [m b]; end

%% create (read-only) copies of individual fields for convenience [baseMVA, bus, gen, branch, gencost, Au, lbu, ubu, mpopt, ... N, fparm, H, Cw, z0, zl, zu, userfcn] = opf_args(mpc, mpopt);

%% warn if there is more than one reference bus refs = find(bus(:, BUS_TYPE) == REF); if length(refs) > 1 && mpopt.verbose > 0 errstr = ['\nopf_setup: Warning: Multiple reference buses.\n', ... ' For a system with islands, a reference bus in each

island\n', ... ' may help convergence, but in a fully connected

system such\n', ... ' a situation is probably not reasonable.\n\n' ]; fprintf(errstr); end

%% set up initial variables and bounds Va = bus(:, VA) * (pi/180); Vm = bus(:, VM); Pg = gen(:, PG) / baseMVA; Qg = gen(:, QG) / baseMVA; Pmin = gen(:, PMIN) / baseMVA; Pmax = gen(:, PMAX) / baseMVA; Qmin = gen(:, QMIN) / baseMVA; Qmax = gen(:, QMAX) / baseMVA;

if dc %% DC model %% more problem dimensions nv = 0; %% number of voltage magnitude vars nq = 0; %% number of Qg vars q1 = []; %% index of 1st Qg column in Ay

%% power mismatch constraints [B, Bf, Pbusinj, Pfinj] = makeBdc(baseMVA, bus, branch); neg_Cg = sparse(gen(:, GEN_BUS), 1:ng, -1, nb, ng); %% Pbus w.r.t. Pg Amis = [B neg_Cg]; bmis = -(bus(:, PD) + bus(:, GS)) / baseMVA - Pbusinj;

%% branch flow constraints il = find(branch(:, RATE_A) ~= 0 & branch(:, RATE_A) < 1e10); nl2 = length(il); %% number of constrained lines if nl2 upf = branch(il, RATE_A) / baseMVA - Pfinj(il); upt = branch(il, RATE_A) / baseMVA + Pfinj(il); else upf = []; upt = []; end

user_vars = {'Va', 'Pg'}; ycon_vars = {'Pg', 'y'}; else %% AC model %% more problem dimensions nv = nb; %% number of voltage magnitude vars nq = ng; %% number of Qg vars q1 = 1+ng; %% index of 1st Qg column in Ay

%% dispatchable load, constant power factor constraints [Avl, lvl, uvl] = makeAvl(baseMVA, gen);

%% generator PQ capability curve constraints [Apqh, ubpqh, Apql, ubpql, Apqdata] = makeApq(baseMVA, gen);

user_vars = {'Va', 'Vm', 'Pg', 'Qg'}; ycon_vars = {'Pg', 'Qg', 'y'}; end

%% voltage angle reference constraints Vau = Inf * ones(nb, 1); Val = -Vau; Vau(refs) = Va(refs); Val(refs) = Va(refs);

%% branch voltage angle difference limits [Aang, lang, uang, iang] = makeAang(baseMVA, branch, nb, mpopt);

%% basin constraints for piece-wise linear gen cost variables if (strcmp(alg, 'PDIPM') && mpopt.pdipm.step_control) || strcmp(alg, 'TRALM') %% SC-PDIPM or TRALM, no CCV cost vars ny = 0; Ay = sparse(0, ng+nq); by =[]; else ipwl = find(gencost(:, MODEL) == PW_LINEAR); %% piece-wise linear costs ny = size(ipwl, 1); %% number of piece-wise linear cost vars [Ay, by] = makeAy(baseMVA, ng, gencost, 1, q1, 1+ng+nq); end if any(gencost(:, MODEL) ~= POLYNOMIAL & gencost(:, MODEL) ~= PW_LINEAR) error('opf_setup: some generator cost rows have invalid MODEL value'); end

%% more problem dimensions nx = nb+nv + ng+nq; %% number of standard OPF control variables if nusr nz = size(mpc.A, 2) - nx; %% number of user z variables if nz < 0 error('opf_setup: user supplied A matrix must have at least %d columns.',

nx); end else nz = 0; %% number of user z variables if nw %% still need to check number of columns of N if size(mpc.N, 2) ~= nx;

error('opf_setup: user supplied N matrix must have %d columns.', nx); end end end

%% construct OPF model object om = opf_model(mpc); if ~isempty(pwl1) om = userdata(om, 'pwl1', pwl1); end if dc om = userdata(om, 'Bf', Bf); om = userdata(om, 'Pfinj', Pfinj); om = userdata(om, 'iang', iang); om = add_vars(om, 'Va', nb, Va, Val, Vau); om = add_vars(om, 'Pg', ng, Pg, Pmin, Pmax); om = add_constraints(om, 'Pmis', Amis, bmis, bmis, {'Va', 'Pg'}); %% nb om = add_constraints(om, 'Pf', Bf(il,:), -upt, upf, {'Va'}); %% nl2 om = add_constraints(om, 'ang', Aang, lang, uang, {'Va'}); %% nang else om = userdata(om, 'Apqdata', Apqdata); om = userdata(om, 'iang', iang); om = add_vars(om, 'Va', nb, Va, Val, Vau); om = add_vars(om, 'Vm', nb, Vm, bus(:, VMIN), bus(:, VMAX)); om = add_vars(om, 'Pg', ng, Pg, Pmin, Pmax); om = add_vars(om, 'Qg', ng, Qg, Qmin, Qmax); om = add_constraints(om, 'Pmis', nb, 'nonlinear'); om = add_constraints(om, 'Qmis', nb, 'nonlinear'); om = add_constraints(om, 'Sf', nl, 'nonlinear'); om = add_constraints(om, 'St', nl, 'nonlinear'); om = add_constraints(om, 'PQh', Apqh, [], ubpqh, {'Pg', 'Qg'}); %% npqh om = add_constraints(om, 'PQl', Apql, [], ubpql, {'Pg', 'Qg'}); %% npql om = add_constraints(om, 'vl', Avl, lvl, uvl, {'Pg', 'Qg'}); %% nvl om = add_constraints(om, 'ang', Aang, lang, uang, {'Va'}); %% nang end

%% y vars, constraints for piece-wise linear gen costs if ny > 0 om = add_vars(om, 'y', ny); om = add_constraints(om, 'ycon', Ay, [], by, ycon_vars); %% ncony end

%% add user vars, constraints and costs (as specified via A, ..., N, ...) if nz > 0 om = add_vars(om, 'z', nz, z0, zl, zu); user_vars{end+1} = 'z'; end if nusr om = add_constraints(om, 'usr', mpc.A, lbu, ubu, user_vars); %% nusr end if nw user_cost.N = mpc.N; user_cost.Cw = Cw; if ~isempty(fparm) user_cost.dd = fparm(:, 1); user_cost.rh = fparm(:, 2);

user_cost.kk = fparm(:, 3); user_cost.mm = fparm(:, 4); end if ~isempty(H) user_cost.H = H; end om = add_costs(om, 'usr', user_cost, user_vars); end

%% execute userfcn callbacks for 'formulation' stage om = run_userfcn(userfcn, 'formulation', om);

function [results, success, raw] = opf_execute(om, mpopt) %OPF_EXECUTE Executes the OPF specified by an OPF model object. % [RESULTS, SUCCESS, RAW] = OPF_EXECUTE(OM, MPOPT) % % RESULTS are returned with internal indexing, all equipment % in-service, etc. % % See also OPF, OPF_SETUP.

% MATPOWER % $Id: opf_execute.m 2375 2014-09-08 18:26:13Z ray $ % by Ray Zimmerman, PSERC Cornell % Copyright (c) 2009-2010 by Power System Engineering Research Center


%% define named indices into data matrices [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ... VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus; [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ... MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ... QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen; [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ... TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ... ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;

%%----- setup ----- %% options dc = strcmp(upper(mpopt.model), 'DC'); alg = upper(mpopt.opf.ac.solver); sdp = strcmp(alg, 'SDPOPF');

%% build user-defined costs

om = build_cost_params(om);

%% get indexing [vv, ll, nn] = get_idx(om);

if mpopt.verbose > 0 v = mpver('all'); fprintf('\nMATPOWER Version %s, %s', v.Version, v.Date); end

%%----- run DC OPF solver ----- if dc if mpopt.verbose > 0 fprintf(' -- DC Optimal Power Flow\n'); end [results, success, raw] = dcopf_solver(om, mpopt); else %%----- run AC OPF solver ----- if mpopt.verbose > 0 fprintf(' -- AC Optimal Power Flow\n'); end

%% if opf.ac.solver not set, choose best available option if strcmp(alg, 'DEFAULT') if have_fcn('pdipmopf') alg = 'PDIPM'; %% PDIPM else alg = 'MIPS'; %% MIPS end mpopt = mpoption(mpopt, 'opf.ac.solver', alg); end

%% Algorithm alg = 'FMINCON'; %% tambahan dari pak rony

%% run specific AC OPF solver switch alg case 'MIPS' [results, success, raw] = mipsopf_solver(om, mpopt); case 'IPOPT' if ~have_fcn('ipopt') error('opf_execute: MPOPT.opf.ac.solver = ''%s'' requires IPOPT (see

https://projects.coin-or.org/Ipopt/)', alg); end [results, success, raw] = ipoptopf_solver(om, mpopt); case 'PDIPM' if mpopt.pdipm.step_control if ~have_fcn('scpdipmopf') error('opf_execute: MPOPT.opf.ac.solver = ''%s'' requires

SCPDIPMOPF (see http://www.pserc.cornell.edu/tspopf/)', alg); end else if ~have_fcn('pdipmopf')

error('opf_execute: MPOPT.opf.ac.solver = ''%s'' requires PDIPMOPF

(see http://www.pserc.cornell.edu/tspopf/)', alg); end end [results, success, raw] = tspopf_solver(om, mpopt); case 'TRALM' if ~have_fcn('tralmopf') error('opf_execute: MPOPT.opf.ac.solver = ''%s'' requires TRALM (see

http://www.pserc.cornell.edu/tspopf/)', alg); end [results, success, raw] = tspopf_solver(om, mpopt); case 'MINOPF' if ~have_fcn('minopf') error('opf_execute: MPOPT.opf.ac.solver = ''%s'' requires MINOPF (see

http://www.pserc.cornell.edu/minopf/)', alg); end [results, success, raw] = mopf_solver(om, mpopt); case 'FMINCON' if ~have_fcn('fmincon') error('opf_execute: MPOPT.opf.ac.solver = ''%s'' requires FMINCON

(Optimization Toolbox 2.x or later)', alg); end [results, success, raw] = fmincopf_solver(om, mpopt); case 'KNITRO' if ~have_fcn('knitro') error('opf_execute: MPOPT.opf.ac.solver = ''%s'' requires KNITRO (see

http://www.ziena.com/)', alg); end [results, success, raw] = ktropf_solver(om, mpopt); case 'SDPOPF' if ~have_fcn('yalmip') error('opf_execute: MPOPT.opf.ac.solver = ''%s'' requires YALMIP (see

http://users.isy.liu.se/johanl/yalmip/)', alg); end [results, success, raw] = sdpopf_solver(om, mpopt); otherwise error('opf_execute: MPOPT.opf.ac.solver = ''%s'' is not a valid AC OPF

solver selection', alg); end end if ~isfield(raw, 'output') || ~isfield(raw.output, 'alg') ||

isempty(raw.output.alg) raw.output.alg = alg; end

if success if ~dc && ~sdp %% copy bus voltages back to gen matrix results.gen(:, VG) = results.bus(results.gen(:, GEN_BUS), VM);

%% gen PQ capability curve multipliers if ll.N.PQh > 0 || ll.N.PQl > 0 mu_PQh = results.mu.lin.l(ll.i1.PQh:ll.iN.PQh) -

results.mu.lin.u(ll.i1.PQh:ll.iN.PQh); mu_PQl = results.mu.lin.l(ll.i1.PQl:ll.iN.PQl) -

results.mu.lin.u(ll.i1.PQl:ll.iN.PQl);

Apqdata = userdata(om, 'Apqdata'); results.gen = update_mupq(results.baseMVA, results.gen, mu_PQh, mu_PQl,

Apqdata); end

%% compute g, dg, f, df, d2f if requested by opf.return_raw_der = 1 if mpopt.opf.return_raw_der %% move from results to raw if using v4.0 of MINOPF or TSPOPF if isfield(results, 'dg') raw.dg = results.dg; raw.g = results.g; end %% compute g, dg, unless already done by post-v4.0 MINOPF or TSPOPF if ~isfield(raw, 'dg') mpc = get_mpc(om); [Ybus, Yf, Yt] = makeYbus(mpc.baseMVA, mpc.bus, mpc.branch); [g, geq, dg, dgeq] = opf_consfcn(results.x, om, Ybus, Yf, Yt, mpopt); raw.g = [ geq; g]; raw.dg = [ dgeq'; dg']; %% true Jacobian organization end %% compute df, d2f [f, df, d2f] = opf_costfcn(results.x, om); raw.df = df; raw.d2f = d2f; end end

%% delete g and dg fieldsfrom results if using v4.0 of MINOPF or TSPOPF if isfield(results, 'dg') rmfield(results, 'dg'); rmfield(results, 'g'); end

%% angle limit constraint multipliers if ~sdp && ll.N.ang > 0 iang = userdata(om, 'iang'); results.branch(iang, MU_ANGMIN) = results.mu.lin.l(ll.i1.ang:ll.iN.ang) *

pi/180; results.branch(iang, MU_ANGMAX) = results.mu.lin.u(ll.i1.ang:ll.iN.ang) *

pi/180; end else %% assign empty g, dg, f, df, d2f if requested by opf.return_raw_der = 1 if ~dc && mpopt.opf.return_raw_der raw.dg = []; raw.g = []; raw.df = []; raw.d2f = []; end end

if ~sdp %% assign values and limit shadow prices for variables om_var_order = get(om, 'var', 'order'); for k = 1:length(om_var_order) name = om_var_order(k).name;

if getN(om, 'var', name) idx = vv.i1.(name):vv.iN.(name); results.var.val.(name) = results.x(idx); results.var.mu.l.(name) = results.mu.var.l(idx); results.var.mu.u.(name) = results.mu.var.u(idx); end end

%% assign shadow prices for linear constraints om_lin_order = get(om, 'lin', 'order'); for k = 1:length(om_lin_order) name = om_lin_order(k).name; if getN(om, 'lin', name) idx = ll.i1.(name):ll.iN.(name); results.lin.mu.l.(name) = results.mu.lin.l(idx); results.lin.mu.u.(name) = results.mu.lin.u(idx); end end

%% assign shadow prices for nonlinear constraints if ~dc om_nln_order = get(om, 'nln', 'order'); for k = 1:length(om_nln_order) name = om_nln_order(k).name; if getN(om, 'nln', name) idx = nn.i1.(name):nn.iN.(name); results.nln.mu.l.(name) = results.mu.nln.l(idx); results.nln.mu.u.(name) = results.mu.nln.u(idx); end end end

%% assign values for components of user cost om_cost_order = get(om, 'cost', 'order'); for k = 1:length(om_cost_order) name = om_cost_order(k).name; if getN(om, 'cost', name) results.cost.(name) = compute_cost(om, results.x, name); end end

%% if single-block PWL costs were converted to POLY, insert dummy y into x %% Note: The "y" portion of x will be nonsense, but everything should at %% least be in the expected locations. pwl1 = userdata(om, 'pwl1'); if ~isempty(pwl1) && ~strcmp(alg, 'TRALM') && ~(strcmp(alg, 'PDIPM') &&

mpopt.pdipm.step_control) %% get indexing vv = get_idx(om); if dc nx = vv.iN.Pg; else nx = vv.iN.Qg; end y = zeros(length(pwl1), 1); raw.xr = [ raw.xr(1:nx); y; raw.xr(nx+1:end)];

results.x = [ results.x(1:nx); y; results.x(nx+1:end)]; end end

function [h, g, dh, dg] = opf_consfcn(x, om, Ybus, Yf, Yt, mpopt, il,

varargin) %OPF_CONSFCN Evaluates nonlinear constraints and their Jacobian for OPF. % [H, G, DH, DG] = OPF_CONSFCN(X, OM, YBUS, YF, YT, MPOPT, IL) % % Constraint evaluation function for AC optimal power flow, suitable % for use with MIPS or FMINCON. Computes constraint vectors and their % gradients. % % Inputs: % X : optimization vector % OM : OPF model object % YBUS : bus admittance matrix % YF : admittance matrix for "from" end of constrained branches % YT : admittance matrix for "to" end of constrained branches % MPOPT : MATPOWER options struct % IL : (optional) vector of branch indices corresponding to % branches with flow limits (all others are assumed to be % unconstrained). The default is [1:nl] (all branches). % YF and YT contain only the rows corresponding to IL. % % Outputs: % H : vector of inequality constraint values (flow limits) % limit^2 - flow^2, where the flow can be apparent power % real power or current, depending on value of % opf.flow_lim in MPOPT (only for constrained lines) % G : vector of equality constraint values (power balances) % DH : (optional) inequality constraint gradients, column j is % gradient of H(j) % DG : (optional) equality constraint gradients % % Examples: % [h, g] = opf_consfcn(x, om, Ybus, Yf, Yt, mpopt); % [h, g, dh, dg] = opf_consfcn(x, om, Ybus, Yf, Yt, mpopt); % [h, g, dh, dg] = opf_consfcn(x, om, Ybus, Yf, Yt, mpopt, il); % % See also OPF_COSTFCN, OPF_HESSFCN.

% MATPOWER % $Id: opf_consfcn.m 2266 2014-01-16 18:12:59Z ray $ % by Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de

Manizales % and Ray Zimmerman, PSERC Cornell % Copyright (c) 1996-2010 by Power System Engineering Research Center

(PSERC) % % This file is part of MATPOWER. % See http://www.pserc.cornell.edu/matpower/ for more info. % % MATPOWER is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published % by the Free Software Foundation, either version 3 of the License, % or (at your option) any later version. % % MATPOWER is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the

% GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with MATPOWER. If not, see . % % Additional permission under GNU GPL version 3 section 7 % % If you modify MATPOWER, or any covered work, to interface with % other modules (such as MATLAB code and MEX-files) available in a % MATLAB(R) or comparable environment containing parts covered % under other licensing terms, the licensors of MATPOWER grant % you additional permission to convey the resulting work.

%%----- initialize ----- %% define named indices into data matrices [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ... VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus; [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ... MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, ~, PC2, QC1MIN, QC1MAX, ... QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen; [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ... TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ... ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;

% xd = x; x = x(1:26, 1); %% tambahan dari pak rony %sizex = size(full(x)) %% unpack data mpc = get_mpc(om); [baseMVA, bus, gen, branch] = deal(mpc.baseMVA, mpc.bus, mpc.gen,

mpc.branch); vv = get_idx(om);

%% problem dimensions ibeban = find(bus(:, PD) > 0); %% mencari bus generator nb = size(bus, 1); %% number of buses nl = size(branch, 1); %% number of branches ng = size(gen, 1); %% number of dispatchable injections nxyz = length(x); %% total number of control vars of all types % k = [45 46 47 48];% untuk case 9 % w = [49 50 51 52];% untuk case 9 %% set default constrained lines if nargin < 7 il = (1:nl); %% all lines have limits by default end nl2 = length(il); %% number of constrained lines

%% grab Pg & Qg x Pg = x(vv.i1.Pg:vv.iN.Pg); %% active generation in p.u. Qg = x(vv.i1.Qg:vv.iN.Qg); %% reactive generation in p.u. % %% grab Pg & Qg untuk kondisi 2 % Pg2 = x(k); %% active generation in p.u. % Qg2 = x(w); %% reactive generation in p.u. % %% put Pg & Qg back in gen gen(:, PG) = Pg * baseMVA; %% active generation in MW

gen(:, QG) = Qg * baseMVA; %% reactive generation in MVAr % gen(:, PG) = Pg2 * baseMVA; %% active generation in MW % gen(:, QG) = Qg2 * baseMVA; %% reactive generation in MVAr

%% rebuild Sbus untuk kondisi 1 dan 2 Sbus = makeSbus(baseMVA, bus, gen); %% net injected power in p.u. Sbus2 = makeSbus2(baseMVA, bus, gen); %% net injected power in p.u. % Sbus = [Sbus; Sbus2]; %% ----- evaluate constraints ----- %% reconstruct V Va = x(vv.i1.Va:vv.iN.Va) Vm = x(vv.i1.Vm:vv.iN.Vm) V = Vm .* exp(1j * Va); % V = [V; V]; % Va2 = x(vv.i1.Va:vv.iN.Va); % Vm2 = x(vv.i1.Vm:vv.iN.Vm); % V2 = Vm2 .* exp(1j * Va2);

%% evaluate power flow equations % Ybus2 = [Ybus; Ybus]; mis = V .* conj(Ybus * V) - Sbus; mis2 = V .* conj(Ybus * V) - Sbus2;

%%----- evaluate constraint function values ----- %% first, the equality constraints (power flow) untuk kondisi 1 g = [ real(mis); %% active power mismatch for all buses imag(mis) ]; %% reactive power mismatch for all buses %% first, the equality constraints (power flow) untuk kondisi 2 g2 = [ real(mis2); %% active power mismatch for all buses imag(mis2) ]; %% reactive power mismatch for all buses % sizeg = size(full(g)); %% then, the inequality constraints (branch flow limits) untuk kondisi 1 if nl2 > 0 flow_max = (branch(il, RATE_A)/baseMVA).^2; flow_max(flow_max == 0) = Inf; if upper(mpopt.opf.flow_lim(1)) == 'I' %% current magnitude limit, |I| If = Yf * V; It = Yt * V; h = [ If .* conj(If) - flow_max; %% branch current limits (from bus) It .* conj(It) - flow_max ]; %% branch current limits (to bus) else %% compute branch power flows Sf = V(branch(il, F_BUS)) .* conj(Yf * V); %% complex power injected at

"from" bus (p.u.) St = V(branch(il, T_BUS)) .* conj(Yt * V); %% complex power injected at

"to" bus (p.u.) if upper(mpopt.opf.flow_lim(1)) == 'P' %% active power limit, P (Pan

Wei) h = [ real(Sf).^2 - flow_max; %% branch real power limits (from

bus) real(St).^2 - flow_max ]; %% branch real power limits (to

bus) else %% apparent power limit, |S| h = [ Sf .* conj(Sf) - flow_max; %% branch apparent power limits

(from bus)

St .* conj(St) - flow_max ]; %% branch apparent power limits

(to bus) end end else h = zeros(0,1); end %% then, the inequality constraints (branch flow limits)untuk kondisi 2 if nl2 > 0 flow_max = (branch(il, RATE_A)/baseMVA).^2; flow_max(flow_max == 0) = Inf; if upper(mpopt.opf.flow_lim(1)) == 'I' %% current magnitude limit, |I| If2 = Yf * V; It2 = Yt * V; h2 = [ If2 .* conj(If2) - flow_max; %% branch current limits (from

bus) It2 .* conj(It2) - flow_max ]; %% branch current limits (to bus) else %% compute branch power flows Sf2 = V(branch(il, F_BUS)) .* conj(Yf * V); %% complex power injected at

"from" bus (p.u.) St2 = V(branch(il, T_BUS)) .* conj(Yt * V); %% complex power injected at

"to" bus (p.u.) if upper(mpopt.opf.flow_lim(1)) == 'P' %% active power limit, P (Pan

Wei) h2 = [ real(Sf2).^2 - flow_max; %% branch real power limits

(from bus) real(St2).^2 - flow_max ]; %% branch real power limits (to

bus) else %% apparent power limit, |S| h2 = [ Sf2 .* conj(Sf2) - flow_max; %% branch apparent power

limits (from bus) St2 .* conj(St2) - flow_max ]; %% branch apparent power limits

(to bus) end end else h2 = zeros(0,1); end %%----- evaluate partials of constraints ----- if nargout > 2 %% index ranges iVa = vv.i1.Va:vv.iN.Va; iVm = vv.i1.Vm:vv.iN.Vm; iPg = vv.i1.Pg:vv.iN.Pg; iQg = vv.i1.Qg:vv.iN.Qg;

%% compute partials of injected bus powers untuk kondisi 1 [dSbus_dVm, dSbus_dVa] = dSbus_dV(Ybus, V); %% w.r.t. V neg_Cg = sparse(gen(:, GEN_BUS), 1:ng, -1, nb, ng); %% Pbus w.r.t. Pg %% Qbus w.r.t. Qg %% construct Jacobian of equality (power flow) constraints and transpose it

untuk kondisi 1 dg = sparse(2*nb, nxyz); sizedg = size(full(dg)); dg(:, [iVa iVm iPg iQg]) = [

real([dSbus_dVa dSbus_dVm]) neg_Cg sparse(nb, ng); %% P mismatch w.r.t

Va, Vm, Pg, Qg imag([dSbus_dVa dSbus_dVm]) sparse(nb, ng) neg_Cg; %% Q mismatch w.r.t

Va, Vm, Pg, Qg ]; dg = dg';

%% compute partials of injected bus powers untuk kondisi 2 [dSbus2_dVm, dSbus2_dVa] = dSbus2_dV(Ybus, V); %% w.r.t. V neg_Cg = sparse(gen(:, GEN_BUS), 1:ng, -1, nb, ng); %% Pbus w.r.t. Pg %% Qbus w.r.t. Qg %% construct Jacobian of equality (power flow) constraints and transpose it

untuk kondisi 2 dg2 = sparse(2*nb, nxyz); dg2(:, [iVa iVm iPg iQg]) = [ real([dSbus2_dVa dSbus2_dVm]) neg_Cg sparse(nb, ng); %% P mismatch w.r.t

Va, Vm, Pg, Qg imag([dSbus2_dVa dSbus2_dVm]) sparse(nb, ng) neg_Cg; %% Q mismatch w.r.t

Va, Vm, Pg, Qg ]; dg2 = dg2'; if nl2 > 0 %% compute partials of Flows w.r.t. V untuk kondisi 1 if upper(mpopt.opf.flow_lim(1)) == 'I' %% current [dFf_dVa, dFf_dVm, dFt_dVa, dFt_dVm, Ff, Ft] = dIbr_dV(branch(il,:),

Yf, Yt, V); else %% power [dFf_dVa, dFf_dVm, dFt_dVa, dFt_dVm, Ff, Ft] = dSbr_dV(branch(il,:),

Yf, Yt, V); end if upper(mpopt.opf.flow_lim(1)) == 'P' %% real part of flow (active

power) dFf_dVa = real(dFf_dVa); dFf_dVm = real(dFf_dVm); dFt_dVa = real(dFt_dVa); dFt_dVm = real(dFt_dVm); Ff = real(Ff); Ft = real(Ft); end

%% squared magnitude of flow (of complex power or current, or real power)

untuk kondisi 1 [df_dVa, df_dVm, dt_dVa, dt_dVm] = ... dAbr_dV(dFf_dVa, dFf_dVm, dFt_dVa, dFt_dVm, Ff, Ft);

%% construct Jacobian of inequality (branch flow) constraints & transpose

untuk kondisi 1 dh = sparse(2*nl2, nxyz); dh(:, [iVa iVm]) = [ df_dVa, df_dVm; %% "from" flow limit dt_dVa, dt_dVm; %% "to" flow limit ]; dh = dh'; else dh = sparse(nxyz, 0); end

if nl2 > 0 %% compute partials of Flows w.r.t. V untuk kondisi 2 if upper(mpopt.opf.flow_lim(1)) == 'I' %% current [dFf2_dVa, dFf2_dVm, dFt2_dVa, dFt2_dVm, Ff2, Ft2] =

dIbr2_dV(branch(il,:), Yf, Yt, V); else %% power [dFf2_dVa, dFf2_dVm, dFt2_dVa, dFt2_dVm, Ff2, Ft2] =

dSbr2_dV(branch(il,:), Yf, Yt, V); end if upper(mpopt.opf.flow_lim(1)) == 'P' %% real part of flow (active

power) dFf2_dVa = real(dFf2_dVa); dFf2_dVm = real(dFf2_dVm); dFt2_dVa = real(dFt2_dVa); dFt2_dVm = real(dFt2_dVm); Ff2 = real(Ff2); Ft2 = real(Ft2); end

%% squared magnitude of flow (of complex power or current, or real power)

untuk kondisi 2 [df2_dVa, df2_dVm, dt2_dVa, dt2_dVm] = ... dAbr2_dV(dFf2_dVa, dFf2_dVm, dFt2_dVa, dFt2_dVm, Ff2, Ft2);

%% construct Jacobian of inequality (branch flow) constraints & transpose

untuk kondisi 2 dh2 = sparse(2*nl2, nxyz); dh2(:, [iVa iVm]) = [ df2_dVa, df2_dVm; %% "from" flow limit dt2_dVa, dt2_dVm; %% "to" flow limit ]; dh2 = dh2'; else dh2 = sparse(nxyz, 0); end % h = h2 % dh = dh2 % g % g2 % dg = dg2 %% multiplier factor for loads % fkali = [1 1.03 1.03 1.035 1.06 1.065 1.065 1.07 1.08 1.095 1.09 1.09 1.125

1.13 1.14 1.25 1.35 1.5 1.6 1.7 1.8 1.9 2 2.1];%coba ramp rate 1 (-2) (1

case14) alhamdulillah berhasil % fkali = [1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7

1.75 1.8 1.85 1.9 1.95 2 2.1 2.15 2.2];%fkali1 alhamdulillah berhasil % % fkali = [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; % always 1 % fkali = [1 1.03 1.03 1.03 1.06 1.06 1.06 1.1 1.2 1.3 1.3 1.3 1.2 1.2 1.3

1.3 1.3 1.4 1.5 1.5 1.5 1.5 1.4 1.3];%coba ramp rate dari pak roni(-2) % fkali = [1 1.03 1.03 1.05 1.06 1.08 1.09 1.1 1.2 1.3 1.3 1.3 1.2 1.2 1.3

1.3 1.3 1.4 1.5 1.5 1.5 1.5 1.4 1.3];%coba ramp rate (-2) % fkali = [1 1 1 0.9 0.95 0.88 0.85 0.8 0.8 0.78 0.78 0.7 0.6 0.6 0.65 0.65

0.8 0.8 0.9 0.9 0.9 1.0 1.0 1.1];%coba ramp rate 3 (-2) % fkali = [1 1.05 1.08 1.09 1.1 1.1 1.16 1.2 1.2 1.24 1.3 1.3 1.4 1.45 1.45

1.5 1.8 1.5 1.5 1.1 1.1 1 1 1];%coba ramp rate 4 (2)

% fkali = [1 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4

1.5 1.5 1.5 1.5 1.6 1.6 1];%coba ramp rate 5 (-2) % fkali = [1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13

1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.22 1.23];%coba ramp rate 6 (-2) % fkali = [1 1.025 1.025 1.025 1.045 1.045 1.045 1.095 1.15 1.215 1.315 1.315

1.315 1.11 1.15 1.15 1.35 1.35 1.45 1.485 1.55 1.55 1.45 1.35];%coba ramp

rate 7 (-2) % fkali = [1 1.015 1.025 1.035 1.045 1.055 1.065 1.075 1.085 1.095 1.15 1.115

1.125 1.135 1.145 1.15 1.165 1.175 1.185 1.195 1.25 1.215 1.225 1.235];%coba

ramp rate 8 (-2) % fkali = [1 1.015 1.025 1.035 1.045 1.055 1.065 1.075 1.085 1.095 1.15 1.115

1.15 1.095 1.085 1.075 1.065 1.055 1.045 1.035 1.025 1.015 1.0 1.0];%coba

ramp rate 9 (1) (0) % fkali = [0.6 0.6 0.65 0.65 0.8 0.8 0.9 0.9 0.9 1.0 1.0 1.1 1.1 1.0 1.0 1.0

0.9 0.95 0.88 0.85 0.8 0.8 0.78 0.7];%coba ramp rate 9 (-2) % fkali = [1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.1 1.12 1.13

1.14 1.15 1.16 1.2 1.2 1.2 1.19 1.18 1.17 1.1];%coba ramp rate 10 (-2) % fkali = [1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.1 1.12 1.13

1.14 1.15 1.16 1.2 1.2 1.2 1.1 1.1 1.1 1.0];%coba ramp rate 11 (0) % fkali = [1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.1 1.12 1.13

1.14 1.15 1.16 1.25 1.25 1.2 1.1 1.1 1.1 1.0];%coba ramp rate 12 (0) % fkali = [1 1.01 1.01 1.01 1.01 1.02 1.03 1.03 1.03 1.03 1.1 1.1 1.12 1.13

1.14 1.15 1.16 1.25 1.25 1.2 1.1 1.1 1.1 1.0];%coba ramp rate 12 (0) % fkali = [0.5 0.5 0.55 0.55 0.55 0.55 0.6 0.6 0.7 0.75 0.8 0.85 0.9 0.9 0.9

1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8 0.5];%coba ramp rate 13 (-2) % fkali = [0.35 0.35 0.35 0.35 0.4 0.4 0.4 0.45 0.45 0.5 0.5 0.5 0.6 0.6 0.65

0.65 0.8 0.8 0.9 0.5 0.5 4.0 0.3 0.3];%coba ramp rate 14 (-2) % fkali = [1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2]; %fkali2 % fkali = [1 1.6]; %fkali3 %% To expand matrixes due to additional considered time T = 2; %%time interval for i=1:T-1; dh = blkdiag(dh, dh2); h = [h; h2]; % fkali(i+1)*BB(igen); % dg(igen)= fkali(i+1)*BB(igen) dg = blkdiag(dg, dg2); % fkali(i+1)*B(ibeban); % g(ibeban)= fkali(i+1)*B(ibeban); g = [g; g2]; end sizeh = size(h); sizedh = size(full(dh)); sizeg = size(g); sizedg = size(full(dg)); h = (h); dh = (full(dh)); g = (g); dg = (full(dg));

end end

function [f, df, d2f] = opf_costfcn(x, om, varargin) %OPF_COSTFCN Evaluates objective function, gradient and Hessian for OPF. % [F, DF, D2F] = OPF_COSTFCN(X, OM) % % Objective function evaluation routine for AC optimal power flow, % suitable for use with MIPS or FMINCON. Computes objective function value, % gradient and Hessian. % % Inputs: % X : optimization vector % OM : OPF model object % % Outputs: % F : value of objective function % DF : (optional) gradient of objective function (column vector) % D2F : (optional) Hessian of objective function (sparse matrix) % % Examples: % f = opf_costfcn(x, om); % [f, df] = opf_costfcn(x, om); % [f, df, d2f] = opf_costfcn(x, om); % % See also OPF_CONSFCN, OPF_HESSFCN.

% MATPOWER % $Id: opf_costfcn.m 1635 2010-04-26 19:45:26Z ray $ % by Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de

Manizales % and Ray Zimmerman, PSERC Cornell % Copyright (c) 1996-2010 by Power System Engineering Research Center


%%----- initialize ----- %% define named indices into data matrices [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ... MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ... QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen; [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ... TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ... ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch; [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;

x = x(1:52, 1); %% tambahan dari pak rony

%% unpack data mpc = get_mpc(om); [baseMVA, gen, gencost] = deal(mpc.baseMVA, mpc.gen, mpc.gencost); cp = get_cost_params(om); [N, Cw, H, dd, rh, kk, mm] = deal(cp.N, cp.Cw, cp.H, cp.dd, ... cp.rh, cp.kk, cp.mm); vv = get_idx(om);

%% problem dimensions ng = size(gen, 1); %% number of dispatchable injections ny = getN(om, 'var', 'y'); %% number of piece-wise linear costs nxyz = length(x); %% total number of control vars of all types k = [45 46 47 48];% untuk case 9 w = [49 50 51 52];% untuk case 9 % k = [133 134 135 136 137 138];% untuk case 30 % w = [139 140 141 142 143 144];% untuk case 30 %% grab Pg & Qg Pg = x(vv.i1.Pg:vv.iN.Pg); %% active generation in p.u. Qg = x(vv.i1.Qg:vv.iN.Qg); %% reactive generation in p.u. Pg2 = x(k); %% active generation in p.u. Qg2 = x(w); %% reactive generation in p.u. %%----- evaluate objective function ----- %% polynomial cost of P and Q % use totcost only on polynomial cost; in the minimization problem % formulation, pwl cost is the sum of the y variables. ipol = find(gencost(:, MODEL) == POLYNOMIAL); %% poly MW and MVAr costs xx = [ Pg; Qg ] * baseMVA; xx2 = [ Pg2; Qg2 ] * baseMVA; if ~isempty(ipol) f = sum( totcost(gencost(ipol, :), xx(ipol)) ); %% cost of poly P or Q f2 = sum( totcost(gencost(ipol, :), xx2(ipol)) ) %% cost of poly P or Q else f = 0; end

%% piecewise linear cost of P and Q if ny > 0 ccost = full(sparse(ones(1,ny), vv.i1.y:vv.iN.y, ones(1,ny), 1, nxyz)); f = f + ccost * x; else ccost = zeros(1, nxyz); end

%% generalized cost term

if ~isempty(N) nw = size(N, 1); r = N * x - rh; %% Nx - rhat iLT = find(r < -kk); %% below dead zone iEQ = find(r == 0 & kk == 0); %% dead zone doesn't exist iGT = find(r > kk); %% above dead zone iND = [iLT; iEQ; iGT]; %% rows that are Not in the Dead region iL = find(dd == 1); %% rows using linear function iQ = find(dd == 2); %% rows using quadratic function LL = sparse(iL, iL, 1, nw, nw); QQ = sparse(iQ, iQ, 1, nw, nw); kbar = sparse(iND, iND, [ ones(length(iLT), 1); zeros(length(iEQ), 1); -ones(length(iGT), 1)], nw, nw) * kk; rr = r + kbar; %% apply non-dead zone shift M = sparse(iND, iND, mm(iND), nw, nw); %% dead zone or scale diagrr = sparse(1:nw, 1:nw, rr, nw, nw);

%% linear rows multiplied by rr(i), quadratic rows by rr(i)^2 w = M * (LL + QQ * diagrr) * rr;

f = f + (w' * H * w) / 2 + Cw' * w; end

%%----- evaluate cost gradient ----- if nargout > 1 %% index ranges iPg = vv.i1.Pg:vv.iN.Pg; iQg = vv.i1.Qg:vv.iN.Qg;

%% polynomial cost of P and Q df_dPgQg = zeros(2*ng, 1); %% w.r.t p.u. Pg and Qg df_dPgQg(ipol) = baseMVA * polycost(gencost(ipol, :), xx(ipol), 1); df = zeros(nxyz, 1); df(iPg) = df_dPgQg(1:ng); df(iQg) = df_dPgQg((1:ng) + ng);

%% piecewise linear cost of P and Q df = df + ccost'; % As in MINOS, the linear cost row is additive wrt % any nonlinear cost.

%% generalized cost term if ~isempty(N) HwC = H * w + Cw; AA = N' * M * (LL + 2 * QQ * diagrr); df = df + AA * HwC;

%% numerical check if 0 %% 1 to check, 0 to skip check ddff = zeros(size(df)); step = 1e-7; tol = 1e-3; for k = 1:length(x) xx = x; xx(k) = xx(k) + step;

ddff(k) = (opf_costfcn(xx, om) - f) / step; end if max(abs(ddff - df)) > tol idx = find(abs(ddff - df) == max(abs(ddff - df))); fprintf('\nMismatch in gradient\n'); fprintf('idx df(num) df diff\n'); fprintf('%4d%16g%16g%16g\n', [ 1:length(df); ddff'; df'; abs(ddff -

df)' ]); fprintf('MAX\n'); fprintf('%4d%16g%16g%16g\n', [ idx'; ddff(idx)'; df(idx)';

abs(ddff(idx) - df(idx))' ]); fprintf('\n'); end end %% numeric check end

%% ---- evaluate cost Hessian ----- if nargout > 2 pcost = gencost(1:ng, :); if size(gencost, 1) > ng qcost = gencost(ng+1:2*ng, :); else qcost = []; end

%% polynomial generator costs d2f_dPg2 = sparse(ng, 1); %% w.r.t. p.u. Pg d2f_dQg2 = sparse(ng, 1); %% w.r.t. p.u. Qg ipolp = find(pcost(:, MODEL) == POLYNOMIAL); d2f_dPg2(ipolp) = baseMVA^2 * polycost(pcost(ipolp, :),

Pg(ipolp)*baseMVA, 2); if ~isempty(qcost) %% Qg is not free ipolq = find(qcost(:, MODEL) == POLYNOMIAL); d2f_dQg2(ipolq) = baseMVA^2 * polycost(qcost(ipolq, :),

Qg(ipolq)*baseMVA, 2); end i = [iPg iQg]'; d2f = sparse(i, i, [d2f_dPg2; d2f_dQg2], nxyz, nxyz);

%% generalized cost if ~isempty(N) d2f = d2f + AA * H * AA' + 2 * N' * M * QQ * sparse(1:nw, 1:nw, HwC,

nw, nw) * N; end end % D = f; % DD = df; % size(f); % size(df); % % fkali = [1 1.6]; %fkali3 % T = 2; %% time interval % for i=1:T-1; % % f = D*fkali(i+1); % f = f+D; % df = [DD; df]; % end

sizef = size(f); sizedf = size(df); f = (f); df = (df); end end

function Lxx = opf_hessfcn(x, lambda, cost_mult, om, Ybus, Yf, Yt, mpopt, il) %OPF_HESSFCN Evaluates Hessian of Lagrangian for AC OPF. % LXX = OPF_HESSFCN(X, LAMBDA, COST_MULT, OM, YBUS, YF, YT, MPOPT, IL) % % Hessian evaluation function for AC optimal power flow, suitable % for use with MIPS or FMINCON's interior-point algorithm. % % Inputs: % X : optimization vector % LAMBDA (struct) % .eqnonlin : Lagrange multipliers on power balance equations % .ineqnonlin : Kuhn-Tucker multipliers on constrained branch flows % COST_MULT : (optional) Scale factor to be applied to the cost % (default = 1). % OM : OPF model object % YBUS : bus admittance matrix % YF : admittance matrix for "from" end of constrained branches % YT : admittance matrix for "to" end of constrained branches % MPOPT : MATPOWER options struct % IL : (optional) vector of branch indices corresponding to % branches with flow limits (all others are assumed to be % unconstrained). The default is [1:nl] (all branches). % YF and YT contain only the rows corresponding to IL. % % Outputs: % LXX : Hessian of the Lagrangian. % % Examples: % Lxx = opf_hessfcn(x, lambda, cost_mult, om, Ybus, Yf, Yt, mpopt); % Lxx = opf_hessfcn(x, lambda, cost_mult, om, Ybus, Yf, Yt, mpopt, il); % % See also OPF_COSTFCN, OPF_CONSFCN.

% MATPOWER % $Id: opf_hessfcn.m 2328 2014-05-23 18:43:00Z ray $ % by Ray Zimmerman, PSERC Cornell % and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Autonoma de


(PSERC) % % This file is part of MATPOWER. % See http://www.pserc.cornell.edu/matpower/ for more info. % % MATPOWER is free software: you can redistribute it and/or modify % it under the terms of the GNU General Public License as published % by the Free Software Foundation, either version 3 of the License, % or (at your option) any later version. % % MATPOWER is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You should have received a copy of the GNU General Public License % along with MATPOWER. If not, see . %

% Additional permission under GNU GPL version 3 section 7 % % If you modify MATPOWER, or any covered work, to interface with % other modules (such as MATLAB code and MEX-files) available in a % MATLAB(R) or comparable environment containing parts covered % under other licensing terms, the licensors of MATPOWER grant % you additional permission to convey the resulting work.

%%----- initialize ----- %% define named indices into data matrices [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ... MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ... QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen; [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ... TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ... ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch; [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;

%% default args if isempty(cost_mult) cost_mult = 1; end

%% unpack data mpc = get_mpc(om); [baseMVA, bus, gen, branch, gencost] = ... deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch, mpc.gencost); cp = get_cost_params(om); [N, Cw, H, dd, rh, kk, mm] = deal(cp.N, cp.Cw, cp.H, cp.dd, ... cp.rh, cp.kk, cp.mm); vv = get_idx(om);

%% unpack needed parameters nb = size(bus, 1); %% number of buses nl = size(branch, 1); %% number of branches ng = size(gen, 1); %% number of dispatchable injections nxyz = length(x); %% total number of control vars of all types

%% set default constrained lines if nargin < 8 il = (1:nl); %% all lines have limits by default end nl2 = length(il); %% number of constrained lines

%% grab Pg & Qg Pg = x(vv.i1.Pg:vv.iN.Pg); %% active generation in p.u. Qg = x(vv.i1.Qg:vv.iN.Qg); %% reactive generation in p.u.

%% put Pg & Qg back in gen gen(:, PG) = Pg * baseMVA; %% active generation in MW gen(:, QG) = Qg * baseMVA; %% reactive generation in MVAr

%% reconstruct V Va = zeros(nb, 1); Va = x(vv.i1.Va:vv.iN.Va);

Vm = x(vv.i1.Vm:vv.iN.Vm); V = Vm .* exp(1j * Va); nxtra = nxyz - 2*nb; pcost = gencost(1:ng, :); if size(gencost, 1) > ng qcost = gencost(ng+1:2*ng, :); else qcost = []; end

%% ----- evaluate d2f ----- d2f_dPg2 = sparse(ng, 1); %% w.r.t. p.u. Pg d2f_dQg2 = sparse(ng, 1); %% w.r.t. p.u. Qg ipolp = find(pcost(:, MODEL) == POLYNOMIAL); d2f_dPg2(ipolp) = baseMVA^2 * polycost(pcost(ipolp, :), Pg(ipolp)*baseMVA,

2); if ~isempty(qcost) %% Qg is not free ipolq = find(qcost(:, MODEL) == POLYNOMIAL); d2f_dQg2(ipolq) = baseMVA^2 * polycost(qcost(ipolq, :),

Qg(ipolq)*baseMVA, 2); end i = [vv.i1.Pg:vv.iN.Pg vv.i1.Qg:vv.iN.Qg]'; d2f = sparse(i, i, [d2f_dPg2; d2f_dQg2], nxyz, nxyz);

%% generalized cost if ~isempty(N) nw = size(N, 1); r = N * x - rh; %% Nx - rhat iLT = find(r < -kk); %% below dead zone iEQ = find(r == 0 & kk == 0); %% dead zone doesn't exist iGT = find(r > kk); %% above dead zone iND = [iLT; iEQ; iGT]; %% rows that are Not in the Dead region iL = find(dd == 1); %% rows using linear function iQ = find(dd == 2); %% rows using quadratic function LL = sparse(iL, iL, 1, nw, nw); QQ = sparse(iQ, iQ, 1, nw, nw); kbar = sparse(iND, iND, [ ones(length(iLT), 1); zeros(length(iEQ), 1); -ones(length(iGT), 1)], nw, nw) * kk; rr = r + kbar; %% apply non-dead zone shift M = sparse(iND, iND, mm(iND), nw, nw); %% dead zone or scale diagrr = sparse(1:nw, 1:nw, rr, nw, nw);

%% linear rows multiplied by rr(i), quadratic rows by rr(i)^2 w = M * (LL + QQ * diagrr) * rr; HwC = H * w + Cw; AA = N' * M * (LL + 2 * QQ * diagrr); d2f = d2f + AA * H * AA' + 2 * N' * M * QQ * sparse(1:nw, 1:nw, HwC, nw,

nw) * N; end d2f = d2f * cost_mult;

%%----- evaluate Hessian of power balance constraints ----- nlam = length(lambda.eqnonlin) / 2; lamP = lambda.eqnonlin(1:nlam); lamQ = lambda.eqnonlin((1:nlam)+nlam);

[Gpaa, Gpav, Gpva, Gpvv] = d2Sbus_dV2(Ybus, V, lamP); [Gqaa, Gqav, Gqva, Gqvv] = d2Sbus_dV2(Ybus, V, lamQ); d2G = [ real([Gpaa Gpav; Gpva Gpvv]) + imag([Gqaa Gqav; Gqva Gqvv]) sparse(2*nb,

nxtra); sparse(nxtra, 2*nb + nxtra) ];

%%----- evaluate Hessian of flow constraints ----- nmu = length(lambda.ineqnonlin) / 2; if nmu muF = lambda.ineqnonlin(1:nmu); muT = lambda.ineqnonlin((1:nmu)+nmu); else %% keep dimensions of empty matrices/vectors compatible muF = zeros(0,1); %% (required to avoid problems when using Knitro muT = zeros(0,1); %% on cases with all lines unconstrained) end if upper(mpopt.opf.flow_lim(1)) == 'I' %% current [dIf_dVa, dIf_dVm, dIt_dVa, dIt_dVm, If, It] = dIbr_dV(branch(il,:), Yf,

Yt, V); [Hfaa, Hfav, Hfva, Hfvv] = d2AIbr_dV2(dIf_dVa, dIf_dVm, If, Yf, V, muF); [Htaa, Htav, Htva, Htvv] = d2AIbr_dV2(dIt_dVa, dIt_dVm, It, Yt, V, muT); else f = branch(il, F_BUS); %% list of "from" buses t = branch(il, T_BUS); %% list of "to" buses Cf = sparse(1:nl2, f, ones(nl2, 1), nl2, nb); %% connection matrix for

line & from buses Ct = sparse(1:nl2, t, ones(nl2, 1), nl2, nb); %% connection matrix for

line & to buses [dSf_dVa, dSf_dVm, dSt_dVa, dSt_dVm, Sf, St] = dSbr_dV(branch(il,:), Yf,

Yt, V); if upper(mpopt.opf.flow_lim(1)) == 'P' %% real power [Hfaa, Hfav, Hfva, Hfvv] = d2ASbr_dV2(real(dSf_dVa), real(dSf_dVm),

real(Sf), Cf, Yf, V, muF); [Htaa, Htav, Htva, Htvv] = d2ASbr_dV2(real(dSt_dVa), real(dSt_dVm),

real(St), Ct, Yt, V, muT); else %% apparent power [Hfaa, Hfav, Hfva, Hfvv] = d2ASbr_dV2(dSf_dVa, dSf_dVm, Sf, Cf, Yf, V,

muF); [Htaa, Htav, Htva, Htvv] = d2ASbr_dV2(dSt_dVa, dSt_dVm, St, Ct, Yt, V,

muT); end end d2H = [ [Hfaa Hfav; Hfva Hfvv] + [Htaa Htav; Htva Htvv] sparse(2*nb, nxtra); sparse(nxtra, 2*nb + nxtra) ];

%%----- do numerical check using (central) finite differences ----- if 0 nx = length(x); step = 1e-5; num_d2f = sparse(nx, nx); num_d2G = sparse(nx, nx); num_d2H = sparse(nx, nx); for i = 1:nx

xp = x; xm = x; xp(i) = x(i) + step/2; xm(i) = x(i) - step/2; % evaluate cost & gradients [fp, dfp] = opf_costfcn(xp, om); [fm, dfm] = opf_costfcn(xm, om); % evaluate constraints & gradients [Hp, Gp, dHp, dGp] = opf_consfcn(xp, om, Ybus, Yf, Yt, mpopt, il); [Hm, Gm, dHm, dGm] = opf_consfcn(xm, om, Ybus, Yf, Yt, mpopt, il); num_d2f(:, i) = cost_mult * (dfp - dfm) / step; num_d2G(:, i) = (dGp - dGm) * lambda.eqnonlin / step; num_d2H(:, i) = (dHp - dHm) * lambda.ineqnonlin / step; end d2f_err = full(max(max(abs(d2f - num_d2f)))); d2G_err = full(max(max(abs(d2G - num_d2G)))); d2H_err = full(max(max(abs(d2H - num_d2H)))); if d2f_err > 1e-6 fprintf('Max difference in d2f: %g\n', d2f_err); end if d2G_err > 1e-5 fprintf('Max difference in d2G: %g\n', d2G_err); end if d2H_err > 1e-6 fprintf('Max difference in d2H: %g\n', d2H_err); end end

Lxx = d2f + d2G + d2H;

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Function Opf Matpower