Description of nlpopf

0001 function [results, success, raw] = nlpopf_solver(om, mpopt)
0002 %NLPOPF_SOLVER  Solves AC optimal power flow using MP-Opt-Model.
0003 %
0004 %   [RESULTS, SUCCESS, RAW] = NLPOPF_SOLVER(OM, MPOPT)
0005 %
0006 %   Inputs are an OPF model object and a MATPOWER options struct.
0007 %
0008 %   Outputs are a RESULTS struct, SUCCESS flag and RAW output struct.
0009 %
0010 %   RESULTS is a MATPOWER case struct (mpc) with the usual baseMVA, bus
0011 %   branch, gen, gencost fields, along with the following additional
0012 %   fields:
0013 %       .order      see 'help ext2int' for details of this field
0014 %       .x          final value of optimization variables (internal order)
0015 %       .f          final objective function value
0016 %       .mu         shadow prices on ...
0017 %           .var
0018 %               .l  lower bounds on variables
0019 %               .u  upper bounds on variables
0020 %           .nln    (deprecated) 2*nb+2*nl - Pmis, Qmis, Sf, St
0021 %               .l  lower bounds on nonlinear constraints
0022 %               .u  upper bounds on nonlinear constraints
0023 %           .nle    nonlinear equality constraints
0024 %           .nli    nonlinear inequality constraints
0025 %           .lin
0026 %               .l  lower bounds on linear constraints
0027 %               .u  upper bounds on linear constraints
0028 %
0029 %   SUCCESS     1 if solver converged successfully, 0 otherwise
0030 %
0031 %   RAW         raw output in form returned by MINOS
0032 %       .xr     final value of optimization variables
0033 %       .pimul  constraint multipliers
0034 %       .info   solver specific termination code
0035 %       .output solver specific output information
0036 %
0037 %   See also OPF, MIPS.
0038 
0039 %   MATPOWER
0040 %   Copyright (c) 2000-2020, Power Systems Engineering Research Center (PSERC)
0041 %   by Ray Zimmerman, PSERC Cornell
0042 %   and Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Nacional de Colombia
0043 %
0044 %   This file is part of MATPOWER.
0045 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0046 %   See https://matpower.org for more info.
0047 
0048 %%----- initialization -----
0049 %% define named indices into data matrices
0050 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0051     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0052 [GEN_BUS, PG, QG, QMAX, QMIN, VG, MBASE, GEN_STATUS, PMAX, PMIN, ...
0053     MU_PMAX, MU_PMIN, MU_QMAX, MU_QMIN, PC1, PC2, QC1MIN, QC1MAX, ...
0054     QC2MIN, QC2MAX, RAMP_AGC, RAMP_10, RAMP_30, RAMP_Q, APF] = idx_gen;
0055 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0056     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0057     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0058 [PW_LINEAR, POLYNOMIAL, MODEL, STARTUP, SHUTDOWN, NCOST, COST] = idx_cost;
0059 
0060 %% options
0061 % mips_opt = mpopt.mips;
0062 % mips_opt.verbose = mpopt.verbose;
0063 % if mips_opt.feastol == 0
0064 %     mips_opt.feastol = mpopt.opf.violation;  %% = MPOPT.opf.violation by default
0065 % end
0066 % if ~isfield(mips_opt, 'cost_mult') || isempty(mips_opt.cost_mult)
0067 %     mips_opt.cost_mult = 1e-4;
0068 % end
0069 % opt = struct('mips_opt', mips_opt);
0070 
0071 %% unpack data
0072 mpc = om.get_mpc();
0073 [baseMVA, bus, gen, branch, gencost] = ...
0074     deal(mpc.baseMVA, mpc.bus, mpc.gen, mpc.branch, mpc.gencost);
0075 [vv, ll, nne, nni] = om.get_idx();
0076 
0077 %% problem dimensions
0078 nb = size(bus, 1);          %% number of buses
0079 nl = size(branch, 1);       %% number of branches
0080 ny = om.getN('var', 'y');   %% number of piece-wise linear costs
0081 
0082 %% options
0083 model = om.problem_type();
0084 opt = mpopt2nlpopt(mpopt, model);
0085 
0086 %% try to select an interior initial point, unless requested not to
0087 if mpopt.opf.start < 2
0088     [x0, xmin, xmax] = om.params_var();     %% init var & bounds
0089     s = 1;                      %% set init point inside bounds by s
0090     lb = xmin; ub = xmax;
0091     lb(xmin == -Inf) = -1e10;   %% replace Inf with numerical proxies
0092     ub(xmax ==  Inf) =  1e10;
0093     x0 = (lb + ub) / 2;         %% set x0 mid-way between bounds
0094     k = find(xmin == -Inf & xmax < Inf);    %% if only bounded above
0095     x0(k) = xmax(k) - s;                    %% set just below upper bound
0096     k = find(xmin > -Inf & xmax == Inf);    %% if only bounded below
0097     x0(k) = xmin(k) + s;                    %% set just above lower bound
0098     Varefs = bus(bus(:, BUS_TYPE) == REF, VA) * (pi/180);
0099     Vmax = min(bus(:, VMAX), 1.5);
0100     Vmin = max(bus(:, VMIN), 0.5);
0101     Vm = (Vmax + Vmin) / 2;
0102     if mpopt.opf.v_cartesian
0103         V = Vm * exp(1j*Varefs(1));
0104         x0(vv.i1.Vr:vv.iN.Vr) = real(V);
0105         x0(vv.i1.Vi:vv.iN.Vi) = imag(V);
0106     else
0107         x0(vv.i1.Va:vv.iN.Va) = Varefs(1);  %% angles set to first reference angle
0108         x0(vv.i1.Vm:vv.iN.Vm) = Vm;         %% voltage magnitudes
0109         if ny > 0
0110             ipwl = find(gencost(:, MODEL) == PW_LINEAR);
0111             c = gencost(sub2ind(size(gencost), ipwl, NCOST+2*gencost(ipwl, NCOST)));    %% largest y-value in CCV data
0112             x0(vv.i1.y:vv.iN.y) = max(c) + 0.1 * abs(max(c));
0113         end
0114     end
0115     opt.x0 = x0;
0116 end
0117 
0118 %% find branches with flow limits
0119 il = find(branch(:, RATE_A) ~= 0 & branch(:, RATE_A) < 1e10);
0120 nl2 = length(il);           %% number of constrained lines
0121 
0122 %%-----  run opf  -----
0123 [x, f, eflag, output, lambda] = om.solve(opt);
0124 success = (eflag > 0);
0125 
0126 %% update solution data
0127 if mpopt.opf.v_cartesian
0128     Vi = x(vv.i1.Vi:vv.iN.Vi);
0129     Vr = x(vv.i1.Vr:vv.iN.Vr);
0130     V = Vr + 1j*Vi;
0131     Va = angle(V);
0132     Vm = abs(V);
0133 else
0134     Va = x(vv.i1.Va:vv.iN.Va);
0135     Vm = x(vv.i1.Vm:vv.iN.Vm);
0136     V = Vm .* exp(1j*Va);
0137 end
0138 Pg = x(vv.i1.Pg:vv.iN.Pg);
0139 Qg = x(vv.i1.Qg:vv.iN.Qg);
0140 
0141 %%-----  calculate return values  -----
0142 %% update voltages & generator outputs
0143 bus(:, VA) = Va * 180/pi;
0144 bus(:, VM) = Vm;
0145 gen(:, PG) = Pg * baseMVA;
0146 gen(:, QG) = Qg * baseMVA;
0147 gen(:, VG) = Vm(gen(:, GEN_BUS));
0148 
0149 %% compute branch flows
0150 [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch);    %% build admittance matrices
0151 Sf = V(branch(:, F_BUS)) .* conj(Yf * V);   %% cplx pwr at "from" bus, p.u.
0152 St = V(branch(:, T_BUS)) .* conj(Yt * V);   %% cplx pwr at "to" bus, p.u.
0153 branch(:, PF) = real(Sf) * baseMVA;
0154 branch(:, QF) = imag(Sf) * baseMVA;
0155 branch(:, PT) = real(St) * baseMVA;
0156 branch(:, QT) = imag(St) * baseMVA;
0157 
0158 %% line constraint is typically on square of limit
0159 %% so we must fix multipliers
0160 muSf = zeros(nl, 1);
0161 muSt = zeros(nl, 1);
0162 if ~isempty(il)
0163     if upper(mpopt.opf.flow_lim(1)) == 'P'
0164         muSf(il) = lambda.ineqnonlin(nni.i1.Sf:nni.iN.Sf);
0165         muSt(il) = lambda.ineqnonlin(nni.i1.St:nni.iN.St);
0166     else
0167         muSf(il) = 2 * lambda.ineqnonlin(nni.i1.Sf:nni.iN.Sf) .* branch(il, RATE_A) / baseMVA;
0168         muSt(il) = 2 * lambda.ineqnonlin(nni.i1.St:nni.iN.St) .* branch(il, RATE_A) / baseMVA;
0169     end
0170 end
0171 
0172 %% update Lagrange multipliers
0173 if mpopt.opf.v_cartesian
0174     if om.userdata.veq
0175         lam = lambda.eqnonlin(nne.i1.Veq:nne.iN.Veq);
0176         mu_Vmax = zeros(size(lam));
0177         mu_Vmin = zeros(size(lam));
0178         mu_Vmax(lam > 0) =  lam(lam > 0);
0179         mu_Vmin(lam < 0) = -lam(lam < 0);
0180         bus(om.userdata.veq, MU_VMAX) = mu_Vmax;
0181         bus(om.userdata.veq, MU_VMIN) = mu_Vmin;
0182     end
0183     bus(om.userdata.viq, MU_VMAX) = lambda.ineqnonlin(nni.i1.Vmax:nni.iN.Vmax);
0184     bus(om.userdata.viq, MU_VMIN) = lambda.ineqnonlin(nni.i1.Vmin:nni.iN.Vmin);
0185 else
0186     bus(:, MU_VMAX)  = lambda.upper(vv.i1.Vm:vv.iN.Vm);
0187     bus(:, MU_VMIN)  = lambda.lower(vv.i1.Vm:vv.iN.Vm);
0188 end
0189 gen(:, MU_PMAX)  = lambda.upper(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0190 gen(:, MU_PMIN)  = lambda.lower(vv.i1.Pg:vv.iN.Pg) / baseMVA;
0191 gen(:, MU_QMAX)  = lambda.upper(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0192 gen(:, MU_QMIN)  = lambda.lower(vv.i1.Qg:vv.iN.Qg) / baseMVA;
0193 if mpopt.opf.current_balance
0194     %% convert current balance shadow prices to equivalent lamP and lamQ
0195     %% P + jQ = (Vr + jVi) * (M - jN)
0196     %% M = (Vr P + Vi Q) / (Vr^2 + Vi^2)
0197     %% N = (Vi P - Vr Q) / (Vr^2 + Vi^2)
0198     %% lamP = df/dP = df/dM * dM/dP + df/dN + dN/dP
0199     %% lamQ = df/dQ = df/dM * dM/dQ + df/dN + dN/dQ
0200     VV = V ./ (V .* conj(V));   %% V / Vm^2
0201     VVr = real(VV);
0202     VVi = imag(VV);
0203     lamM = lambda.eqnonlin(nne.i1.rImis:nne.iN.rImis);
0204     lamN = lambda.eqnonlin(nne.i1.iImis:nne.iN.iImis);
0205     bus(:, LAM_P) = (VVr.*lamM + VVi.*lamN) / baseMVA;
0206     bus(:, LAM_Q) = (VVi.*lamM - VVr.*lamN) / baseMVA;
0207 else
0208     bus(:, LAM_P) = lambda.eqnonlin(nne.i1.Pmis:nne.iN.Pmis) / baseMVA;
0209     bus(:, LAM_Q) = lambda.eqnonlin(nne.i1.Qmis:nne.iN.Qmis) / baseMVA;
0210 end
0211 branch(:, MU_SF) = muSf / baseMVA;
0212 branch(:, MU_ST) = muSt / baseMVA;
0213 
0214 %% package up results
0215 nlnN = 2*nb + 2*nl;     %% because muSf and muSt are nl x 1, not nl2 x 1
0216 
0217 %% extract multipliers for nonlinear constraints
0218 kl = find(lambda.eqnonlin(1:2*nb) < 0);
0219 ku = find(lambda.eqnonlin(1:2*nb) > 0);
0220 nl_mu_l = zeros(nlnN, 1);
0221 nl_mu_u = [zeros(2*nb, 1); muSf; muSt];
0222 nl_mu_l(kl) = -lambda.eqnonlin(kl);
0223 nl_mu_u(ku) =  lambda.eqnonlin(ku);
0224 
0225 if isfield(lambda, 'ineqnonlin')
0226     lam_nli = lambda.ineqnonlin;
0227 else
0228     lam_nli = [];
0229 end
0230 
0231 mu = struct( ...
0232   'var', struct('l', lambda.lower, 'u', lambda.upper), ...
0233   'nln', struct('l', nl_mu_l, 'u', nl_mu_u), ...
0234   'nle', lambda.eqnonlin, ...
0235   'nli', lam_nli, ...
0236   'lin', struct('l', lambda.mu_l, 'u', lambda.mu_u) );
0237 
0238 results = mpc;
0239 [results.bus, results.branch, results.gen, ...
0240     results.om, results.x, results.mu, results.f] = ...
0241         deal(bus, branch, gen, om, x, mu, f);
0242 
0243 pimul = [ ...
0244   results.mu.nln.l - results.mu.nln.u;
0245   results.mu.lin.l - results.mu.lin.u;
0246   -ones(ny>0, 1);
0247   results.mu.var.l - results.mu.var.u;
0248 ];
0249 raw = struct('xr', x, 'pimul', pimul, 'info', eflag, 'output', output);
nlpopf_solver

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