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function [f, g] = fun_copf(x, om, Ybus, Yf, Yt, Afeq, bfeq, Af, bf, mpopt, il)
%------------------------------ deprecated ------------------------------
% OPF solvers based on CONSTR & LPCONSTR to be removed in future version.
%--------------------------------------------------------------------------
%FUN_COPF Evaluates objective function and constraints for OPF.
% [F, G] = FUN_COPF(X, OM, YBUS, YF, YT, AFEQ, BFEQ, AF, BF, MPOPT)
% [F, G] = FUN_COPF(X, OM, YBUS, YF, YT, AFEQ, BFEQ, AF, BF, MPOPT, IL)
%
% Objective and constraint evaluation function for AC optimal power
% flow, suitable for use with CONSTR.
%
% 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
% AFEQ : sparse A matrix for linear equality constraints
% BFEQ : right hand side vector for linear equality constraints
% AF : sparse A matrix for linear inequality constraints
% BF : right hand side vector for linear inequality constraints
% MPOPF : MATPOWER options vector
% 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:
% F : value of objective function
% G : vector of constraint values, in the following order
% nonlinear equality (power balance)
% linear equality
% nonlinear inequality (flow limits)
% linear inequality
% The flow limits (limit^2 - flow^2) can be apparent power
% real power or current, depending on value of OPF_FLOW_LIM
% in MPOPT (only for constrained lines)
% MATPOWER
% $Id: fun_copf.m,v 1.17 2010/06/09 14:56:58 ray Exp $
% 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 <http://www.gnu.org/licenses/>.
%
% 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 nargin < 11
il = [];
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);
%% problem dimensions
ny = getN(om, 'var', 'y'); %% number of piece-wise linear costs
nxyz = length(x); %% total number of control vars of all types
%% set default constrained lines
if isempty(il)
nl = size(branch, 1); %% number of branches
il = (1:nl); %% all lines have limits by default
end
%% 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
%%----- 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 = [ gen(:, PG); gen(:, QG)];
if ~isempty(ipol)
f = sum( totcost(gencost(ipol, :), xx(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;
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 constraints -----
%% reconstruct V
Va = x(vv.i1.Va:vv.iN.Va);
Vm = x(vv.i1.Vm:vv.iN.Vm);
V = Vm .* exp(1j * Va);
%% rebuild Sbus
Sbus = makeSbus(baseMVA, bus, gen); %% net injected power in p.u.
%% evaluate power flow equations
mis = V .* conj(Ybus * V) - Sbus;
%%----- evaluate constraint function values -----
%% first, the equality constraints (power flow)
geq = [ real(mis); %% active power mismatch for all buses
imag(mis) ]; %% reactive power mismatch for all buses
%% then, the inequality constraints (branch flow limits)
flow_max = (branch(il, RATE_A)/baseMVA).^2;
flow_max(flow_max == 0) = Inf;
if mpopt(24) == 2 %% current magnitude limit, |I|
If = Yf * V;
It = Yt * V;
gineq = [ 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 mpopt(24) == 1 %% active power limit, P (Pan Wei)
gineq = [ 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|
gineq = [ Sf .* conj(Sf) - flow_max; %% branch apparent power limits (from bus)
St .* conj(St) - flow_max ]; %% branch apparent power limits (to bus)
end
end
g = [geq; Afeq * x - bfeq; gineq; Af * x - bf];