GET_LOSSES Returns series losses (and reactive injections) per branch.
LOSS = GET_LOSSES(RESULTS)
LOSS = GET_LOSSES(BASEMVA, BUS, BRANCH)
[LOSS, CHG] = GET_LOSSES(RESULTS)
[LOSS, FCHG, TCHG] = GET_LOSSES(RESULTS)
[LOSS, FCHG, TCHG, DLOSS_DV] = GET_LOSSES(RESULTS)
[LOSS, FCHG, TCHG, DLOSS_DV, DCHG_DVM] = GET_LOSSES(RESULTS)
Computes branch series losses, and optionally reactive injections from
line charging, as functions of bus voltages and branch parameters, using the
following formulae:
loss = abs( Vf / tau - Vt ) ^ 2 / (Rs - j Xs)
fchg = abs( Vf / tau ) ^ 2 * Bc / 2
tchg = abs( Vt ) ^ 2 * Bc / 2
Optionally, computes the partial derivatives of the line losses with
respect to voltage angles and magnitudes.
Input:
RESULTS - a MATPOWER case struct with bus voltages corresponding to
a valid power flow solution.
(Can optionally be specified as individual fields BASEMVA,
BUS, and BRANCH.)
Output(s):
LOSS - complex NL x 1 vector of losses (in MW), where NL is the number
of branches in the system, representing only the losses in the
series impedance element of the PI model for each branch.
CHG - NL x 1 vector of total reactive injection for each line
(in MVAr), representing the line charging injections of both
of the shunt elements of PI model for each branch.
FCHG - Same as CHG, but for the element at the "from" end of the
branch only.
TCHG - Same as CHG, but for the element at the "to" end of the branch.
DLOSS_DV - Struct with partial derivatives of LOSS with respect to bus
voltages, with fields:
.a - Partial with respect to bus voltage angles.
.m - Partial with respect to bus voltage magnitudes.
DCHG_DVM - Struct with partial derivatives of FCHG and TCHG with
respect to bus voltage magnitudes, with fields:
.f - Partial of FCHG with respect to bus voltage magnitudes.
.t - Partial of TCHG with respect to bus voltage magnitudes.
Example:
results = runpf(mycase);
total_system_real_losses = sum(real(get_losses(results)));
[loss, fchg, tchg, dloss_dV] = get_losses(results);0001 function [loss, fchg, tchg, dloss_dV, dchg_dVm] = get_losses(baseMVA, bus, branch) 0002 %GET_LOSSES Returns series losses (and reactive injections) per branch. 0003 % 0004 % LOSS = GET_LOSSES(RESULTS) 0005 % LOSS = GET_LOSSES(BASEMVA, BUS, BRANCH) 0006 % 0007 % [LOSS, CHG] = GET_LOSSES(RESULTS) 0008 % [LOSS, FCHG, TCHG] = GET_LOSSES(RESULTS) 0009 % [LOSS, FCHG, TCHG, DLOSS_DV] = GET_LOSSES(RESULTS) 0010 % [LOSS, FCHG, TCHG, DLOSS_DV, DCHG_DVM] = GET_LOSSES(RESULTS) 0011 % 0012 % Computes branch series losses, and optionally reactive injections from 0013 % line charging, as functions of bus voltages and branch parameters, using the 0014 % following formulae: 0015 % 0016 % loss = abs( Vf / tau - Vt ) ^ 2 / (Rs - j Xs) 0017 % fchg = abs( Vf / tau ) ^ 2 * Bc / 2 0018 % tchg = abs( Vt ) ^ 2 * Bc / 2 0019 % 0020 % Optionally, computes the partial derivatives of the line losses with 0021 % respect to voltage angles and magnitudes. 0022 % 0023 % Input: 0024 % RESULTS - a MATPOWER case struct with bus voltages corresponding to 0025 % a valid power flow solution. 0026 % (Can optionally be specified as individual fields BASEMVA, 0027 % BUS, and BRANCH.) 0028 % 0029 % Output(s): 0030 % LOSS - complex NL x 1 vector of losses (in MW), where NL is the number 0031 % of branches in the system, representing only the losses in the 0032 % series impedance element of the PI model for each branch. 0033 % CHG - NL x 1 vector of total reactive injection for each line 0034 % (in MVAr), representing the line charging injections of both 0035 % of the shunt elements of PI model for each branch. 0036 % FCHG - Same as CHG, but for the element at the "from" end of the 0037 % branch only. 0038 % TCHG - Same as CHG, but for the element at the "to" end of the branch. 0039 % DLOSS_DV - Struct with partial derivatives of LOSS with respect to bus 0040 % voltages, with fields: 0041 % .a - Partial with respect to bus voltage angles. 0042 % .m - Partial with respect to bus voltage magnitudes. 0043 % DCHG_DVM - Struct with partial derivatives of FCHG and TCHG with 0044 % respect to bus voltage magnitudes, with fields: 0045 % .f - Partial of FCHG with respect to bus voltage magnitudes. 0046 % .t - Partial of TCHG with respect to bus voltage magnitudes. 0047 % 0048 % Example: 0049 % results = runpf(mycase); 0050 % total_system_real_losses = sum(real(get_losses(results))); 0051 % 0052 % [loss, fchg, tchg, dloss_dV] = get_losses(results); 0053 0054 % MATPOWER 0055 % $Id: get_losses.m 2473 2014-12-16 21:32:31Z ray $ 0056 % by Ray Zimmerman, PSERC Cornell 0057 % Copyright (c) 1996-2014 by Power System Engineering Research Center (PSERC) 0058 % 0059 % This file is part of MATPOWER. 0060 % See http://www.pserc.cornell.edu/matpower/ for more info. 0061 % 0062 % MATPOWER is free software: you can redistribute it and/or modify 0063 % it under the terms of the GNU General Public License as published 0064 % by the Free Software Foundation, either version 3 of the License, 0065 % or (at your option) any later version. 0066 % 0067 % MATPOWER is distributed in the hope that it will be useful, 0068 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0069 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0070 % GNU General Public License for more details. 0071 % 0072 % You should have received a copy of the GNU General Public License 0073 % along with MATPOWER. If not, see <http://www.gnu.org/licenses/>. 0074 % 0075 % Additional permission under GNU GPL version 3 section 7 0076 % 0077 % If you modify MATPOWER, or any covered work, to interface with 0078 % other modules (such as MATLAB code and MEX-files) available in a 0079 % MATLAB(R) or comparable environment containing parts covered 0080 % under other licensing terms, the licensors of MATPOWER grant 0081 % you additional permission to convey the resulting work. 0082 0083 %% default arguments 0084 if isstruct(baseMVA) 0085 mpc = baseMVA; 0086 [baseMVA, bus, branch] = deal(mpc.baseMVA, mpc.bus, mpc.branch); 0087 end 0088 0089 %% define named indices into bus, gen, branch matrices 0090 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ... 0091 VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus; 0092 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ... 0093 TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ... 0094 ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch; 0095 0096 %% create map of external bus numbers to bus indices 0097 i2e = bus(:, BUS_I); 0098 e2i = sparse(max(i2e), 1); 0099 e2i(i2e) = (1:size(bus, 1))'; 0100 out = find(branch(:, BR_STATUS) == 0); %% out-of-service branches 0101 0102 %% sizes of things 0103 nb = size(bus, 1); %% number of buses 0104 nl = size(branch, 1); %% number of branches 0105 0106 %% construct complex bus voltage vector 0107 V = bus(:, VM) .* exp(sqrt(-1) * pi/180 * bus(:, VA)); 0108 0109 %% parameters 0110 Cf = sparse(1:nl, e2i(branch(:, F_BUS)), branch(:, BR_STATUS), nl, nb); 0111 Ct = sparse(1:nl, e2i(branch(:, T_BUS)), branch(:, BR_STATUS), nl, nb); 0112 tap = ones(nl, 1); %% default tap ratio = 1 for lines 0113 xfmr = find(branch(:, TAP)); %% indices of transformers 0114 tap(xfmr) = branch(xfmr, TAP); %% include transformer tap ratios 0115 tap = tap .* exp(1j*pi/180 * branch(:, SHIFT)); %% add phase shifters 0116 A = spdiags(1 ./ tap, 0, nl, nl) * Cf - Ct; 0117 Ysc = 1 ./ (branch(:, BR_R) - 1j * branch(:, BR_X)); 0118 Vdrop = A * V; %% vector of voltage drop across series impedance element 0119 loss = baseMVA * Ysc .* Vdrop .* conj(Vdrop); 0120 % loss = baseMVA * abs(V(e2i(branch(:, F_BUS))) ./ tap - V(e2i(branch(:, T_BUS)))) .^ 2 ./ ... 0121 % (branch(:, BR_R) - 1j * branch(:, BR_X)); 0122 % loss(out) = 0; 0123 0124 if nargout > 1 0125 Vf = Cf * V; 0126 Vt = Ct * V; 0127 fchg = real(baseMVA / 2 * branch(:, BR_B) .* Vf .* conj(Vf) ./ (tap .* conj(tap))); 0128 tchg = real(baseMVA / 2 * branch(:, BR_B) .* Vt .* conj(Vt)); 0129 % fchg = abs(V(e2i(branch(:, F_BUS))) ./ tap) .^ 2 .* branch(:, BR_B) * baseMVA / 2; 0130 % tchg = abs(V(e2i(branch(:, T_BUS))) ) .^ 2 .* branch(:, BR_B) * baseMVA / 2; 0131 fchg(out) = 0; 0132 tchg(out) = 0; 0133 0134 if nargout == 2 0135 fchg = fchg + tchg; 0136 end 0137 end 0138 0139 if nargout > 3 0140 B = spdiags(A * V, 0, nl, nl) * conj(A) * spdiags(conj(V), 0, nb, nb); 0141 dYsc = spdiags(Ysc, 0, nl, nl); 0142 dloss_dV = struct(... 0143 'a', -1j * baseMVA * dYsc * (B - conj(B)), ... 0144 'm', baseMVA * dYsc * (B + conj(B)) * spdiags(1 ./ abs(V), 0, nb, nb) ... 0145 ); 0146 if nargout > 4 0147 Bc = spdiags(branch(:, BR_B), 0, nl, nl); 0148 tt = spdiags(1 ./ (tap .* conj(tap)), 0, nl, nl); 0149 dchg_dVm = struct(... 0150 'f', baseMVA * Bc * tt * spdiags(Cf * bus(:, VM), 0, nb, nb) * Cf, ... 0151 't', baseMVA * Bc * spdiags(Ct * bus(:, VM), 0, nb, nb) * Ct ... 0152 ); 0153 end 0154 end