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 % Copyright (c) 1996-2015 by Power System Engineering Research Center (PSERC) 0056 % by Ray Zimmerman, PSERC Cornell 0057 % 0058 % $Id: get_losses.m 2644 2015-03-11 19:34:22Z ray $ 0059 % 0060 % This file is part of MATPOWER. 0061 % Covered by the 3-clause BSD License (see LICENSE file for details). 0062 % See http://www.pserc.cornell.edu/matpower/ for more info. 0063 0064 %% default arguments 0065 if isstruct(baseMVA) 0066 mpc = baseMVA; 0067 [baseMVA, bus, branch] = deal(mpc.baseMVA, mpc.bus, mpc.branch); 0068 end 0069 0070 %% define named indices into bus, gen, branch matrices 0071 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ... 0072 VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus; 0073 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ... 0074 TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ... 0075 ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch; 0076 0077 %% create map of external bus numbers to bus indices 0078 i2e = bus(:, BUS_I); 0079 e2i = sparse(max(i2e), 1); 0080 e2i(i2e) = (1:size(bus, 1))'; 0081 out = find(branch(:, BR_STATUS) == 0); %% out-of-service branches 0082 0083 %% sizes of things 0084 nb = size(bus, 1); %% number of buses 0085 nl = size(branch, 1); %% number of branches 0086 0087 %% construct complex bus voltage vector 0088 V = bus(:, VM) .* exp(sqrt(-1) * pi/180 * bus(:, VA)); 0089 0090 %% parameters 0091 Cf = sparse(1:nl, e2i(branch(:, F_BUS)), branch(:, BR_STATUS), nl, nb); 0092 Ct = sparse(1:nl, e2i(branch(:, T_BUS)), branch(:, BR_STATUS), nl, nb); 0093 tap = ones(nl, 1); %% default tap ratio = 1 for lines 0094 xfmr = find(branch(:, TAP)); %% indices of transformers 0095 tap(xfmr) = branch(xfmr, TAP); %% include transformer tap ratios 0096 tap = tap .* exp(1j*pi/180 * branch(:, SHIFT)); %% add phase shifters 0097 A = spdiags(1 ./ tap, 0, nl, nl) * Cf - Ct; 0098 Ysc = 1 ./ (branch(:, BR_R) - 1j * branch(:, BR_X)); 0099 Vdrop = A * V; %% vector of voltage drop across series impedance element 0100 loss = baseMVA * Ysc .* Vdrop .* conj(Vdrop); 0101 % loss = baseMVA * abs(V(e2i(branch(:, F_BUS))) ./ tap - V(e2i(branch(:, T_BUS)))) .^ 2 ./ ... 0102 % (branch(:, BR_R) - 1j * branch(:, BR_X)); 0103 % loss(out) = 0; 0104 0105 if nargout > 1 0106 Vf = Cf * V; 0107 Vt = Ct * V; 0108 fchg = real(baseMVA / 2 * branch(:, BR_B) .* Vf .* conj(Vf) ./ (tap .* conj(tap))); 0109 tchg = real(baseMVA / 2 * branch(:, BR_B) .* Vt .* conj(Vt)); 0110 % fchg = abs(V(e2i(branch(:, F_BUS))) ./ tap) .^ 2 .* branch(:, BR_B) * baseMVA / 2; 0111 % tchg = abs(V(e2i(branch(:, T_BUS))) ) .^ 2 .* branch(:, BR_B) * baseMVA / 2; 0112 fchg(out) = 0; 0113 tchg(out) = 0; 0114 0115 if nargout == 2 0116 fchg = fchg + tchg; 0117 end 0118 end 0119 0120 if nargout > 3 0121 B = spdiags(A * V, 0, nl, nl) * conj(A) * spdiags(conj(V), 0, nb, nb); 0122 dYsc = spdiags(Ysc, 0, nl, nl); 0123 dloss_dV = struct(... 0124 'a', -1j * baseMVA * dYsc * (B - conj(B)), ... 0125 'm', baseMVA * dYsc * (B + conj(B)) * spdiags(1 ./ abs(V), 0, nb, nb) ... 0126 ); 0127 if nargout > 4 0128 Bc = spdiags(branch(:, BR_B), 0, nl, nl); 0129 tt = spdiags(1 ./ (tap .* conj(tap)), 0, nl, nl); 0130 dchg_dVm = struct(... 0131 'f', baseMVA * Bc * tt * spdiags(Cf * bus(:, VM), 0, nb, nb) * Cf, ... 0132 't', baseMVA * Bc * spdiags(Ct * bus(:, VM), 0, nb, nb) * Ct ... 0133 ); 0134 end 0135 end