Home > matpower6.0 > get_losses.m

get_losses

PURPOSE ^

GET_LOSSES Returns series losses (and reactive injections) per branch.

SYNOPSIS ^

function [loss, fchg, tchg, dloss_dV, dchg_dVm] = get_losses(baseMVA, bus, branch)

DESCRIPTION ^

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);

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

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) 1996-2016, Power Systems Engineering Research Center (PSERC)
0056 %   by Ray Zimmerman, PSERC Cornell
0057 %
0058 %   This file is part of MATPOWER.
0059 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0060 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0061 
0062 %% default arguments
0063 if isstruct(baseMVA)
0064     mpc = baseMVA;
0065     [baseMVA, bus, branch] = deal(mpc.baseMVA, mpc.bus, mpc.branch);
0066 end
0067 
0068 %% define named indices into bus, gen, branch matrices
0069 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
0070     VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
0071 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
0072     TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
0073     ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;
0074 
0075 %% create map of external bus numbers to bus indices
0076 i2e = bus(:, BUS_I);
0077 e2i = sparse(max(i2e), 1);
0078 e2i(i2e) = (1:size(bus, 1))';
0079 out = find(branch(:, BR_STATUS) == 0);          %% out-of-service branches
0080 
0081 %% sizes of things
0082 nb = size(bus, 1);      %% number of buses
0083 nl = size(branch, 1);   %% number of branches
0084 
0085 %% construct complex bus voltage vector
0086 V = bus(:, VM) .* exp(sqrt(-1) * pi/180 * bus(:, VA));
0087 
0088 %% parameters
0089 Cf = sparse(1:nl, e2i(branch(:, F_BUS)), branch(:, BR_STATUS), nl, nb);
0090 Ct = sparse(1:nl, e2i(branch(:, T_BUS)), branch(:, BR_STATUS), nl, nb);
0091 tap = ones(nl, 1);                              %% default tap ratio = 1 for lines
0092 xfmr = find(branch(:, TAP));                    %% indices of transformers
0093 tap(xfmr) = branch(xfmr, TAP);                  %% include transformer tap ratios
0094 tap = tap .* exp(1j*pi/180 * branch(:, SHIFT)); %% add phase shifters
0095 A = spdiags(1 ./ tap, 0, nl, nl) * Cf - Ct;
0096 Ysc = 1 ./ (branch(:, BR_R) - 1j * branch(:, BR_X));
0097 Vdrop = A * V;      %% vector of voltage drop across series impedance element
0098 loss = baseMVA * Ysc .* Vdrop .* conj(Vdrop);
0099 % loss = baseMVA * abs(V(e2i(branch(:, F_BUS))) ./ tap - V(e2i(branch(:, T_BUS)))) .^ 2 ./ ...
0100 %             (branch(:, BR_R) - 1j * branch(:, BR_X));
0101 % loss(out) = 0;
0102 
0103 if nargout > 1
0104     Vf = Cf * V;
0105     Vt = Ct * V;
0106     fchg = real(baseMVA / 2 * branch(:, BR_B) .* Vf .* conj(Vf) ./ (tap .* conj(tap)));
0107     tchg = real(baseMVA / 2 * branch(:, BR_B) .* Vt .* conj(Vt));
0108 %     fchg = abs(V(e2i(branch(:, F_BUS))) ./ tap) .^ 2 .* branch(:, BR_B) * baseMVA / 2;
0109 %     tchg = abs(V(e2i(branch(:, T_BUS)))       ) .^ 2 .* branch(:, BR_B) * baseMVA / 2;
0110     fchg(out) = 0;
0111     tchg(out) = 0;
0112 
0113     if nargout == 2
0114         fchg = fchg + tchg;
0115     end
0116 end
0117 
0118 if nargout > 3
0119     B = spdiags(A * V, 0, nl, nl) * conj(A) * spdiags(conj(V), 0, nb, nb);
0120     dYsc = spdiags(Ysc, 0, nl, nl);
0121     dloss_dV = struct(...
0122         'a', -1j * baseMVA * dYsc * (B - conj(B)), ...
0123         'm',       baseMVA * dYsc * (B + conj(B)) * spdiags(1 ./ abs(V), 0, nb, nb) ...
0124     );
0125     if nargout > 4
0126         Bc = spdiags(branch(:, BR_B), 0, nl, nl);
0127         tt = spdiags(1 ./ (tap .* conj(tap)), 0, nl, nl);
0128         dchg_dVm = struct(...
0129             'f', baseMVA * Bc * tt * spdiags(Cf * bus(:, VM), 0, nb, nb) * Cf, ...
0130             't', baseMVA * Bc      * spdiags(Ct * bus(:, VM), 0, nb, nb) * Ct ...
0131         );
0132     end
0133 end

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