MAKEBDC Builds the B matrices and phase shift injections for DC power flow.
[BBUS, BF, PBUSINJ, PFINJ] = MAKEBDC(MPC)
[BBUS, BF, PBUSINJ, PFINJ] = MAKEBDC(BASEMVA, BUS, BRANCH)
Returns the B matrices and phase shift injection vectors needed for
a DC power flow. The bus real power injections are related to bus
voltage angles by
P = BBUS * Va + PBUSINJ
The real power flows at the from end the lines are related to the bus
voltage angles by
Pf = BF * Va + PFINJ
Does appropriate conversions to p.u.
Bus numbers must be consecutive beginning at 1 (i.e. internal ordering).
Example:
[Bbus, Bf, Pbusinj, Pfinj] = makeBdc(baseMVA, bus, branch);
See also DCPF.0001 function [Bbus, Bf, Pbusinj, Pfinj] = makeBdc(baseMVA, bus, branch) 0002 %MAKEBDC Builds the B matrices and phase shift injections for DC power flow. 0003 % [BBUS, BF, PBUSINJ, PFINJ] = MAKEBDC(MPC) 0004 % [BBUS, BF, PBUSINJ, PFINJ] = MAKEBDC(BASEMVA, BUS, BRANCH) 0005 % 0006 % Returns the B matrices and phase shift injection vectors needed for 0007 % a DC power flow. The bus real power injections are related to bus 0008 % voltage angles by 0009 % P = BBUS * Va + PBUSINJ 0010 % The real power flows at the from end the lines are related to the bus 0011 % voltage angles by 0012 % Pf = BF * Va + PFINJ 0013 % Does appropriate conversions to p.u. 0014 % Bus numbers must be consecutive beginning at 1 (i.e. internal ordering). 0015 % 0016 % Example: 0017 % [Bbus, Bf, Pbusinj, Pfinj] = makeBdc(baseMVA, bus, branch); 0018 % 0019 % See also DCPF. 0020 0021 % MATPOWER 0022 % Copyright (c) 1996-2016, Power Systems Engineering Research Center (PSERC) 0023 % by Carlos E. Murillo-Sanchez, PSERC Cornell & Universidad Nacional de Colombia 0024 % and Ray Zimmerman, PSERC Cornell 0025 % 0026 % This file is part of MATPOWER. 0027 % Covered by the 3-clause BSD License (see LICENSE file for details). 0028 % See https://matpower.org for more info. 0029 0030 %% extract from MPC if necessary 0031 if nargin < 3 0032 mpc = baseMVA; 0033 baseMVA = mpc.baseMVA; 0034 bus = mpc.bus; 0035 branch = mpc.branch; 0036 end 0037 0038 %% constants 0039 nb = size(bus, 1); %% number of buses 0040 nl = size(branch, 1); %% number of lines 0041 0042 %% define named indices into bus, branch matrices 0043 [PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ... 0044 VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus; 0045 [F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ... 0046 TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ... 0047 ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch; 0048 0049 %% check that bus numbers are equal to indices to bus (one set of bus numbers) 0050 if any(bus(:, BUS_I) ~= (1:nb)') 0051 error('makeBdc: buses must be numbered consecutively in bus matrix; use ext2int() to convert to internal ordering') 0052 end 0053 0054 %% for each branch, compute the elements of the branch B matrix and the phase 0055 %% shift "quiescent" injections, where 0056 %% 0057 %% | Pf | | Bff Bft | | Vaf | | Pfinj | 0058 %% | | = | | * | | + | | 0059 %% | Pt | | Btf Btt | | Vat | | Ptinj | 0060 %% 0061 stat = branch(:, BR_STATUS); %% ones at in-service branches 0062 b = stat ./ branch(:, BR_X); %% series susceptance 0063 tap = ones(nl, 1); %% default tap ratio = 1 0064 i = find(branch(:, TAP)); %% indices of non-zero tap ratios 0065 tap(i) = branch(i, TAP); %% assign non-zero tap ratios 0066 b = b ./ tap; 0067 0068 %% build connection matrix Cft = Cf - Ct for line and from - to buses 0069 f = branch(:, F_BUS); %% list of "from" buses 0070 t = branch(:, T_BUS); %% list of "to" buses 0071 i = [(1:nl)'; (1:nl)']; %% double set of row indices 0072 Cft = sparse(i, [f;t], [ones(nl, 1); -ones(nl, 1)], nl, nb); %% connection matrix 0073 0074 %% build Bf such that Bf * Va is the vector of real branch powers injected 0075 %% at each branch's "from" bus 0076 Bf = sparse(i, [f; t], [b; -b], nl, nb); % = spdiags(b, 0, nl, nl) * Cft; 0077 0078 %% build Bbus 0079 Bbus = Cft' * Bf; 0080 0081 %% build phase shift injection vectors 0082 Pfinj = b .* (-branch(:, SHIFT) * pi/180); %% injected at the from bus ... 0083 % Ptinj = -Pfinj; %% ... and extracted at the to bus 0084 Pbusinj = Cft' * Pfinj; %% Pbusinj = Cf * Pfinj + Ct * Ptinj;