makeYbus.m

function [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch)
%MAKEYBUS   Builds the bus admittance matrix and branch admittance matrices.
%   [YBUS, YF, YT] = MAKEYBUS(MPC)
%   [YBUS, YF, YT] = MAKEYBUS(BASEMVA, BUS, BRANCH)
%   
%   Returns the full bus admittance matrix (i.e. for all buses) and the
%   matrices YF and YT which, when multiplied by a complex voltage vector,
%   yield the vector currents injected into each line from the "from" and
%   "to" buses respectively of each line. Does appropriate conversions to p.u.
%   Inputs can be a MATPOWER case struct or individual BASEMVA, BUS and
%   BRANCH values. Bus numbers must be consecutive beginning at 1 (internal
%   ordering).
%
%   See also MAKEJAC, MAKESBUS, EXT2INT.

%   MATPOWER
%   $Id: makeYbus.m,v 1.17 2010/06/25 17:37:40 ray Exp $
%   by 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.

if nargin < 3
    mpc     = baseMVA;
    baseMVA = mpc.baseMVA;
    bus     = mpc.bus;
    branch  = mpc.branch;
end

%% constants
nb = size(bus, 1);          %% number of buses
nl = size(branch, 1);       %% number of lines

%% define named indices into bus, branch matrices
% bus related indexes
BUS_I = 1;
GS = 5;
BS = 6;
% branch related indexes
F_BUS = 1;
T_BUS = 2;
BR_R = 3;
BR_X = 4;
BR_B = 5;
TAP = 9;
SHIFT = 10;
BR_STATUS = 11;

%% check that bus numbers are equal to indices to bus (one set of bus numbers)
if any(bus(:, BUS_I) ~= (1:nb)')
    error('buses must appear in order by bus number')
end

%% for each branch, compute the elements of the branch admittance matrix where
%%
%%      | If |   | Yff  Yft |   | Vf |
%%      |    | = |          | * |    |
%%      | It |   | Ytf  Ytt |   | Vt |
%%
stat = branch(:, BR_STATUS);                    %% ones at in-service branches
Ys = stat ./ (branch(:, BR_R) + 1j * branch(:, BR_X));  %% series admittance
Bc = stat .* branch(:, BR_B);                           %% line charging susceptance
tap = ones(nl, 1);                              %% default tap ratio = 1
i = find(branch(:, TAP));                       %% indices of non-zero tap ratios
tap(i) = branch(i, TAP);                        %% assign non-zero tap ratios
tap = tap .* exp(1j*pi/180 * branch(:, SHIFT)); %% add phase shifters
Ytt = Ys + 1j*Bc/2;
Yff = Ytt ./ (tap .* conj(tap));
Yft = - Ys ./ conj(tap);
Ytf = - Ys ./ tap;

%% compute shunt admittance
%% if Psh is the real power consumed by the shunt at V = 1.0 p.u.
%% and Qsh is the reactive power injected by the shunt at V = 1.0 p.u.
%% then Psh - j Qsh = V * conj(Ysh * V) = conj(Ysh) = Gs - j Bs,
%% i.e. Ysh = Psh + j Qsh, so ...
Ysh = (bus(:, GS) + 1j * bus(:, BS)) / baseMVA; %% vector of shunt admittances

%% build connection matrices
f = branch(:, F_BUS);                           %% list of "from" buses
t = branch(:, T_BUS);                           %% list of "to" buses
Cf = sparse(1:nl, f, ones(nl, 1), nl, nb);      %% connection matrix for line & from buses
Ct = sparse(1:nl, t, ones(nl, 1), nl, nb);      %% connection matrix for line & to buses

%% build Yf and Yt such that Yf * V is the vector of complex branch currents injected
%% at each branch's "from" bus, and Yt is the same for the "to" bus end
i = [1:nl; 1:nl]';                              %% double set of row indices
Yf = sparse(i, [f; t], [Yff; Yft], nl, nb);
Yt = sparse(i, [f; t], [Ytf; Ytt], nl, nb);
% Yf = spdiags(Yff, 0, nl, nl) * Cf + spdiags(Yft, 0, nl, nl) * Ct;
% Yt = spdiags(Ytf, 0, nl, nl) * Cf + spdiags(Ytt, 0, nl, nl) * Ct;

%% build Ybus
Ybus = Cf' * Yf + Ct' * Yt + ...                %% branch admittances
        sparse(1:nb, 1:nb, Ysh, nb, nb);        %% shunt admittance