function [Ybus, Yf, Yt] = makeYbus(baseMVA, bus, branch)
%MAKEYBUS   Builds the bus admittance matrix and branch admittance matrices.
%   [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.

%   MATPOWER
%   $Id: makeYbus.m,v 1.13 2009/12/04 20:31:20 ray Exp $
%   by Ray Zimmerman, PSERC Cornell
%   Copyright (c) 1996-2005 by Power System Engineering Research Center (PSERC)
%   See http://www.pserc.cornell.edu/matpower/ for more info.

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

%% define named indices into bus, branch matrices
[PQ, PV, REF, NONE, BUS_I, BUS_TYPE, PD, QD, GS, BS, BUS_AREA, VM, ...
    VA, BASE_KV, ZONE, VMAX, VMIN, LAM_P, LAM_Q, MU_VMAX, MU_VMIN] = idx_bus;
[F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, ...
    TAP, SHIFT, BR_STATUS, PF, QF, PT, QT, MU_SF, MU_ST, ...
    ANGMIN, ANGMAX, MU_ANGMIN, MU_ANGMAX] = idx_brch;

%% 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
