In
recent years, the analysis and design of power system have been influenced
greatly by the high end performance of personal computers. These computers can
be used to perform the steady-state and transient analysis of large
interconnected power systems.

MATLAB
which stands for MATrix LABoratory, is a powerful software package developed by
MathWorks Inc. This software having
analysis capability, flexibility, reliability and powerful graphics is
currently the main software package used by power system engineers. MATLAB
provides matrix as one of the basic elements and does the basic operation as
addition, subtraction, multiplication using simple mathematical operators. With
hundreds of reliable and built in functions, MATLAB helps in solving a variety
of mathematical problems including differential equations, linear systems,
non-linear systems, optimization and many other type of engineering
computations.The
most appreciable feature of MATLAB is its programming capability and the
several optional toolboxes for simulating specialized problems of different
areas.

In
power system,

**nodal admittance matrix**or**bus admittance matrix**or**Y matrix**or**Y bus**is an*n*x*n*matrix describing a power system with*n*buses. It represents the nodal admittance of the buses in a power system. In a real power system, each bus is usually connected to only a few other buses, hence the Y bus matrix is sparse. The Y bus is one of the data requirements needed to formulate a power flow study.
Power
flow studies, commonly known as load flow, are necessary for planning,
operation, economic scheduling and exchange of power between utilities. Power
flow analysis is also required for transient stability and contingency studies.

Y
bus is a tool that provides a method of systematically reducing a complex power
system to a matrix that can be solved by a computer program. The equation used
to formulate Y bus is based on Kirchhoff’s Current Law (KCL) and Kirchhoff’s
Voltage Law (KVL), applied to a circuit with steady state sinusoidal operation.
These laws are applied to all the nodes of a power system and elements of the
admittance matrix are determined, which then represents the admittance
relationship between nodes to further find the voltages, currents and power
flows in the system.

The
below given MATLAB program is for the formulation of

**bus admittance matrix**or the**Y bus**.
The
input data required for Y bus formulation is “linedata” which contains 4 columns. The
1

^{st}column gives the branch number. The 2^{nd}column is the “from bus” number whereas the 3^{rd}column is the “to bus” number. The 4^{th}column is the admittance of the corresponding branch.
%
Declaring function [Y] that takes the “linedata” as input and returns Y bus matrix
as output.

function [Y]=ybus(linedata)

% extracting the maximum
numerical value of column 1 of the “linedata” which gives the maximum number of %branches in the network.

elements=max(linedata(:,1));

% defining the total number of buses in the
network.

buses=max(max(linedata(:,2)),max(linedata(:,3)));

Y=zeros(buses,buses);

% defining a loop
for the diagonal and off-diagonal elements of Y -bus

for row=1:elements,

i1=linedata(row,2);

j1=linedata(row,3);

Y(i1,i1) =Y(i1,i1) + linedata(row,4);

Y(i1,j1) =Y(i1,j1) -
linedata(row,4);

Y(j1,i1) =Y(i1,j1);

Y(j1,j1) =Y(j1,j1) + linedata(row,4);

end

Y