MATLAB coding for Y-bus

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

Basics of Shunt Reactive Compensation

Purpose of providing Reactive Compensation:

The purpose of providing reactive compensation is to change the natural electrical characteristics of a transmission line. Shunt connected capacitors are used to maintain the voltage of the transmission system at desired levels during the loaded condition whereas shunt connected reactors are employed to reduce line overvoltages under light load or no-load conditions.

The voltage sag is largest at the midpoint for an uncompensated transmission line. Thus, the optimum location to place a shunt compensator is at the midpoint. Also, the compensator at the midpoint segments the line into two equal sections for each of which the maximum transmittable power is the same. The midpoint shunt compensation can significantly increase the transmittable power but the reactive power demand on the compensator increases rapidly with the increase in transmitted power.

Multiple shunt compensators can be placed on the transmission line located equidistance from each other. With the increase in number of compensators and hence the segments of the line, the voltage profile of the line approaches a flat profile. Theoretically the power which can be transferred over a transmission line doubles with each doubling of the segment. Such a system however would become too complex and costly.

Machine Angle Oscillation in Under-damped Power System:

In an under-damped power system, a small disturbance may cause the machine angle to oscillate around its steady-state value at the natural frequency of the entire electro-mechanical system. This oscillation of angle results in a corresponding sustained power oscillation. By appropriate variations in the shunt reactive compensation and hence in the voltage of the transmission line, the accelerating and decelerating swings of the disturbed machine or machines can be neutralized. 

When the oscillating generator accelerates and the machine angle increases, the electric power transferred must be increased to compensate for the excess mechanical input power. On the other hand the power transmitted must be reduced to counter the reduced mechanical input when the generator decelerates and the angle decreases. 

Thus, with appropriate and fast controls, shunt reactive compensation is able to change the power flow in a system during and following dynamic disturbances. This increases the transient stability and damps the power oscillations. Hence reactive or VAr compensation is used for voltage regulation at the midpoint or at some intermediate locations in the transmission line and at the end of a radial transmission line to avoid voltage instability, to increase transient stability and to damp power oscillations.

Ref: Hingorani and Gyugyi, “Understanding FACTS”, John Wiley & Sons, UK