Wavelet transform for Fault Detection in Transmission lines

INTRODUCTION

This project focuses on finding faults in power systems using wavelet transform

and neural networks. These days distance relays are used to find out the zones in

which the fault has occurred but they cannot precisely tell us where the fault has

occurred. Similarly the signal processing techniques like Fourier transform fail to

tell us the complete story about the faults. It is here that we intend to use the

wavelet transform as an aid to know the exact fault location.

The advantage of the wavelet transform is that the band of analysis can be adjusted

to allow high-frequency and low-frequency components to be precisely detected.

As a result, the wavelet transform is not intended to replace the Fourier transform

in analyzing steady state signals. It is an alternative tool for analyzing non-

stationary or non-steady state signals. This is due to that the wavelet transform is

very effective in detecting transient signals generated by the faults.

The scheme can be divided into two stages

i) The time-frequency analysis of transients using wavelet transforms

ii) Pattern recognition to identify causes of faults

Discrete Wavelet Transform is applied for determining the fundamental

component, which can be useful to provide valuable information to the relay to

respond to a fault. The Wavelet Transform provides sufficient information both for

analysis and synthesis of original signal, with a significant reduction in the

computation of time. By using the Wavelet Transform it is possible to know what

spectral components occur at a particular time. The Discrete Wavelet

Transform (DWT) can be implemented to extract the fundamental frequency

components of voltages and currents, which can be used to calculate the impedance

up to the fault

point.

WAVELET TRANSFORM

From Fourier Theory, it is known that a signal can be expressed as the sum of

possibly infinite, series of sines and cosines. This sum is also referred to as Fourier

expansion. FT gives the frequency information of the signal, which means that the

frequency components exist in the signal can be known. But, it does not give any

information about at the time of these frequency components exist. This

information is not required when the signal is stationary. Most of the waveforms

associated with fast electromagnetic transients are non-stationary signals which

contain both high frequency oscillations and localized impulses super imposed on

the power frequency and its harmonics. With FT, it is impossible to find a

particular fault location. It is very much needed in transient signals. This is a

serious drawback of Fourier

Analysis. The Wavelet transform is the most recent solution to overcome the

shortcomings of Fourier transform. In the wavelet analysis the use of a fully

scalable modulated window solves the signals. The window is shifted along the

signal and for every position the frequency spectrum is calculated. Then this

process is repeated many times with slightly shorter (or longer) windows for every

new cycle. In the end, the result will be a collection of time representation of the

signal, with all different resolutions.

The Discrete Wavelet Transform (DWT) of the signal X (k) is defined as

(1)

(2)

The above eqn (2) is the complex conjugate of dilated and shifted version of

mother wavelet ȥ(k), a and b are the scaling and translation parameters. The

parameters a & b are functions of the parameter m,

TRANSMISSION LINE EQUATIONS

A transmission line is a system of conductors connecting one point to

another and along which electromagnetic energy can be sent. Power

transmission lines are a typical example of transmission lines. The

transmission line equations that govern general two-conductor uniform

transmission lines, including two and three wire lines, and coaxial cables, are

called the telegraph equations. The general transmission line equations are

named the telegraph equations because they were formulated for the first

time by Oliver Heaviside (1850-1925) when he was employed by a telegraph

company and used to investigate disturbances on telephone wires [1]. When

one considers a line segment dx with parameters resistance (R), conductance

(G), inductance (L), and capacitance (C), all per unit length,(see Figure 3.1)

the line constants for segment dx are Rdx, Gdx, Ldx, and Cdx. The electric flux ψ

and the magnetic flux Ф created by the electromagnetic wave, which causes the

instantaneous voltage u(x,t)and current i(x,t)

Calculating the voltage drop in the positive direction of dx of the distance dx one

obtains

If dx cancelled from both sides of equation (4), the voltage equation becomes,

Similarly, for the current flowing through G and the current charging C,

Kirchhoff‟s current law can be applied as

If dx cancelled from both sides of (6), the current

equation becomes

The negative sign in these equations is caused by the fact that

when the current and voltage waves propagates in the positive x-direction,

i(x,t),& and u(x,t),& will decrease in amplitude for increasing x,

The expressions of line impedance, Z and admittance Y are given by

Differentiate once more with respect to x, the second-order

partial differential equations

In this equation, 8 is a complex quantity which is known as the propagation

constant, and is given by,

Where, α is the attenuation constant which has an influence on the amplitude of

the wave, and β is the phase constant which has an influence on the phase shift of

the wave.

Equations (7) and (8) can be solved by transform or classical methods in

the form of two arbitrary functions that satisfy the partial differential

equations. Paying attention to the fact that the second derivatives of the

voltage v and current 'functions, with respect to t and x, have to be directly

proportional to each other, so that the independent variables t and x appear in the

form [1]

Where Z is the characteristic impedance of the line and is given by

A1 and A2 are arbitrary functions, independent of x

To find the constants A1and A2 it has been noted that when x = 0, U(x) =u(r) and

i(x) =i(r)

from equations (13) and (14) these constants are found to be

Upon substitution in equation in (13) and (14) the general expression for voltage

and current along long transmission line become

The equation for voltage and currents can be rearranged as follows

The equation for voltage and currents can be rearranged as follows

The equation for voltage and currents can be rearranged as follows

Recognizing the hyperbolic functions sinh and cosh, the above equations (20) and

(21)

Are known as follows:

The interest is in the relation between the sending end and receiving end of the

line. Setting x=l,u(l)=vs, i(l)=is,

IV. TRANSMISSION LINE MODEL

In this paper fault location was performed on power system model which is

shown in figure. The line is a 300km, 330kv, 50Hz over head power transmission

line. The simulation was performed using MATLAB SIMULINK

.

SIMULATION RESULTS

Figure 3 shows the normal load current flowing prior to the application of the fault,

while the fault current is shown in figure 4, which is cleared in approximately one

second.

The voltage and current graphs are shown in the figure:

The post fault current:

The wavelet transform of current and voltage waveforms done throuf=gh

WAVELET toolbox are:

CURRENT WAVELET TRANSFORM

VOLTAGE WAVELET TRANSFORM

V. CONCLUSIONS

The application of the wavelet transform to estimate the fault location on

transmission line has been investigated. The most suitable wavelet family has

been made to identify for use in estimating the fault location on transmission

line. Four different types of wavelets have been chosen as a mother wavelet

for the study. It was found that better result was achieved using Daubechies

„db5‟ wavelet with an error of 3%. Simulation of single line to ground fault (S-L-

G) for 330kv, 300km transmission line was performed using SIMULINK

MATLAB SOFTWARE. The waveforms obtained from SIMULINK have

been converted as a MATLAB file for feature extraction. DWT has been

used to analyze the signal to obtain the coefficients for estimating the fault

location. Finally it was shown that the proposed method is accurate enough to be

used in detection of transmission line fault location.

[1] Abdelsalam .M. (2008) “Transmission Line Fault Location Based on

Travelling Waves”Dissertation submitted to Helsinki University, Finland, pp 108-

114.

[2] Aguilera, A.,(2006) “ Fault Detection, classification and faulted phase

selection approach” IEE Proceeding on Generation Transmission and Distribution

vol.153 no. 4 ,U.S.A pp 65-70

[3] Benemar, S. (2003) “Fault Locator For Distribution System Using

Decision Rule and DWT”Engineering system Conference, Toranto, pp 63-68

[4] Bickford, J. (1986) “Transient over Voltage” 3rd

Edition, Finland, pp245-250

[5] Chiradeja , M (1997) “New Technique For Fault Classification using

DWT” Engineering system Conference, UK, pp 63-68

[6] Elhaffa, A. (2004) “Travelling Waves Based Earth Fault Location on

transmission Network” Engineering system Conference, Turkey, pp 53-56

[7] Ekici, S. (2006) “Wavelet Transform Algorithm for Determining Fault

on Transmission Line‟‟ IEE Proceeding on transmission line protection. Vol. 4

no.5, Las Vegas, USA, pp 2-5

[8] Florkowski, M. (1999) “Wavelet based partial discharge image de-

noising” 11th

International

symposium on High Voltage Engineering, UK, pp. 22-24.