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.