International Journal of Advances in Engineering & Technology, Nov 2011.
(c)IJAET ISSN: 22311963
FAULT LOCATION AND DISTANCE ESTIMATION ON POWER
TRANSMISSION LINES USING DISCRETE WAVELET
TRANSFORM
Sunusi. Sani Adamu1, Sada Iliya2
1Department of Electrical Engineering, Faculty of Technology, Bayero University Kano,
Nigeria
2Department of Electrical Engineering, College of Engineering, Hassan Usman Katsina
Polytechnic
ABSTRACT
Fault location is very important in power system engineering in order to clear fault quickly and restore power
supply as soon as possible with minimum interruption. In this study a 300km, 330kv, 50Hz power transmission
line model was developed and simulated using power system block set of MATLAB to obtain fault current
waveforms. The waveforms were analysed using the Discrete Wavelet Transform (DWT) toolbox by selecting
suitable wavelet family to obtain the prefault and postfault coefficients for estimating the fault distance. This
was achieved by adding non negative values of the coefficients after subtracting the prefault coefficients from
the postfault coefficients. It was found that better results of the distance estimation, were achieved using
Daubechies `db5'wavele,t with an error of three percent (3%).
KEYWORDS: Transmission line, Fault location, Wavelet transforms, signal processing
I. INTRODUCTION
Fault location and distance estimation is very important issue in power system engineering in order to
clear fault quickly and restore power supply as soon as possible with minimum interruption. This is
necessary for reliable operation of power equipment and satisfaction of customer. In the past several
techniques were applied for estimating fault location with different techniques such as, line
impedance based numerical methods, travelling wave methods and Fourier analysis [1]. Nowadays,
high frequency components instead of traditional method have been used [2]. Fourier transform were
used to abstract fundamental frequency components but it has been shown that Fourier Transform
based analysis sometimes do not perform time localisation of time varying signals with acceptable
accuracy. Recently wavelet transform has been used extensively for estimating fault location
accurately. The most important characteristic of wavelet transform is to analyze the waveform on time
scale rather than in frequency domain. Hence a Discrete Wavelet Transform (DWT) is used in this
paper because it is very effective in detecting fault generated signals as time varies [8].
This paper proposes a wavelet transform based fault locator algorithm. For this purpose,
330KV,300km,50Hz transmission line is simulated using power system BLOCKSET of MATLAB
[5].The current waveform which are obtained from receiving end of power system has been analysed.
These signals are then used in DWT. Four types of mother wavelet, Daubechies (db5), Biorthogonal
(bio5.5), Coiflet (coif5) and Symlet (sym5) are considered for signal processing.
II. WAVELET TRANSFORM
Wavelet transform (WT) is a mathematical technique used for many application of signal processing
[5].Wavelet is much more powerful than conventional method in processing the stochastic signal
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Vol. 1, Issue 5, pp. 6976
International Journal of Advances in Engineering & Technology, Nov 2011.
(c)IJAET ISSN: 22311963
because of analysing the waveform in time scale region. In wavelet transform the band of analysis can
be adjusted so that low frequency and high frequency components can be windowing by different
scale factors. Recently WT is widely used in signal processing application such as de noising,
filtering, and image compression [3]. Many pattern recognition algorithms were developed based on
the wavelet transform. According to scale factors used the wavelet can be categorized into different
sections. In this work, the discrete wavelet transform (DWT) was used. For any function (f), DWT is
written as.
, =
[
]
(1)
Where is the mother wavelet [3],
is the scale parameter
, , are the translation parameters.
III. 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 twoconductor 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 (18501925) when he was employed by a telegraph company and used
to investigate disturbances on telephone wires [1]. When one considers a line segment
with
parameters resistance (R), conductance (G), inductance (L), and capacitance (C), all per unit length,
(see Figure 3.1) the line constants for segment
are , , , and . The electric flux
and the magnetic flux created by the electromagnetic wave, which causes the instantaneous voltage
, and current , ,
are:
= , (2)
= , (3)
Calculating the voltage drop in the positive direction of x of the distance
one obtains
,  + , = , = , = +
, (4)
If
cancelled from both sides of equation (4), the voltage equation becomes
, = ,  , (5)
Similarly, for the current flowing through G and the current charging C, Kirchhoff's current law can
be applied as
,  + , = , = , = +
, (6)
If
cancelled from both sides of (6), the current equation becomes
, = ,  ,
(7)
The negative sign in these equations is caused by the fact that when the current and voltage waves
propagates in the positive xdirection,
, and , will decrease in amplitude for increasing .
The expressions of line impedance, Z and admittance Y are given by
= + ,
(8)
= + ,
(9)
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Vol. 1, Issue 5, pp. 6976
International Journal of Advances in Engineering & Technology, Nov 2011.
(c)IJAET ISSN: 22311963
Differentiate once more with respect to x, the secondorder partial differential equations
, = , = , = , (10)
, = , = , = ,
(11)
Figure 1 Single phase transmission line model
In this equation, is a complex quantity which is known as the propagation constant, and is given by
= = +
(12)
Where, is the attenuation constant which has an influence on the amplitude of the wave, and 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 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]
, =
+
(13)
, = [
+
(14)
Where Z is the characteristic impedance of the line and is given by
=
(15)
A1 and A2 are arbitrary functions, independent of x
To find the constants A1and A2 it has been noted that when = , = R and = r from
equations (13) and (14) these constants are found to be
= (16)
= (17)
Upon substitution in equation in (13) and (14) the general expression for voltage and current along a
long transmission line become
= + (18)
=

(19)
International Journal of Advances in Engineering & Technology, Nov 2011.
(c)IJAET ISSN: 22311963
The equation for voltage and currents can be rearranged as follows
=
+
(20)
=
+
(21)
Recognizing the hyperbolic functions
, , the above equations (20) and (21)
are written as follows:
= + (22)
= + (23)
The interest is in the relation between the sending end and receiving end of the line. Setting =
, = = , the result is
= + (24)
= + (25)
Rewriting the above equations (24) and (25) in term of ABCD constants we have
= (26)
Where
= , = , = =
IV. TRANSMISSION LINE MODEL
In this paper fault location was performed on power system model which is shown in figure 2. The
line is a 300km, 330kv, 50Hz over head power transmission line. The simulation was performed using
MATLAB SIMULINK.
Continuous
powergui
Step 2
Scope 1
V'T
x1
x3
x4
+
Step 1
v

+ v

Scope 4
c
2
C'B
V'T
x2
1
Scope 3
c
2
Scope 2
C'B
C'T
1
Ac voltage source
i
i
+ 
+

C'T
A
a
A
B
b
B
C
C
c
Ditributed line 1
Distributed line
6
Distributed line
2
Distributed line
3
Distributed line
4
Distributed line
5
400MVA Transformer
RLC Load
A
B
C
Three phase Fault breaker
FIG 3.1 300KM,50Hz, 330kV Transmission line model
Figure 2: Simulink transmission line model
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Vol. 1, Issue 5, pp. 6976
International Journal of Advances in Engineering & Technology, Nov 2011.
(c)IJAET ISSN: 22311963
The fault is created after every 50km distance, with a simulation time of 0.25sec, sample time = 0,
resistance per unit length = 0.012ohms, inductance per unit length = 0.9H and capacitance per unit
length = 127farad.
4.1 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.
Fig 3: Prefault current waveform at 300km
Fig 4: Fault current waveform at 50km
4.2 DISCRETE WAVELET COEFFICIENTS.
Figures 5 and 6 showed prefault/post fault wavelets coefficients (approximate, horizontal
detail, diagonal detail and vertical detail) at 3 00km using the following db5 wavelet familioes.
International Journal of Advances in Engineering & Technology, Nov 2011.
(c)IJAET ISSN: 22311963
Fig 5: Pre fault wavelet coefficients
Fig. 6: Post fault wavelet coefficients at 50km
4.2.1 TABLES OF THE COEFFICIENTS
The tables below present the minimum / maximum scales of the coefficients using db5.
Table 1: Prefault wavelet coefficients using db5
Coefficients
Max. Scale
Min. Scale
Approximate(A1)
693.54
0.00
Horizontal(H1)
205.00
214.44
Vertical (V1)
235.56
218.67
Diagonal (D1)
157.56
165.78
International Journal of Advances in Engineering & Technology, Nov 2011.
(c)IJAET ISSN: 22311963
Table 2: Prefault wavelet coefficients using db5
Coefficients
Max. Scale
Min.
Scale
Approximate(A1)
693.54
34.89
Horizontal(H1)
218.67
201.33
Vertical (V1)
201.33
218.67
Diagonal (D1)
157.56
148.89
Table 3: Differences between maximum and minimum scale of the coefficients using db5
db5 max
db5 min
Coefficients
A1
H1
V1
D1
A1
H1
V1
D1
Coefficients. At
50km
693.54
218.67
201.33
157.56
34.89
201.33
218.67
148.89
Prefault
coefficients.
693.54
205.00
235.56
157.56
0.00
214.44
218.67
165.78
Differences
0.00
13.67
34.23
0.00
34.89
13.11
0.00
16.89
Estimated distance (km) = 13.67 + 34.89 = 48.5
Table 4: Actual and estimated fault location
Actual location(km)
db5
bio5.5
coif5
Sym5
50
48.5
39.33
47.32
26.23
100
97.44
173.78
04.37
43.56
4.3 DISCUSSION OF THE RESULTS.
The results are presented in figures 5 and 6, and tables 1 to 4. Figure 3 is the simulation result of
prefault current waveform which indicates that the normal current amplitude reaches 420A. When a
fault was created at 50km from the sending end point, figure 4 shows that the fault current amplitude
reaches up to 14 kA.
The waveforms obtained from figures 3 and 4 were imported into the wavelet toolbox of MATLAB
for proper analysis to generate the coefficients. Figures 5 and 6 presents the discrete wavelet
transform coefficients in scale time region. The scales of the coefficients are based on minimum scale
and maximum scale. These scales for both prefault and post fault coefficients were recorded from
the work space environment of the MATLAB which was presented in tables 1and 2.
The estimated distance was obtained by adding non negative values of the scales after subtracting the
prefault coefficients from the postfault coefficients; this is presented in table 4.
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 (SLG) 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.
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Vol. 1, Issue 5, pp. 6976
International Journal of Advances in Engineering & Technology, Nov 2011.
(c)IJAET ISSN: 22311963
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Authors' Biography
Sunusi Sani Adamu receives the B.Eng degree from Bayero University Kano, Nigeria in
1985; the MSc degree in electrical power and machines from Ahmadu Bello University,
Zaria, Nigeria in 1996; and the PhD in Electrical Engineering, from Bayero University, Kano,
Nigeria in 2008. He is a currently a senior lecturer in the Department of Electrical
Engineering, Bayero University, Kano. His main research area includes power systems
simulation and control, and development of microcontroller based industrial retrofits. Dr
Sunusi is a member of the Nigerian Society of Engineers and a registered professional
engineer in Nigeria.
Sada Iliya receives the B.Eng degree in Electrical Engineering from Bayero University
Kano, Nigeria,in 2001. He is about to complete the M.Eng degree in Electrical Engineering
from the same University. He is presently a lecturer in the Department of Electrical
Engineering, Hassan Usman Ploytechnic, Katsina, Nigeria. His research interest is in power
system operation and control.
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