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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 4, OCTOBER 2005
High Impedance Fault Detection Based on Wavelet
Transform and Statistical Pattern Recognition
Ali-Reza Sedighi, Mahmood-Reza Haghifam, Member, IEEE, O. P. Malik, Life Fellow, IEEE, and
Mohammad-Hassan Ghassemian
Abstract—A novel method for high impedance fault (HIF)
detection based on pattern recognition systems is presented in
this paper. Using this method, HIFs can be discriminated from
insulator leakage current (ILC) and transients such as capacitor
switching, load switching (high/low voltage), ground fault, inrush
current and no load line switching. Wavelet transform is used for
the decomposition of signals and feature extraction, feature selection is done by principal component analysis and Bayes classifier
is used for classification. HIF and ILC data was acquired from
experimental tests and the data for transients was obtained by
simulation using EMTP program. Results show that the proposed
procedure is efficient in identifying HIFs from other events.
Index Terms—Bayes classifier, high impedance fault, principal
component analysis, protection, wavelet transform.
I. INTRODUCTION
H
IGH IMPEDANCE FAULTs (HIFs), usually occur at primary network level in electric distribution systems. Detection of HIFs is generally difficult by conventional over-current protection devices, because they have high impedance at
the fault point and don’t cause an excessive change of current
in the affected line. These faults often occur when an overhead
conductor breaks or touches a high impedance surface such as
asphalt road, sand, cement or tree. When this type of fault happens, energized high voltage conductor may fall within reach of
personnel.
Also, arcing often accompanies these faults, which poses a
fire hazard. Therefore, from both public safety and operational
reliability viewpoints, detection of HIFs is critically important.
In the past two decades many techniques have been proposed
to improve the detection of HIFs in power distribution systems
[1]. Generally, detection techniques are divided in mechanical
[2], and electrical detection methods. In mechanical methods,
some devices are used to provide low impedance by catching
the fallen conductor.
Electrical detection methods can be divided into two groups,
time domain and frequency domain algorithms. In time domain,
Manuscript received August 30, 2004; revised December 1, 2004. Paper no.
TPWRD-00400-2004.
A.-R. Sedighi and M.-H. Ghassemian are with the Department of Electrical
Engineering, Tarbiat Modarres University, Tehran, Iran (e-mail: sedighi@
yazduni.ac.ir; ghassemi@modares.ac.ir).
M.-R. Haghifam is with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4 Canada, on leave from
the Department of Electrical Engineering, Tarbiat Modarres University, Tehran,
Iran (e-mail: haghifam@ucalgary.ca).
O. P. Malik is with the Department of Electrical and Computer Engineering,
University of Calgary, Calgary, AB T2N 1N4 Canada (e-mail: maliko@
ucalgary.ca).
Digital Object Identifier 10.1109/TPWRD.2005.852367
Fig. 1.
Automatic pattern recognition.
ratio ground relay, proportional relay algorithm [3], [4], and a
smart relay based on time domain feature extraction [5], have
been proposed. Also arc detection method has been proposed
[6]. In frequency domain, using Fourier transform, several
articles have been published based on harmonic components
[7], [8]; inter harmonic component [9], and high frequency
spectra [10]. Other methods that try to reduce the limitation of
the Fourier analysis are: Kalman filtering [11]; use of the fractal
theory [12]; and use of neural networks [13]. Recently wavelet
transform has been proposed to achieve a better solution [14].
Wavelet method analyzes the transient behavior of a signal
in both time domain and frequency domain. In this paper a new
HIF detection method that uses wavelet transform and statistical
techniques is presented. HIF data was gathered from a 20-kV
radial distribution feeder in a real network. Transient state data
was produced by simulation using EMTP program. The pattern
recognition system design is introduced in Section II. A case
study and performance procedure are explained in Section III
and results are shown in Section IV.
II. PATTERN RECOGNITION SYSTEM DESIGN
An automatic pattern recognition system is shown in Fig. 1.
It consists of three main sections: data collection, preprocessing
and feature extraction/selection, and determination of optimum
classifier [15], [16].
A. Data Collection
This section is a sensitive part of pattern recognition system
and depends on problem in hand. Details are explained in the
next section.
B. Preprocessing and Feature Extraction/Selection
Before a pattern classifier can be properly designed, it is necessary to consider the feature extraction and feature selection.
The aim of feature extraction/selection is to obtain a few features
that discriminate classes with high degree of accuracy. This object has been recognized as an important issue in the design of
pattern recognition systems. The difference between feature extraction and selection should be clearly kept in mind. The feature
0885-8977/$20.00 © 2005 IEEE
SEDIGHI et al.: HIGH IMPEDANCE FAULT DETECTION BASED ON WAVELET TRANSFORM
extraction refers to techniques that create new features based on
transformation and combination of original feature set. Methods
that select the best subset of input feature set are called feature selection. In this paper discrete wavelet transform (DWT) is
used as a method for feature extraction and principal component
analysis (PCA) technique for dimension reduction and feature
selection. These techniques are briefly explained below.
1) Discrete Wavelet Transform: Wavelet transform (WT)
was introduced by J Morlet at the beginning of 1985 and has
attracted much interest in the fields of speech and image processing. Applications of DWT in power systems are reported
for
• power system transients [17];
• power-quality assessment [18];
• modeling of system component in wavelet domain [19].
In this section an introduction to wavelet transform is presented. More details can be found in [20], [21].
The WT was developed as an alternative to the short time
Fourier Transform (STFT) to overcome problems related to its
frequency and time resolution properties. More specifically, unlike the STFT that provides uniform time resolution for all frequencies, the DWT provides high time resolution and low frequency resolution for high frequencies and high frequency resolution and low time resolution for low frequencies. The DWT
is a special case of the WT that provides a compact representation of a signal in time and frequency that can be computed
efficiently.
The DWT is defined by the following equation:
(1)
is a time function with finite energy and fast decay
where
called the mother wavelet. The DWT analysis can be performed
using a fast, pyramidal algorithm related to multi-rate filter
banks. As a multi-rate filter bank DWT can be viewed as a
constant Q filter bank with octave spacing between the centers
of the filters. Each sub-band contains half the samples of the
neighboring higher frequency sub band. In the pyramidal algorithm the signal is analyzed at different frequency bands with
different resolution by decomposing the signal into a coarse
approximation and detail information. The coarse approximation is then further decomposed using the same wavelet
decomposition step. This is achieved by successive high pass
and low pass filtering of the time domain signal and is defined
by the following equations:
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role in time frequency analysis. It also depends on a particular
application. In this work all wavelets available in the Wavelet
Toolbox of MATLAB program [22] were used for the decomposition of the signals and the best answer was obtained with
rbio3.1 mother wavelet. It was found to have the most correlation with the decomposed signals and was selected for this
procedure.
2) Dimension Reduction: The objective of dimension reduction is to reduce the dimension of the pattern recognition
problem as much as possible with minimum loss of information. Dimension reduction can be achieved by means of feature
extraction or selection. Principal component analysis (PCA,
also called K-L transformation) is one of the most widely used
dimension reduction technique in most practical cases [16],
[23]. PCA finds the linear subspace that best represents data
without using information of class labels, which is usually
called, unsupervised dimension reduction method. In PCA, at
first a vector is decomposed into a linear combination of orthogonal basis functions in which the combination coefficients
are uncorrelated, and then the dimension of the feature vector is
reduced as described below. Supposing the distribution of data
is Gaussian, the variance-covariance matrix of feature vectors,
, is
(4)
where
is the number of feature vectors,
is the feature
vector, and is the mean of feature vectors.
is symmetrical and positive definite. Thus, there exists a
matrix similar to which is diagonal, (called ). For this purpose an matrix is constructed such that
diag
(5)
where is the th eigenvalue of , and th row of is the corresponding normalized eigenvector. is a transformation matrix
that converts the original features into new space with uncorrelated features. If the distribution of data is not Gaussian, the
feature in new space will be correlated. It can be shown that the
optimum properties of PCA are satisfied if the rows of transformation matrix are chosen as the (out of ) normalized
eigenvectors corresponding to the largest eigenvalues of diag. The ratio of eigenvalues to sum
onal covariance matrix,
of eigenvalues expresses the percentage of MSE (mean square
error) introduced by the elimination of the th eigenvector. So
the dimension of feature vectors can be reduced until a desired
accuracy is achieved
(2)
MSE
(6)
(3)
and
are the outputs of the high pass (g)
where
and low pass (h) filters, respectively after sub sampling by 2.
Down sampling the number of resulting wavelet coefficients becomes exactly the same as the number of input points.
A variety of different wavelet families have been proposed in
the literature. The choice of mother wavelet plays a significant
C. Determination of Optimum Classifier
The second-stage classifier is the Bayes classifier, which minimizes the total expected loss. From a statistical point of view,
the Bayes classifier represents the optimum measure of performance. It minimizes the average probability of error by calcufor all classes
and
lating a posterior probability
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 4, OCTOBER 2005
assigning the input vector
sented as follows:
Decide
to a class. This rule can be repre-
if
for all
Now, the classifier can be represented by the following decision
function
(7)
According to the Bayes formula
Fig. 2. Schematic of instrument connection.
(8)
where
is the probability density function of class
and
is the probability of occurrence of class . Since
is positive and common to all
, it can be dropped from
the decision function. Then the decision function becomes
(9)
pattern classes governed by the multivariable
Consider
normal density functions
(10)
Fig. 3. Experiment site.
where each density is completely specified by its mean vector
and covariance matrix .
Substituting (10) into (9), taking the natural logarithm, and
beeliminating the constant term from the expression,
comes
(11)
From the output of the decision functions, input vector can be
classified into the corresponding class, which has the maximum
value of decision function.
III. CASE STUDY
With respect to the stochastical behavior of HIF, in this research HIF and insulator leakage current (ILC) data was gathered from tests on a real network. Due to some practical limitations other transient data such as capacitor switching, load
switching (high/low voltage), ground fault, inrush current and
no load line switching, were obtained by a simulation of the
feeder using EMTP program. Data collection, preprocessing of
data and Bayes classifier for HIF detection are explained below.
A. Data Collection
An un-loaded 20 kV radial feeder located in Qeshm Island,
Iran, was chosen for collection of data on high impedance
faults. Feeder length is 19.5 km and HIF locations were approximately 8.5 km from the source end. The feeder was energized
from another 20 kV feeder through two distribution transkV 100 kVA) connected back to back. The
formers (
high and low voltage connections of transformers were
,
respectively. The high voltage sides are connected to feeders
and low voltage sides are connected together through the low
voltage switch. This configuration was chosen to protect the
Fig. 4.
Connection of a conductor to one phase.
loaded feeder from possible outages during the HIF tests. A
side of the back to
grounding transformer was used on the
back transformer to ground the test feeder.
Although only current signals are used in the studies described in this paper, three phase currents and also the three
phase voltages for future work were recorded using Hall effect
current transformers, resistive voltage divider, power analyzer
and computer. High frequencies between 2 and 10 kHz can
be generated during HIFs. For anti-aliasing filtering the data
was recorded at a sampling frequency 24.670 kHz and total
recorded time was 15 s for each test. Schematic of connections
is shown in Fig. 2, and the site is shown in Fig. 3.
For HIF test a conductor was connected to one phase of the
feeder (Fig. 4) and for each test it was dropped to the ground.
The fault studies were conducted on seven types of surfaces
(wet and dry asphalt, cement and soil, and dry tree) at two locations, approximately 8209 m and 8446 m from the site. Three
tests were conducted for each type of surface at each location
for a total of 42 data sets. For the reason that two data set were
not recorded correctly, 40 data sets were used in this work.
A window of seven faulted phase current signals on different
surfaces is shown in Fig. 5. The first few cycles that are saved in
SEDIGHI et al.: HIGH IMPEDANCE FAULT DETECTION BASED ON WAVELET TRANSFORM
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and other transient data are other classes. ILC data is recorded
in HIF data files. Before HIF occurred the recorded currents are
ILC. 40 files were recorded for HIF and thus there were 40 data
files for ILC.
Due to some practical limitations for collecting signals of
other transients in practical tests, the primary 20 kV electrical
distribution radial feeder (Fig. 6) has been used to generate data
for others transients such as capacitor switching, load switching
(high/low voltage), ground fault, inrush current and no load
line switching using ATP-EMTP program. Actual field data has
been used for feeders, loads and transformers. The feeder information is given in the Appendix. For line and load model,
model and load frequency model (CIGRE) are used [24], respectively. Saturable model is used for all transformers. Magnetizing curve is produced with modal program of SATURA for
saturable transformers [25]. Sampling rate for simulation data
and experimental data are the same. The number of transient
data is 40, thus the number of data for design and test of classifiers is 120.
B. Preprocessing
Fig. 5. HIF current waveforms on different surfaces. (a) Dry asphalt. (b) Wet
asphalt. (c) Dry cement. (d) Wet cement. (e) Dry soil. (f) Wet soil. (g) Dry wood.
the HIF files are the ILC. Because the test feeder is on an island
with high humidity and insulator surfaces on test feeder were
covered with salt and carbonic pollution, ILC magnitude was
significant in comparison with small feeder capacitance current.
As seen in Fig. 5, ILC waveform with respect to numerous partial discharges on insulator surfaces is not sinusoidal. It is somewhat similar to the HIF current. To prevent wrong operation of
HIF relays it is necessary to recognize ILC and HIF individually. Therefore, in this paper ILC is considered as a class. HIFs
1) Denoising: After data gathering, experiment data must
be denoised. Wavelet transform is used for denoising of HIF
and ILC data. Noise is a high frequency signal that has been
added to the original signal. At first each sample is decomposed
with wavelets and then the first three levels, that have high frequency part of the signal, are denoised. Soft and hard threshold
for rescaling threshold by a level-dependent estimation of level
noise are checked for all definition wavelets. Then the signals
are reconstructed each iteration. The signal, which has minimum mean square error with original signal, is selected as the
denoised signal.
2) Feature Extraction: 2048 samples of each current curve
are used for processing. These samples consist of almost 4 cycles of each record in the 50 Hz network and the event occurs
in the first cycle. Using all wavelets available in the MATLAB
Wavelet Toolbox, many simulations were performed. Decomposition of currents in each test was checked and the best answer
was received with rbio3.1 mother wavelet. So rbio3.1, which
has the most correlation with signals, was chosen as the suitable mother wavelet.
HIFs were with arc and therefore caused high frequency signals (2–10 kHz) combined with the main HIF signal [26]. First,
two levels of decomposed signals were chosen for feature extraction. These levels contain high frequency part of the signals
with a central frequency of 12.335 kHz and 6.16 kHz, respectively. The number of coefficient in the first level (cd1) is almost
1024 and for the second level (cd2) is 512. 1000 of those for
cd1 and 500 of cd2 are used for processing. After many tests
and trial and error, coefficients of each level divided in to 4 segments and mean of each segment for cd1 and root mean square
of each segment for cd2 are chosen as features. Thus eight features are extracted for each current curve.
3) Feature Selection: Natural events usually have normal
distribution. In this work it was supposed that all transient states
have normal distribution. PCA, introduced in the previous section, was used to reduce the dimension of feature vectors from 8
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Fig. 6. Simulated 20-kV distribution system.
TABLE I
SUMMARY OF RESULTS
to 2. The ratio of the sum of eigenvalues of ignored eigenvectors
to the sum of eigenvalues is less than 0.1.
C. Bayes Classifier
In this paper it is proposed to discriminate three classes (HIF,
ILC and other transients) from each other. Half of the data for
each class (20 vectors) is chosen for training and the other half
for test. Bayes classifier is used for the classification of these 3
classes and so for HIF detection.
Fig. 7. Results of study 1.
IV. RESULTS AND DISCUSSION
A number of studies have been conducted to check the performance of the Bayes classifier with values of the MSE ranging
from 1.00E-07 to 1.00E-01, the dimension of the features vector
varying from 2 to 7 and the number of segments varying between 4 and 10 in various combinations. A summary of the results of these studies is given in Table I. A few studies from this
table are described below for illustration.
Study 1: Bayes classifier with four segments, two elements
feature vector and an MSE of 1.00E-02 gave three incorrect
identifications in 20 HIF states. All 20 other transient states and
20 ILC states were identified correctly. This means that 85% of
HIF states and 100% of other states were identified correctly.
Overall this procedure is successful in 95% of cases as illustrated in Fig. 7.
Study 2: If training data and test data are interchanged, successful detection of HIF and other states becomes 95% and
Fig. 8. Results of study 2.
100%, respectively. In this case, overall success rate will be
98.3%. Results of this state are shown in Fig. 8.
Comparing studies 1&2 shows that the success of this procedure for HIF detection is 90% and for others states is 100% and
overall 96.7% of states are correctly identified. These results are
shown in Fig. 9.
Study 3: If in the feature extraction section the number of
segments is decreased from 4 to 3 using sum of MSE equal 1E-3,
SEDIGHI et al.: HIGH IMPEDANCE FAULT DETECTION BASED ON WAVELET TRANSFORM
Fig. 12.
Fig. 9.
Results of study 1&2 or 3.
Fig. 10.
Results of study 5.
Fig. 11.
Results of study 8.
overall success of classifier is the same as the combination of
studies 1&2 as shown in Fig. 9.
Study 5: Reducing the sum of MSE from IE-3 (study 3) to
IE-5 in the feature selection section, the dimension of the selected feature vector increased from 3 to 5 and the results show
that the overall success of the classifier, 93.3%, is less than the
combination studies 1&2 or 3 and 4 as shown in Fig. 10.
Study 8: With ignoring of PCA and using all extracted feature for classifying, overall success is 86.7% equal to study7 as
illustrated in Fig. 11.
It can be seen from the summary of results given in Table I
that the proposed procedure can identify HIF from other transients with a high percentage of accuracy.
Results in Table I. show the importance of preprocessing in
pattern recognition systems. Pattern recognition includes feature extraction and feature selection. Feature extraction refers
to techniques that create new features based on transformation
and combination of the original feature set. PCA was used for
feature selection and MSE criterion that shows percentage of
overall loss of data was used for dimension reduction. Successful operation of classifier depends strongly on these two
stages as seen from the results in Table I.
Because of practical limitations, a larger set of data for HIF
tests could not be obtained from the real network. In study 1
and 2 the success rate of the proposed method has been tested
using maximum available data by interchanging the training and
the test data. Therefore, the success rate of studies 1& 2 (third
row of Table I) is more accurate in comparison to the results
of study 1 or 2. Comparison of studies 3 and 1&2 shows that
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Configuration of phases and mechanical data.
the optimum reduction in feature dimensions have no negative
effect on the success rate of the classifier. As shown in Table I
the overall success in both studies is 96.7%.
Comparison of the results of study 3 with the results of
studies 4–7 shows that decreasing MSE and relatively increasing the feature dimension can decrease the overall success
rate. As shown in Table I, by decreasing MSE from 1.00E-2 in
study 1&2 to 1.00E-7 in study 7 and increasing the dimension
from 2 to 7, the overall success rate of the classifier decreases
from 96.7% to 86.7%. This shows the effect of optimal feature
selection and loss of unsuitable data in increasing the accuracy
of the classifier. In study 8, PCA procedure was not applied
and the overall success of the classifier reduced to 86.7%. This
shows the effect of PCA. In studies 1&2 the first two level
coefficients of the decomposition signals are divided in to 4
segments but in study 9 there are 10 segments. Dimension of
the selected feature vectors in the two cases is the same. Overall
success of the classifier is 97.6% and 89.1%, respectively.
This result again shows the importance of the role of optimal
extraction of data and features.
V. CONCLUSION
In this paper a new HIF detection method that uses combination of wavelet transform and statistical technique as a fault detector is suggested. For HIF detection the purposed method utilizes the coefficients of level 1 and 2 of current decomposed with
rbior3.1 as mother wavelet for feature extraction. Principal component analysis (PCA) is used for feature selection and Bayes
classifier for HIF detection. Various staged HIF data (wet and
dry asphalt, cement and soil, and dry tree) and ILC are gathered from experimental tests and transient states data (capacitor switching, load switching (high/low voltage), ground fault,
inrush current and no load line switching) are simulated using
EMTP program. The sampling rate of all recorded data is 24.670
kHz. The results show a high success rate of this procedure to
detect HIF.
APPENDIX
DATA FOR TEST FEEDER
A. Impedance
km
cm
Outside radius of conductor
B. Configuration of Phases and Mechanical Data
Configuration of phases and mechanical data is shown in Fig.
12.
Height of pole
Sag in mid span
m
cm
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 4, OCTOBER 2005
TABLE II
LOAD DATA
TABLE III
TRANSFORMER DATA
C. Load Data
Load data for the network in Fig. 5 are shown in Table II.
Constant parameters of the CIGRE load model usually considered in the EMTP program are the following:
D. Transformer Data
The transformer data for the network in Fig. 5 are shown in
Table III.
ACKNOWLEDGMENT
The authors wish to thank G. Khoshkholg, General Manager,
Garb Regional Electric Company, Iran, M.-H. Aghdaei, General
Manager, Hormozgan Regional Electric Company, Iran, and G.
Sharifi, Manager of Electrical Utility in Qeshm Island, Iran, for
support in the data gathering process.
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SEDIGHI et al.: HIGH IMPEDANCE FAULT DETECTION BASED ON WAVELET TRANSFORM
Ali-Reza Sedighi was born in Anarak, Iran, on September 15, 1968. He received
the B.S. degree in electrical engineering from Isfahan University of Technology,
Isfahan, Iran, in 1990 and the M.S. degree in electrical engineering in 1994 from
Tarbiat Modarres University, Tehran, Iran, where he is currently pursuing the
Ph.D. degree.
Mahmood-Reza Haghifam (M’98) received the B.Sc. degree from Tabriz University in 1988; the M.Sc. degree from Tehran University, Tehran, Iran, in 1990;
and the Ph.D. degree from Tarbiat Modarres University, Tehran, in 1995, all in
power engineering.
Currently, he is Associate Professor of Electrical Engineering at Tarbiat
Modarres University. His research interests are electric distribution systems,
power system reliability, and soft computing applications in power systems. He
has published many technical papers in these areas.
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O. P. Malik (M’66–SM’69–F’87–LF’00) graduated in electrical engineering
from Delhi Polytechnic, India, in 1952, and received the M.E. degree in electrical machine design from the University of Roorkee, India, in 1962. He received the Ph.D. degree from the University of London, London, U.K., and the
D.I.C. from the Imperial College of Science and Technology, London, U.K., in
1965.
He became Professor at the University of Calgary in 1974 and is a faculty
professor emeritus.
Dr. Malik is a Fellow of the Institution of Electrical Engineers (London).
Mohammad-Hassan Ghassemian received the B.S.E.E. degree from the
Tehran College of Telecommunication, Tehran, Iran in 1980, and the M.S.E.E.
and Ph.D. degrees from Purdue University, West Lafayette, IN, in 1984 and
1988, respectively.
Currently, he is Professor of Electrical Engineering at Tarbiat Modarres University, Tehran, Iran. His research interests are signal and image analysis, pattern
recognition, multisensor data fusion, and remote sensing.