Performance of Modified S-Transform for Power Quality Disturbance Detection and Classification

TELKOMNIKA, Vol.15, No.4, December 2017, pp. 1520~1529
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013
DOI: 10.12928/TELKOMNIKA.v15i4.7230  1520
Received September 10, 2017; Revised November 12, 2017; Accepted November 28, 2017
Performance of Modified S-Transform for Power Quality
Disturbance Detection and Classification
Faridah Hanim M. Noh*
1
, Munirah Ab. Rahman
2
, M. Faizal Yaakub
3
1,2
Faculty of Electrical and Electronic Engineering, Universiti Tun Hussien Onn Malaysia,
Universiti Tun Hussien Onn Malaysia, 86400, Parit Raja, Batu Pahat, Johor, Malaysia
3
Faculty of Engineering Technology, Universiti Teknikal Malaysia Melaka,
Hang Tuah Jaya, 76100 Durian Tunggal, Melaka
3
Center for Robotics and Industrial Automation, Universiti Teknikal Malaysia Melaka,
Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
*Corresponding author, e-mail: hanim@uthm.edu.my
Abstract
Detection and classification of power quality (PQ) disturbances are an important consideration to
electrical utility companies and many industrial customers so that diagnosis and mitigation of such
disturbance can be implemented quickly. Power quality signal consists of stationary and non-stationary
events which need a robust signal processing technique to analyse the signals. In this paper, Modified S-
Transform (MST) was used to analyse single and multiple power quality signals. MST is a modified version
of S-transform with improved time-frequency resolution. The power quality signals that are considered in
this study are voltage swell, sag, interruption, harmonic, interharmonic, transient, sag plus harmonic and
swell plus harmonics. The performance of the proposed method has been studied under noisy and unnoisy
condition. Hard thresholding technique has been applied with MST while analysing noisy PQ signals. The
result shows that MST is able to give higher classification rate with better time and frequency distribution
(TFD) spectrum of the PQ disturbances.
Keywords: detection and classification, power quality disturbances, MST, time and frequency distribution
Copyright © 2017 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
The increased requirements for supervision, control, and performance in modern power
systems make power quality monitoring a common practice for utilities. With the growth of the
number of monitors installed in the system, the amount of data collected is growing; making the
individual inspection of the entire wave shapes no longer an option [1]. Interests in fast
disturbances detection have resulted to special requirements for PQ monitoring equipment and
invented a necessity for sophisticated software to automatically analyse the monitored data. As
far as PQ monitoring, mitigation, protection, and control in power system are concerned, an
accurate measurement in real-time circumstances for power distribution is extremely crucial and
important [2]. PQ signal consists of stationary and non-stationary components. In the analysis of
the nonstationary signals, one often needs to examine their time-varying spectral
characteristics. Since time-frequency representations (TFR) indicate variations of the spectral
characteristics of the signal as a function of time, they are ideally suited for nonstationary
signals [3]. The Fast Fourier transform (FFT) and the short time Fourier Transform (STFT) are
the most used techniques for detection and classification for different types of PQ disturbance
occurred in power system [4]. Nevertheless, they are also several other signal processing
techniques can be applied for a similar purpose. FFT is usually used to analyse harmonics in
the signal. The information given are mainly in the frequency spectrum only, which make it
unsuitable to analyse PQ signal which consists of transient. On the other hand, time information
is also required. STFT had been introduced to overcome the inadequacy of FFT. It uses a fixed
analysis window but has a major disadvantage that there is a compromise between time and
frequency resolution [5]. S-transform was then introduced by Stockwell et all in 1996. The S-
transform is a time-frequency spectral localisation method, similar to the short-time Fourier
transform (STFT), but with a Gaussian window whose width scales inversely, and whose height
scales linearly with the frequency [6]. The scaling property of the Gaussian window is

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Performance of Modified S-Transform for Power Quality …. (Faridah Hanim M. Noh)
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reminiscent of the scaling property of continuous wavelets [7], however, it is not categorised in
wavelet group. Due to its characteristic, S-transform has been reckoned as an algorithm which
is conceptually a hybrid of short-time Fourier analysis and wavelet analysis, containing of both
elements but falling entirely into neither category [8].
Several researchers have proposed a few variants of Stockwell transform by adjusting
and modifying its Gaussian window function. Masinha et. al (1997) have proposed of adding
parameter γGS to the standard deviation of the Gaussian window [7]. By doing this, the user will
be able to specify the time and frequency resolution of S-transform on its time-frequency plane.
In 1999, Mc Fadden et. al. proposed a generalised S-transform which includes windows which
are asymmetrical. They applied an asymmetrical window to decomposition and analysis of
gearbox vibration data in mechanical engineering [9]. Another generalised S-transform is
presented by Pinnegar et. al [8] which is stated as the extension of Mc Fadden generalised S-
transform, that is to include windows which have complicated scaling properties, including
frequency-dependent shape. In the same year, the same author proposed to use generalised S-
transform with the bi-Gaussian window which shows remarkable performance for time series
sharp onset event. In 2012, Assous et al. have proposed a Modified S-Transform, where he
introduced new parameters that able to control the scale and shape of the analysing window
[10]. The proposed parameter able to gives a better time and frequency resolution of S-
transform, and at the same time determine the phase synchrony of electroencephalogram
(EEG) seizure signal using the cross-MST technique. In this paper, the Modified S-Transform
has been used to analyse the PQ disturbance signal in noisy and unnoisy condition. Several
signal indices have been generated based on the TFD of the MST. Features of each PQ
disturbance signal are then constructed from the generated signal indices. Thus, the capability
of the studied method is shown in its classification rate.
2. Modified S-Transform
The standard S-transform which has been proposed by Stockwell et. al in 1996 is given
as follow [11]:
𝑆(𝑡, 𝑓) = ∫ 𝑥(𝑡)𝑔(𝑡 − 𝜏, 𝑓)𝑒−𝑗2𝜋𝑓𝜏
𝑑𝜏
+∞
−∞
(1)
where 𝑔(𝑡 − 𝜏, 𝑓) is the Gaussian window function of the S-transform. The Gaussian window
function was generated with the assumption that the window's width, is proportionate to the
inverse of frequency, 𝑓. Thus the window function of standard ST is given as follow:
𝑔(𝑡 − 𝜏, 𝑓) =
1
𝜎√2𝜋
𝑒
−(𝑡−𝜏)2
2𝜎2
=
|𝑓|
√2𝜋
𝑒
−𝑓2(𝑡−𝜏)2
2 (2)
In 1997, Masinha et. al have proposed a generalised ST which introducing a new
constant, γGS in equation 𝜎(𝑓)so that the frequency resolution of ST can be adjusted
accordingly [7]. The new  is given by:
𝜎(𝑓, 𝛾) =
𝛾 𝐺𝑆
|𝑓|
(3)
The parameter 𝛾 𝐺𝑆 denotes the set of parameters that determine the shape and
properties of the window function. Parameter t controls the position of the generalized window
on the time axis. Higher values of 𝛾 𝐺𝑆 will give better frequency resolution of ST, but reduce its
time resolution. With the new parameter, the Gaussian window function can be written as:
𝑔(𝑡 − 𝜏, 𝑓) =
|𝑓|
𝛾 𝐺𝑆√2𝜋
𝑒
−𝑓2(𝑡−𝜏)2
2𝛾 𝐺𝑆
2
(4)
The value of 𝛾 𝐺𝑆 which proposed by Masinha et. al is a constant value, which is an
integer values that larger than unity [7]. For modified S-transform, Assous et. al has proposed to
scale the parameter 𝛾 𝐺𝑆 so that the Gaussian window function of S-transform can vary linearly
with frequency [10]. The modified 𝛾 𝐺𝑆 is given as bellow:

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𝛾 𝐺𝑆(𝑓) = 𝑚𝑓 + 𝑘 (5)
where m is the slope and k is the intercept for a linear change in frequency. By using the new
𝛾 𝐺𝑆 formula, the modified S-transform becomes:
𝑀𝑆𝑇(𝑡, 𝑓, 𝑚, 𝑘) = ∫ 𝑥(𝑡)𝑔(𝑡 − 𝜏, 𝑓, 𝑚, 𝑘)𝑑𝜏
+∞
−∞
(6)
where 𝑔(𝑡 − 𝜏, 𝑓, 𝑚, 𝑘) is the window function of MST. The equation is stated as below:
𝑔(𝑡 − 𝜏, 𝑓, 𝑚, 𝑘) =
|𝑓|
(𝑚𝑓+𝑘)√2𝜋
𝑒
−𝑓2(𝑡−𝜏)2
2(𝑚𝑓+𝑘)2
(7)
The MST new window function also satisfies the normalization condition and hence it is
invertible [10]. The value of m and k has been selected by Assous et. al. empirically. m is
defined as four times the variance of the signal x(t) and value of k is 1 N, where N is the total
samples points in a signal [10]. In this study, the value of m and k will remain the same as
suggested by Assous et. al.
3. Power Quality Disturbance Signal Model
The PQ disturbance signals have been simulated based on the signal model proposed
by Abdullah et al [12]. The signals are divided into three categories: voltage variation, waveform
distortion, and transient signal. The model of each signal categories is formed based on IEEE
Standard 1159-2009 [13]. The equations are given as:
𝑧 𝑣𝑣(𝑡) = 𝑒 𝑗2𝜋𝑓1 𝑡 ∑ 𝐴 𝐾 ∏(𝑡 − 𝑡 𝐾−1)3
𝐾=1 (8)
𝑧 𝑤𝑑(𝑡) = 𝑒 𝑗2𝜋𝑓2 𝑡
+ 𝐴𝑒 𝑗2𝜋𝑓2 𝑡
(9)
𝑧𝑡𝑟𝑎𝑛𝑠(𝑡) = 𝑒 𝑗2𝜋𝑓1 𝑡 ∑ ∏ (𝑡 − 𝑡 𝐾−1)𝐾 + 𝐴𝑒−1.25(𝑡−𝑡1)/(𝑡2−𝑡1)
𝑒 𝑗2𝜋𝑓2(𝑡−𝑡1) ∏ (𝑡 − 𝑡1)2
3
𝐾=1 (10)
where
∏ = {
1 0 ≪ 𝑡 ≪ 𝑡 − 𝑡 𝐾−1
0 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒𝐾 (11)
zvv(t) represent voltage variation signal, zwd represents waveform distortion signal and
ztrans(t) represent transient signal. The PQ disturbance which falls in voltage variation signals are
voltage sag, voltage swell and voltage interruption. Interharmonic and harmonic signal fall under
waveform distortion signal. Transient signal was modeled by by ztrans(t) equation. In these
equations, K is the signal component sequence, AK is the signal component amplitude, f1 and f2
are the signal frequency, t is time while ∏ (t) is a box function of the signal. In this analysis, f1, t0,
t1 and t3 are set at 60 Hz, 0 s, 0.05 s and 0.1666 s, respectively. The introduced parameters in
each signal are generated randomly in the adequate intervals in order to generate 100
realizations of each class of signals. Others parameters are defined as follow:
1. Voltage sag: A1 = A3 =1pu , 0.1pu ≤ A2 ≤ 0.9pu and 0.05s< t2 < t3
2. Voltage swell: A1 = A3 =1pu , 1.1pu ≤ A2 ≤ 1.8pu and 0.05s< t2 < t3
3. Voltage interruption: A1 = A3 =1pu , 0pu< A2 <0.1pu and 0.05s< t2 ≤ t3
4. Harmonic: A=0.02pu , f2 =( 2n )*60 Hz where n=1,2,3,...,50 .
5. Interharmonic: A=0.02pu, f2 =( x* f1 /10 )+ fH where 1 ≤ x ≤ 8 and fH is even harmonic
frequency component.
6. Transient: 0<A ≤ 4pu , 65Hz ≤ f2 <5000Hz and 0.3ms< t2 - t1 <50ms
The multiple PQ disturbance signals are generated by combining the two single PQ
signal model. For this research, the multiple PQ disturbances signals are the swell plus
harmonic signal and sag plus harmonic signal. The equation can be stated as:

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𝑧𝑠𝑤𝑒𝑙𝑙ℎ𝑎𝑟(𝑡) = 𝑧 𝑣𝑣(𝑠𝑤𝑒𝑙𝑙) + 𝑧 𝑤𝑑 (12)
𝑧𝑠𝑎𝑔ℎ𝑎𝑟(𝑡) = 𝑧 𝑣𝑣(𝑠𝑎𝑔) + 𝑧 𝑤𝑑 (13)
In this research, the generated PQ disturbances signals are a single phase sinusoidal
voltage with nominal amplitude of 1 p.u. and phase 0 radians. Each PQ disturbance signal
consists of 10 cycles and each cycle consists of 256 sample points. The sampling frequency is
15.36 kHz.
4. Power Quality Signal Indices and Features Construction
The time-frequency distribution is employed to generate a set of indices which are used
in the classification process. The indices are extracted from the parameters of the signal. In this
study, the parameters of the signal obtained from optimized TFR are the instantaneous values
of RMS voltage, RMS fundamental voltage, total harmonic distortion (THD), total non-harmonic
distortion (TnHD), total waveform distortion (TWD). The instantaneous RMS voltage can be
defined as below:
𝑉𝑟𝑚𝑠(𝑡) = √∫ |𝑀𝑆𝑇𝑥(𝑡, 𝑓)|2 𝑑𝑓
𝑓 𝑚𝑎𝑥
0
(14)
fmax is the maximum frequency that being considered in MST. Instantaneous RMS
fundamental voltage is defined as the RMS voltage at power system frequency [12]. It can be
calculated as:
𝑉1𝑟𝑚𝑠(𝑡) = √∫ |𝑀𝑆𝑇𝑥(𝑡, 𝑓)|2 𝑑𝑓
𝑓 𝐻
𝑓 𝐿
(15)
where 𝑓𝐻 is the frequency when the lobe of fundamental frequency end, and 𝑓𝐿 is the frequency
at the starting point of the fundamental frequency lobe. Waveform distortion represents all
deviations of the voltage waveform from the ideal sinusoidal waveform in terms of magnitude or
frequency the signal [9,14]. The instantaneous total waveform distortion can be expressed as:
𝑇𝑊𝐷(𝑡) =
√𝑉𝑟𝑚𝑠(𝑡)−𝑉1𝑟𝑚𝑠(𝑡)
𝑉1𝑟𝑚𝑠(𝑡)
(16)
where V1rms(t) is the instantaneous RMS fundamental voltage and Vrms(t) is the instantaneous
RMS voltage. Total harmonic distortion, THD is used to measure of how much harmonic content
in a signal [9,15]. It and can be defined as:
𝑇𝐻𝐷(𝑡) =
√∑ 𝑉ℎ,𝑟𝑚𝑠(𝑡)2𝐻
ℎ=2
(17)
where Vh,rms(t) is the RMS harmonic voltage and H is the highest measured harmonic
component. While total non-harmonic distortion which is used to characterized the existence of
interharmonics components can be calculated as:
𝑇𝑛𝐻𝐷(𝑡) =
√𝑉𝑟𝑚𝑠(𝑡)2−∑ 𝑉ℎ,𝑟𝑚𝑠(𝑡)2𝐻
ℎ=0
(18)
The instataneous frequency, IF(t) , of the signals were determined based on maximum
peak of the MST matrix in the frequency spectrum for each sampling time, t s . The equation is
given as follow [16]:
𝐼𝐹(𝑡) = 𝑎𝑟𝑔 [max 𝑓∈𝑄 𝑓
Ʌ(𝑡, 𝑓)] (20)

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with Qf = { f : 0 ≤ f ≤ fmax } being a basic interval along the frequency axis.
Feature extraction, which is a mapping process from the measured signal space to the
feature space, can be regarded as the most important step for automatic PQ signal detection
and classification system. In this study, Support Vector Machine (SVM) with radial basic function
(RBF) kernel has been selected as the classification algorithm. Several signal's features have
been extracted for training and testing data set of the classification algorithm. The extracted
features are:
1. Minimum magnitude of instantaneous RMS voltage, F1.
2. Maximum magnitude of instantaneous RMS voltage, F2.
3. Minimum magnitude of instantaneous RMS fundamental voltage, F3.
4. Maximum magnitude of instantaneous RMS fundamental voltage, F4.
5. Magnitude difference of instantaneous RMS voltage, F5.
6. Magnitude difference of instantaneous RMS fundamental voltage, F6.
7. Average total harmonic distortion, F7.
8. Average total non-harmonic distortion, F8.
9. Average total waveform distortion, F9.
10. Maximum magnitude of instantaneous total harmonic distortion, F10.
11. Maximum magnitude of instantaneous total non-harmonic distortion, F11.
12. Maximum magnitude of instantaneous total waveform distortion, F12.
13. Minimum magnitude of instantaneous total harmonic distortion, F13.
14. Minimum magnitude of instantaneous total non-harmonic distortion, F14.
15. Minimum magnitude of instantaneous total waveform distortion, F15.
16. Magnitude difference of instantaneous total harmonic distortion, F16.
17. Magnitude difference of instantaneous total non-harmonic distortion, F17.
18. Magnitude difference of instantaneous total waveform distortion, F18.
19. Instantaneous frequency, F19.
5. Results and Analysis
In this section, it is explained the results of research and at the same time is given the
comprehensive discussion. Results can be presented in figures, graphs, tables and others that
make the reader understand easily [2,5]. The discussion can be made in several sub-chapters.
5.1. MST Spectrum versus ST Spectrum
In this study, the performance of the MST was first being analysed from the time-
frequency spectrum that it can be generated with three (3) signal models that being used in this
study, which are voltage variation, waveform variation and transient signal model. The MST
spectrum is then compared with the spectrum generated by the standard S-transform (ST). The
standard ST was simulated by setting the value of γGS (f) in MST Gaussian window’s equation
equal to 1. By doing this, the resulted window function of MST will be the same as standard ST
window function which is given in Eq. 1.
The resulted spectrums of the three signal models are shown in Fig. 1 in a contour plot
graph. From the TFD shown in Fig. 1, it is observed that MST gives excellent frequency
information for voltage variation signal, waveform distortion signal, as well as transient signal.
The frequency spectrum in MST has less smearing contour as compared to standard ST’s TFD.
We can also see in Figure 1 that the detection of interharmonic and harmonic frequency
components was substantial in MST’s TFD. However, in terms of temporal resolution, the MST
showing less precise detection as compared to standard ST.
5.2. MST Spectrum and Signal Indices
Eight (8) types of PQ disturbance signal have been analysed using MST in this
research. The PQ disturbances are voltage sag, swell, interruption, transient, even harmonic,
interharmonic, sag plus even harmonic and swell plus even harmonic. The resulted spectrums
for voltage sag, voltage transient and harmonic plus interharmonic signal, as well as the
resulted signal indices are shown in Figure 1 - 3 respectively.
From the result, it is observed that the resulted TFD from MST is able to display the
existence of the PQ disturbances in the input signal. For voltage sag signal, the highest peak of
the MST's TFD contour occurs at the frequency of 60 Hz, and the peak magnitude reduces in

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the middle of the time plane, showing a drop of the magnitude of the input signal during the
given time. The contour, however, remains in the same frequency of 60 Hz while the magnitude
drop occurs. This shows that the analysed signal is having a change in the magnitude only, not
in its frequency. The signal's indices, which consist of the instantaneous RMS voltage,
instantaneous RMS fundamental voltage, instantaneous THD, instantaneous TnHD, and
instantaneous TWD were also giving the correct information about frequency and magnitude
condition of the analysed signals. These mean that correct features can be obtained from the
extracted indices of the resulted MST time-frequency distribution.
As for transient signal, the resulted TFD from MST matrix in Figure 2(b) shows an
abrupt change in signal frequency for a specific duration. For this signal, the transient frequency
that has been generated is 3458 Hz, which is exactly as depicted in the transient TFD of MST
matrix. The magnitude of the transient signal, however, cannot be estimated from the MST
contour plot. It can be estimated from the curve of the instantaneous RMS fundamental signal,
where we can see the increment of RMS voltage magnitude. The signal indices of transient are
also able to give the correct features which will help the classification system to perform well.
(a)
(b)
(c)
Figure 1. Time and frequency spectrum of ST and MST for (a) voltage variation signal,
(b) waveform variation signal and (c) transient

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Figure 2. (a) Voltage sag signal construction, (b) MST time-frequency distribution, (c)
Instantaneous RMS voltage, (d) Instantaneous RMS fundamental voltage, (e) Instantaneous
THD, (f) Instantaneous TnHD and (g) Instantaneous TWD for voltage sag

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Figure 3. (a) Transient signal construction, (b) MST time-frequency distribution, (c)
Instantaneous RMS voltage, (d) Instantaneous RMS fundamental voltage, (e) Instantaneous
THD, (f) Instantaneous TnHD and (g) Instantaneous TWD for voltage swell signal
5.3. Power Quality Classification using SVM
Support Vector Machines (SVM) is a powerful technique for rectify problems in
nonlinear classification, function estimation, and density estimation in kernel based methods in
general [17,18]. In this study, RBF support vector machine (RBF SVM) were utilised to classify
all these eight types of PQ disturbances. More steps on analysing the PQ disturbance signal
were further proceeded by generating 100 signals of each type from the 8 classes of PQ
disturbance signal using Equations (8) - (10) using Matlab R2012a. The description of the

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classes of the power quality disturbances to be predicted by the SVM is shown in Table 1. To
obtain the outcome, the training and testing data were divided by using 1/3 distribution,
indicating that 2/3 of the generated signals will be used for training, and the rest will be used as
testing data. A total of 19 features*100 signals were extracted from each class of simulated PQ
signals. By using five cross-validation technique, the optimised value of C and γ was determined
iteratively. In order to verify the robustness of the proposed method, detection and classification
of PQ signals added with a random white Gaussian noise (AWGN) of zero mean and signal to
noise ratio (SNR) varying from 50dB to 10dB was observed. The results are shown in Table 2
and 3.
Table 1. Description of Classes of PQ Disturbances
Type of PQ Disturbances Classes
Voltage sag C1
Voltage swell C2
Voltage interruption C3
Oscillatory transient C4
Interharmonics C5
Even harmonic C6
Sag + even harmonic C7
Swell + even harmonic C8
Table 2. Classification Rate for the PQ Disturbance Signal Without the Presence of Noise
C1 C2 C3 C4 C5 C6 C7 C8
Classification
rate (%)
C1 32 0 1 0 0 0 0 0 97
C2 0 33 0 0 0 0 0 0 100
C3 0 0 33 0 0 0 0 0 100
C4 0 0 0 33 0 0 0 0 100
C5 0 0 0 0 33 0 0 0 100
C6 0 0 0 0 0 33 0 0 100
C7 0 0 0 0 0 0 33 0 100
C8 0 0 0 0 0 0 0 33 100
Average classification rate: 99.7%
Table 3. Classification Rate for The PQ Disturbance Signal with the Presence of Noise
SNR of AWGN (dB) Classification rate (%)
50 98
40 98
30 98
20 98
10 92
From the result shown in Table 2 and 3, it is observed that the combination of MST with
RBF kernel SVM is able to give a higher classification rate for detection and classification of
single and multiple PQ disturbance signals. As for the noisy PQ disturbance signal, the
classification rate is almost constant at 98% for 50dB until 20dB range of SNR of AWGN, and
almost 92% of classification rate for 10dB SNR of AWGN. This shows that MST is suitable for
the PQ disturbance signal features extraction and can be used in the real-time automatic PQ
disturbance signal analysis system.
6. Conclusion
In this paper, a new signal processing method which is known as MST is studied for the
application of automatic PQ disturbance detection and classification system. Nineteen (19)
signal features have been proposed and extracted from each signal of each class of PQ
disturbance signals. The result obtained is remarkably high, in which almost 100% classification
rate is achieved for clean PQ disturbance signals. The performance of the method was also
analysed in noisy corrupted disturbance signal. The resulted classification rate for the noisy
corrupted signal (SNR = 10 dB) gives higher percentage values above 92%. As for higher SNR

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values (50 dB to 20 dB), the result is almost constant at 98%. From this result, we can conclude
that the studied method is a robust method to analyse PQ disturbance signal in noisy and
unnoisy environments. It is also concluded that the extracted features proposed in this paper
are able to characterise each type of disturbance into a unique and detectable manner.
Acknowledgments
The authors would like to thank the Office for Research, Innovation, Commercialization
and Consultancy Management (ORICC) and Universiti Tun Hussein Onn Malaysia (UTHM) for
providing resources and financial support for this research.
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