Journal of Power and Energy Engineering, 2015, 3, 215-223
Published Online April 2015 in SciRes. http://www.scirp.org/journal/jpee
http://dx.doi.org/10.4236/jpee.2015.34030
How to cite this paper: Noh, F.H.M. , Miyauchi, H. and Yaakub, M.F. (2015) Application of Slantlet Transform Based Support
Vector Machine for Power Quality Detection and Classification. Journal of Power and Energy Engineering, 3, 215-223.
http://dx.doi.org/10.4236/jpee.2015.34030
Application of Slantlet Transform Based
Support Vector Machine for Power Quality
Detection and Classification
Faridah Hanim M. Noh1,2*, Hajime Miyauchi1, M. Faizal Yaakub3
1Department of Frontier Technology for Energy & Devices, Kumamoto University, Kumamoto, Japan
2Department of Electrical Power Engineering, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia
3Department of Electrical Engineering Technology, Universiti Teknikal Malaysia Melaka, Melaka, Malaysia
Email: *han im@ st.c s.ku mamo to-u.ac.jp
Received January 2015
Abstract
Concern towards power quality (PQ) has increased immensely due to the growing usage of high
technology devices which are very sensitive towards voltage and current variations and the
de-regulation of the electricity market. The impact of these voltage and current variations can lead
to devices malfunction and production stoppages which lead to huge financial loss for the produc-
tion company. The deregulation of electricity markets has made the industry become more com-
petitive and distributed. Thus, a higher demand on reliability and quality of services will be re-
quired by the end customers. To ensure the power supply is at the highest quality, an automatic
system for detection and localization of PQ activities in power system network is required. This
paper proposed to use Slantlet Transform (SLT) with Support Vector Machine (SVM) to detect and
localize several PQ disturbance, i.e . voltage sag, voltage swell, oscillatory-transient, odd-harmon ics,
interruption, voltage sag plus odd-harmonics, voltage swell plus odd-harmonics, voltage sag plus
transient and pure sinewave signal were studied. The analysis on PQ disturbances signals was
performed in two steps, which are extraction of feature disturbance and classification of the dis-
turbance based on its type. To take on the characteristics of PQ signals, feature vector was con-
structed from the statistical value of the SLT signal coefficient and wavelets entropy at different
nodes. The feature vectors of the PQ disturbances are then applied to SVM for the classification
process. The result shows that the proposed method can detect and localize different type of single
and multiple power quality signals. Finally, sensitivity of the proposed algorithm under noisy con-
dition is investigated in this paper.
Keywords
Features Ex tr acti on, Power Quality Disturbances, Slantlet Transfor m, Support Vector Machine
1. Introduction
In recent years, the traditional structures of power system have changed, and the electrical system can no longer
F. H. M. Noh et al.
216
be handled as a single entity. The electricity industry is evolving into a distributed and competitive industry in
which market forces drive the price of electricity and reduce the net cost through increased competition [1]. This
changes which is known as the deregulation of the electricity industry, has changes the status of electrical power
into a product based quantity. These have changed the electricity market to be customer oriented market [1]. On
the other hand, the growing usage of high technology devices at the customer side as well as at the generation
side had contributes toward the generation of power quality disturbances in the power network. And ironically,
all of these equipments are also very sensitive towards power quality disturbances [2]. Owing to the fact that these
problems directly affect consumers in production times and costs, nowadays there is a demand by industry for
continuous monitoring power systems [3].
Signal processing has been widely used for analyzing power signals for purpose of automatic PQ disturbance
recognition. The most widely used signal processing techniques in extracting features of disturbances from a
large number of power signals are the fast Fourier transform (FFT) and the windowed Fourier transform which
comprises of the short time Fourier transform (STFT) and the wavelet transform [4]. Wavelets have been exten-
sively used by the researchers during the last decade due to its capability to decompose signals into frequency-
dependent components. It is equivalent to applying a set of subband filters with an octave bandwidth relation,
however. The DWTs has been identified as an excellent tool for automatically detecting multiscale singularities
in a signal [1].
Recently, SLT has been proved as a better compression technique for PQ data [5]. SLT which has a better
time localization as compared to discrete wavelet transform (DWT), is actually an orthogonal DWT with two
zero moments. It use a special cases of a class of bases described by Alpert, retains the octave-band characteris-
tic and piecewise linear (but discontinuous). The SLT filter is implemented in the parallel structure and each of
the filters are not products. Therefore, SLT has extra degree of freedom and lengths of the filter are shorter
compare to DWT. In this paper, the applications of SLT in detecting and extracting features of single and mul-
tiple power quality disturbances has been investigated.
Eight types PQ disturbances signals which are voltage sag, voltage swell, oscillatory-transient, odd-harmonics,
interruption, voltage sag plus odd-harmonics, voltage swell plus odd-harmonics, and pure sine-wave signal have
been generated using parametric equation and have been analyzed using SLT. In this work, the features are ob-
tained from the time-frequency domain data of approximation and details signal of SLT. The standard statistical
features and wavelet entropies that have been extracted are max, min, standard deviation, mean, energy entropy
and log energy entropy. The result shows that the proposed method can detect and extract several features of
different type of single and multiple power quality signals. Finally, sensitivity of the proposed algorithm under
noisy condition is investigated in this paper.
2. Methodology
2.1. PQ Data Generation
In this paper, the eight types of the PQ disturbance signals have been generated using parametric equations
based on the given IEEE Standards 1159-2009 and the equations are given in Table 1. Waveform with 256
cycles at sampling frequency 12.8 kHz have been generated for a total of 65,536 sample points. The fundamen-
tal frequency is generated at 50 Hz frequency.
2.2. The Slantlet Transform
The SLT was first introduced by Ivan W. Selesnick in 1999 [6]. The SLT is an orthogonal Discrete Wavelet
Transform (DWT) with two zero moments, improved time localization, and is based on designing different fil-
ters that are not product for each scale [7].
The structure of SLT filter bank depends on the number of scale of SLT that being used. For l-scale SLT filter
bank has 2l channels. The first channel consists of filter
( )
l
hn
, followed by filter
()
l
fn
in the second channel.
Both
( )
l
hn
and
( )
l
fn
are to be followed by down sampling by 2l. The remaining 2l-2 channels are filtered
by
( )
i
gn
and its shifted time-reverse for
1, ,1il= −
. These remaining channels are to be followed by down
sampling by
1
2
i+
[6] . The proposed SLT filter bank in this study use 2-scales and it have 4 channels of filters.
The general structure of 2-scales SLT filter bank is shown in Figure 1.
The
( )
l
hn
( )
l
fn
and
( )
i
gn
filters are piecewise linear, hence each filter can be represented as the sum
F. H. M. Noh et al.
217
Table 1. Parametric equation for PQ disturbances signal.
PQ Disturbance Signal Generation
Equation Parameter Variation
Pure
( )()
sinft At
ω
=
Frequency = 50 Hz, A = 1
Sag
( )()()
( )
( )
( )
12
1 sinftAut tut tt
αω
=−−− −
,
21
9
Tt tT≤−≤
Swell
( )()()
( )
( )
( )
12
1 sinftAut tut tt
αω
=+−− −
,
21
9
Tt tT
≤−≤
Interruption
( )()()
( )
( )
( )
12
1 sinftAut tut tt
αω
=−−− −
0.9 1
α
≤≤
,
21
9
Tt tT≤−≤
Odd-Harmonics
( )()( )( )( )
( )
13 5 7
sinsin 3sin 5sin 7
ft Atttt
α ωαωαωαω
= +++
3
0.05 0.15
α
≤≤
,
5
0.05 0.15
α
≤≤
,
7
0.05 0.15
α
≤≤
,
21
i
α
∑=
Oscillatory
Transient
()( )( )
( )
()
( )
( )
11
sin expsin
oscosc osc
ft ttttt
ωατ ω
=+ −−−
osc
0.0080.04 s
τ
= −
,
osc 15 kHz
ω
= −
Sag + Harmonic
( )() ( )
()
( )
( )
()( )()( )
( )
12
13 5 7
1 sin
sinsin3sin5sin7
ftAuttut tt
tttt
αω
α ωαωαωαω
=−−−−
×+ + +
,
21
9Tt tT≤−≤
,
3
0.05 0.15
α
≤≤
,
5
0.05 0.15
α
≤≤
,
7
0.05 0.15
α
≤≤
,
21
i
α
∑=
Swell + Har monic
( )()()
( )
( )
( )
( )()()()
( )
12
13 5 7
1 sin
sinsin3sin5sin7
ftAuttut tt
tttt
αω
α ωαωαωαω
=−−+−
×+ + +
,
21
9
Tt tT≤−≤
,
3
0.05 0.15
α
≤≤
,
5
0.05 0.15
α
≤≤
,
7
0.05 0.15
α
≤≤
21
i
α
∑=
of a DC and a linear term. The general equation of
( )
l
hn
,
( )
l
fn
and
()
i
gn
are given as follow [6]:
()( )
0,0 0,1
1
1,01,1
,for 0,,21;
1,for 2 ,,21.
i
iii
a ann
gn a ann
+
+=−
=+−=−
(1)
( )( )
0,0 0,1
1
1,01,1
,for 0,,21;
1,for 2,,21.
l
lll
b bnn
hn bbnn
+
+=−
=+−= −
(2)
()()
0,0 0,1
1
1,01,1
,for 0,,21;
1,for 2,,21.
l
lll
c cnn
fn c cnn
+
+=−
=+−= −
(3)
The SLT filters fulfilled the following conditions in order to have the orthogonality and zero moment condi-
tions [3]:
1) The SLT filters are off to unit norms.
2) They are orthogonal to theirs shifted time reverse.
3) The
( )
i
gn
and
( )
i
fn
filters annihilate linear discrete time polynomials.
Now since the coefficient of each filter is orthogonal to its corresponding shifted time-reversal while preserv-
ing their piecewise linear characteristics, a satisfactory computation performance can be also ensured. As stated
by [7], it is observed that SLT fulfilled most of the properties for PQ event analysis. This is because the SLT
consist of oscillatory function so that analysis on oscillated signal can be performed. It also has short support of
filter and has two vanishing moments which can be used to reduce the number of coefficient to be analyzed [7].
In this study, the features of the PQ disturbances have been extracted from all of the decomposition level of SLT
filterbank.
2.3. Support Vector Machine
Support Vector Machines is a powerful methodology for solving problems in nonlinear classification, function
F. H. M. Noh et al.
218
Figure 1. The structure of 2 scales SLT filterbank.
estimation and density estimation in kernel based methods in general [8]-[10]. The basic idea is to find a hyper-
plane which separates the d-dimensional data perfectly into its two classes. Given the training data (x1, y1)
(xl, yl),
xR
, where each data consists of M features. These features describes for a two-class problem as:
{ }
1, 1
i
y∈− +
(4)
The SVM constructs the decision function given as,
( )
gxwx b= ⋅+
, where w is the optimal solution and b
is the bias parameter. These parameters are derived to classify the data correctly. An important concept in SVMs
is the margin. A margin of a classifier is defined as the shortest distance between the separating boundary and an
input training vector that can be correctly classified. For a soft-margin SVM, support vectors can lie on the mar-
gins as well as inside the margins. A soft-margin SVM is described as a quadratic optimization problem:
2
,, 1
1
min 2
N
i
wb i
wC
ξ
ξ
=

+


(5)
where
0C
is a user-specified regularization parameter that determines the trade-off between the upper bound
on the complexity term and the empirical error [8].
If there were a “kernel function” K such that K
( )
( )
( )
,
ijij
xxx x
ϕϕ
= ⋅
, then only K is used in training algo-
rithm, and never need to explicitly determine φ. Thus, kernel is a special class of function that allows inner
products to be calculated directly in feature space. In this paper, the application of radial basis function (RBF)
kernel has been used in order to classify the single and multiple PQ disturbance signals. The RBF kernel has
been defined as in Equation (6).
( )
( )
2
, expK xyxy
γ
= −−
(6)
where
γ
is the width parameter of RBF function. The accuracy of the selected SVM relies on the selection of
the kernel parameter,
γ
, and the regularization parameter,
C
. The proper value of
( )
,C
γ
will give higher
classification rate and reduce the processing time [9]. The parameters
( )
,C
γ
should be determined prior to the
training process. In this paper, parameters
C
and
γ
were chosen using 5 cross validation technique.
2.4. Features Extraction
The coefficient of
ij
D
at all decomposition levels are used to extract the feature of different type of PQ distur-
bances. Statistical feature and wavelet entropy like mean, maximum, minimum, standard deviation, energy and
log energy entropy of the decomposition coefficient of
ij
D
are calculated using the equations in Table 2 [10] .
2.5. The Overall Framework
In this study, the use of the 2 scales SLT filter bank has been proposed. It consist of 4 channels of filters, which
are
( )
2
hn
,
( )
2
fn
,
( )
1
gn
and its shifted time reverses. The parameter values of the filters are calculated using
Equations (1)-(3).
The process flow of extracting features with the application of 2 scales SLT filter bank are given in Fig ure 2.
The process starts by applying the PQ signal for the transformation. Then the process of thresholding is done in
which suitable threshold is chosen for discarding the SLT coefficients which are not having significant energy.
x(n)
z-3G1(1/z)
H2(z)
F2(z)
G1(z)
4
4
4
4
F. H. M. Noh et al.
219
Table 2. Equation for features of PQ disturbances.
Features Features Extraction
Equation
Energy
Mean
1
1
N
ij ij
j
D
N
µ
=
=
Standard Deviation
( )
2
1
1
1
N
ijij ij
j
D
N
σµ
=

= −


Minimum
( )
Min min
i ij
D=
Maximum
( )
Max max
i ij
D=
Log Energy Entropy
1
LgEn log
N
i ij
j
E
=
= −
a
1, 2,,il
=
is the number of decomposition scales, while
1, 2,,jN
=
represent the number of coefficient for each decomposition level.
Figure 2. The overall process flow of PQ detection and classification using SLT based SVM.
The output signal from the analysis filterbank after the thresholding process, i.e. d1, d2, d3 and d4, will then be
analyzed and processed so that several feature of PQ event can be extracted. These features will be used in clas-
sification system to identify the type of disturbance that exists in the given signals. Then the signal will be
transform again by using inverse SLT/synthesis filterbank in order reconstructed original signal. Based on the
constructed signal, the effectiveness of the thresholding process can be observed.
The wavelet thresholding process has been applied to the SLT coefficient signals in order to de-noised the noisy
signals. The threshold method for SLT coefficient that being used in this paper are hard threshold rule with Ri-
gorous SURE (RigSURE) and Heuristic SURE (HeurSURE) threshold selection method.
3. Result and Analysis
Figure 3 shows PQ signals generated based on the given parametric equation in Table 1. In this study, the appli-
cations of 2 scale SLT filters to analyze PQ disturbance signals have been performed. Similar to wavelet trans-
form, SLT deals with expansion of function in terms of a set of basic function which allowed the signals to be
analyzed in time and frequency domain. The signal generated in wavelet domain will give some information due
to the existence of disturbances in the signal and the duration of the disturbances.
Figure 4 sho ws the output signal of 2 scale SLT synthesis filterbank for single PQ disturbance signal. Figures
4(a) -(c) show the capabilities of SLT to detect single PQ disturbance signal at different frequency level. Center
frequency for each SLT filterbank is calculated using Equation (7) [1] and the values are given in Table 3.
2
,
31, 2,,
2
s
kk
f
f kM
+
==
(7)
where
s
f
is the sampling frequency and M is the total number of scales.
1k
f
=
represents the center frequency
of the highest scale or high pass filter of SLT (g1(n)) and
kM
f=
is the center frequency of the lowpass filter of
SLT
( )
( )
2
hn
.
In this study, the harmonic signals contain odd harmonics components, which are the third, fifth and seventh
harmonics component. Since the harmonic component is in the range of 150 Hz to 350 Hz, the detection of the
harmonic can be seen in the output filter of
( )
2
hn
, along with the fundamental component of the signals. How-
F. H. M. Noh et al.
220
Figure 3. Generated signal using parametric equation.
F. H. M. Noh et al.
221
ever, as for higher frequency component of PQ signals, such as transient signals in Figure 4(c) , the existence of
the transient component can only be seen at the output signal of filter
()
2
fn
, as well as filter
()
1
gn
. Detection
of multiple PQ disturbances is shown in Figures 5(a)-( b).
RBF support vector machine have been utilized to classify all these eight types of PQ disturbance that have
been studied in this paper. The classification process is made in Matlab2009a environment and 150 signals for
each type of PQ disturbances have been generated using parametric equation in Table 1. The training and testing
data are divided by using 1/3 distribution, which mean 2/3 of the generated signals will be used for training, and
the rest will be used as testing data. Total of 6 × 4 × 150 × 8 features have been extracted from the simulated PQ
signals. By using five cross validation technique, the optimized value of C and γ have been determined iteratively.
In order to verify the robustness of the proposed method, several PQ signal added with AWGN with SNR 20 dB,
25 dB and 30 dB have been feed to the proposed PQ detection and classification system. RigSURE and Heur-
SURE threshold selection method combined with hard threshold techniques have been applied to SLT coefficient
signals. The results are shown in Table 4.
(a)
(b) (c)
Figure 4. SLT signal coefficient for single PQ disturbance signal. (a) Sag; (b) Harmonics; (c) Tran s i en t.
(a) (b)
Figure 5. SLT signal coefficient for multiple PQ disturbance signal. (a) Sag and harmonics; (b) Sag and transient.
F. H. M. Noh et al.
222
Table 3. Center frequency for SLT filters.
Filter Center Frequency
h2(n) 1200 Hz
f2(n) 2400 Hz
g1(n) 4800 Hz
aThe shifted-time reverse filter of g1(n) has the same center frequency with g1(n).
Table 4. Classification results.
PQ Signals Classification Accuracy
SLT + SVM SLT + RigS URE + SVM SLT + HeurSURE + SVM
Clean Signals 98% - -
20 dB AWGN - 70% 79%
25 dB AWGN - 75% 81%
30 dB AWGN - 79% 87%
4. Conclusion
The application of 2 scales SLT filter has been studied and analyzed. According to the simulated result, it is ob-
served that the 2 scales SLT capable to detect the single and multiple PQ disturbance signals with precise time
localization. The extracted statistical and wavelet entropy data gives unique values and trend for different type
of PQ disturbances signals, which are suitable for event identification. However, with the existence of noises in
the signals, the performance of the proposed techniques degraded. This shows that the studied features of PQ
signals varied or destroyed with this AWGN. Thus, more robust features for PQ disturbance signals should be
proposed in future.
Acknowledgements
The authors wish to thank Ministry of Education Malaysia and Kumamoto University for providing resources
and financial support for this research.
References
[1] Bollen, M.H.J. and Gu, I.Y.H. (2006) Signal Processing of Power Quality Disturbances. IEEE Press Series on Power
Engineering, John Wiley & Sons Inc., Hoboken. http://dx.doi.org/10.1002/0471931314
[2] Thapar , A., Saha, T.K. and Dong, Z.Y. (2004) Investigation of Power Quality Categorisation and Simulating It’s Im-
pact on Sensitive Electronic Equipment. IEEE Power Engineering Society General Meeting, 1, 528 -533.
[3] Gra nados -Lieberman, D., Romero-Troncoso, R.J., Osornio-Rios, R.A., Garcia-Pere z, A. and Cabal-Yepez, E. (2011) Tech-
niques and Methodologies for Power Quality Analysis and Disturbance Classification in Power System: A Review. IET
Generation Transmission & Distribution, 5, 519-529. http://dx.doi.org/10.1049/iet-gtd.2010.0466
[4] Moussa, A., El-Gammal, M., Abdallah, E.N. and El-Sloud, A.A. (2004) Hardware-Software Structure for On-Line Po-
wer Quality Assessment. Proceedings of the 2004 ASME/IEEE Joint, Baltimore, 8 April 2004, 147-15 2.
http://dx.doi.org/10.1115/RTD2004-66022
[5] P anda, G., Dash, P.K.A., Pradhan, K. and Meher, S.K. (2002) Data Compression of Power Quality Events Using the
Slantlet Transform. IEEE Transactions on Power Delivery, 17, 662-667. http://dx.doi.org/10.1109/61.997957
[6] Selesnick, I.W. (1999) The Slantlet Transform. IEEE Transactions on Signal Processing, 47, 1304-1313.
http://dx.doi.org/10.1109/78.757218
[7] Meher, S.K. (2008) A Novel Power Quality Event Classification Using Slantlet Transform and Fuzzy Logic. Proceed-
ing of Power System Technology and IEEE Power India Conference, New Delhi, 12-15 Octob er 2008, 1-4.
http://dx.doi.org/10.1109/ICPST.2008.4745234
[8] Burges, C.J.C. (1998) A Tutorial on Support Vector Machine Pattern Recognition. Data Mining and Knowledge Dis-
covery, 2, 121-167. http://dx.doi.org/10.1023/A:1009715923555
F. H. M. Noh et al.
223
[9] V apni k, V.N. (2000) The Nature of Statistical Learning Theory. 2nd Edition, Springer-Verlag, New York.
[10] Cortes, C. and Vapnik, V.N. (1998) Support Vector Network. Machine Learning, 20, 121 -167 .