Sci.Int.(Lahore),26(4),1447-1456,2014
ISSN 1013-5316; CODEN: SINTE 8
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CLASSIFICATION ANALYSIS OF POWER SYSTEM
TRANSIENT DISTURBANCES WITH SOFTWARE
CONCEPTS
Aslam P. Memon1, M. Aslam Uqaili3, Zubair A. Memon3, Waqar Adil2, M. Usman Keerio4
1
Mehran University of Engineering, & Technology, Jamshoro & Department of Electrical, Quaid-e- Awam U.E.S.T,
Nawabshah, Sindh, Pakistan; aslam@quest.edu.pk
2,4
Department of Electrical Engineering, Quaid-e-Awam University of Engineering, Science & Technology,
Nawabshah, Sindh, Pakistan.
3
Department of Electrical Engineering, Mehran University of Engineering, & Technology, Jamshoro, Sindh, Pakistan
.ABSTRACT: Power system transients cause serious disturbances in the reliability, safety and economy of
the power system network. These disturbances occur in a few cycles, which are difficult to be identified and
classified by digital measuring and recording instrumentations. The transient signals are the transitory for
which the frequencies as well as varying time information are compulsory for the analytic purposes.
Various types of transients indicate various behaviors and measuring characteristics, but it is vital, first to
detect and classify the type of fault and then to mitigate them.
In digital signal processing, Fast Fourier transformation is a powerful technique traditionally utilized to
measure the disturbances of such signals, but it is more suitable for periodic analysis where time
information of the signal is not necessary.
In this work power system transient disturbances are detected, analyzed and classified with the help of
time-frequency analysis technique of discrete wavelet transformation with multiresolution analysis (MRA)
algorithm choosing the most suitable wavelet function as mother wavelet.
This proposed methodology possesses the ability to de-noise and decompose the various types of transient
using Matlab/Simulink and Wavelet toolbox and the simulation results prove their simplicity, accurateness
and effectiveness for the detection and classification of power system transient signal disturbances.
Keywords: Power Quality, Power System Transient, Discrete Wavelet Transform, Symlet Mother Wavelet,
Development of Numerical, Simulink and GUI models
.INTRODUCTION
The transients occur due to switching, lighting strikes, and
various types of faults and other intended or unintended
causes. They become the detrimental reasons of power
system components which suffer from the enormous amount
of currents and voltages. Transients are also known as
voltage disturbances less than sag or swell and caused by
sudden variations in electrical power system [1-3].
PST is a sub-category of electrical power quality (EPQ),
arising as a result of variation in sinusoidal nature of power
system (PS) supply voltage which is said to be nonrepetitive, random and causes equipment failure. Various
types of PSTs indicate various behaviors and measuring
characteristics. The severe magnitude and energy content
make them necessary to be investigated for their detection
and classification to facilitate the various power system
protection equipment [1-4].
Therefore, it is imperative to understand the characteristics
of the transient to identify its causes and sources in order to
develop appropriate mitigation methodology to prevent the
damage of sensitive equipment [5].
To analyze transient signals, we can either generate them by
simulation methods or collect them in a real time
environment. Real time collection of transient data is
expensive and time consuming. The next step in the analysis
is to choose an effective signal processing technique which
is normally a mapping the signals in he frequency domain
and is known as Fast Fourier transformation (FFT). FFT is
unfortunately not effective in detecting the aperiodic
elements of the signals. A time-frequency mapping known
as wavelets transform (WT) is preferred over other
techniques in such time varying cases [6-8].
1.1
Literature Review
Fourier transform, which is considered as conventional
signal analysis methods, and uses sine waves with infinite
support, find limited usage in the analysis of transient
disturbances. In general, transients are non-stationary and
short-term waveforms that change the sinusoidal voltage and
current waveforms in an aperiodic manner.
More advanced techniques, such as the wavelet transform,
are more suitable. In these techniques waves with compact
(finite) support are used [8-10] and these techniques reveal
signal properties while retaining its time information. This is
known as fractal analysis [11-12]. As a result of analyzing
transient with these techniques, one can obtain features of
transients that can be used in a classifier for differentiating
their various types.
PST is the important part of power quality issue which is
aperiodic in nature. The chances of occurrence PST
disturbances are uncertain and hence they are difficult to be
measured, recorded and analyzed. Due to unavailability of
real time transient data, it is again difficult for researchers
and academicians to focus on research related to transient
disturbance phenomenon. FFT deals only in frequencydomain periodic signals hence its signal analysis technique
is not capable to detect localized and classify the PST
disturbances [13-15].
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Therefore, it is imperative to understand the various
characteristics of PST disturbances to identify its causes and
sources in order to develop appropriate mitigation
methodology to prevent the damage of sensitive equipment.
This work proposes the detection and classification of PST
signal disturbances with the help of time-frequency
technique of discrete wavelet transformation (DWT). The
multiresolution analysis (MRA) as the algorithm is
suggested and the suitable mother wavelet is also chosen
from some of the mostly used mother wavelet functions
which produce the feature extraction data for the
classification of PST signals. All the major categories of
PSTs defined by IEEE-1159 are developed using the
mathematical equations and graphical user interfacing (GUI)
in Matlab.
1.
POWER QUALITY (PQ) AND POWER
SYSTEM TRANSIENT DISTURBANCE (PSTD)
The IEEE Standards Coordinating Committee 22 (IEEE
SCC22) has led the main effort to coordinate power quality
standards. It has classified power quality problems as [1-3]:

Disturbances

Waveform distortion

Voltage unbalance

Voltage flicker


Power frequency variations
Transients are sub-category of power disturbances which
have a high frequency. The IEEE 1159 standard defines two
types of transients [1-3];
 Impulsive transients
 Oscillatory transients
Fig. 01: Voltage transients
An electrical transient is the outward manifestation of a
sudden change in circuit conditions, as when a switch opens
or closes or a fault occurs on a system. Transient period is
very short relative to the time spent in steady state
operations, but is extremely important because greatest
stress occurs on circuit components due to excessive
currents and voltages which cause damage to the circuit.
Transients can be classified depending upon their wave
shape, their origin, and their mode of generation [1-3].
Wave shape based classification includes:
 Oscillatory (Ringing wave)
 Impulsive
Origin based classification includes:
 Atmospheric origin i.e. lightning
 Switching origin i.e. switching operation and faults.
On the other hand mode of generation based classification
includes:
Sci.Int.(Lahore),26(4),1447-1456,2014

Electromagnetic transients. (Interaction between
capacitive and inductive elements)
 Electromechanical transients
Interaction between capacitive and inductive elements
results in travelling waves and oscillations [16].
This work mainly deals with the electromagnetic transients.
2.
DIGITAL SIGNAL PROCESSING (DSP) AND
WAVELET TRANSFORM (WT)
Although root mean square (RMS) method is not an inherent
signal processing technique, yet it is the most used tool.
RMS gives a good approximation of the fundamental
frequency, amplitude profile of a waveform. A great
advantage of this algorithm is its simplicity, speed of
calculation and less requirement of memory, because rms
can be stored periodically instead of per sample [17].
However, its dependency of window length is considered as
a disadvantage. One cycle window length will give better
results in terms of profile than a half cycle window.
Moreover, rms does not distinguish fundamental frequency,
harmonics or noise components. On the other hand, rms
voltage profiles are used for event analysis and
automatic classification as proposed in [18].
Monitoring of power quality problem using advanced DSP
techniques comprises:
 Processing of stationary signals
Processing of non-stationary signals
Processing techniques of power quality data are further
classified based on their method of analyzing the waveform
data. These are “Parametric or model based methods for
processing of PQ data”, and “Non-parametric or
transformation based processing of PQ waveform data”.
Parametric or model based methods for processing of PQ
data include:
 Harmonic or sinusoidal model
 Multiple Signal Classification model
 ESPRIT method
 Kalman Filtering based method
Non-parametric or transformation based processing of PQ
waveform data include:
 Fourier Transform
 Short Time Fourier Transform
 Wavelet Transform
In this work transformation based processing techniques
have been discussed and utilized.
Traditionally, the Fourier transforms permits mapping
signals from time domain to the frequency domain by
decomposing the signals into several frequency components.
This technique is criticized in that the time information
of transients is totally lost, although the accuracy of
frequency components is high. Fourier transform does not fit
the analysis of transients owing to the non-stationary
property of its signals in both time and frequency
domains. Wavelet transform generally offers this facility
[19]
3.1
Wavelet analysis
The wavelet analysis calculates the correlation between the
signal under consideration and a wavelet function ψ (t). The
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similarity between the signal and the analyzing wavelet
function is computed separately for different time intervals,
resulting in a two dimensional representation. The analyzing
wavelet function ψ (t) is also referred to as the mother
wavelet.
An analyzing function ψ (t) is classified as a wavelet if the
following mathematical criteria are satisfied [20]:
1. A wavelet must have finite energy

E
  (t )
2
(1)
The energy E equals the integrated squared magnitude of the
analyzing function ψ (t) and must be less than infinity.
2. If Ψ(f) is the Fourier transform of the wavelet ψ(t), the
following condition must hold
C  
 ( f )
f
0
2
df  
(2)
This condition implies that the wavelet has no zero
frequency component (Ψ (0) = 0), i.e. the mean of the
wavelet ψ (t) must equal zero. This condition is known as
the admissibility constant. The value of Cψ depends on the
chosen wavelet.
3. For complex wavelets the Fourier transform Ψ (f) must
be both real and vanish for negative frequencies.
For computer implementations discrete wavelet transform
(DWT) is utilized as:
W m, n  
a0
 k  a 0 m nb0
xk 

m

a0
k  


1
m




(3)
 a0 , b  a0 nb0 , m and n are the integer
numbers provided a 0 1 and b0  0 [19].
m
Where a
m
Due to this process redundancy of continuous form must be
eliminated hence a 0 and b0 be selected as to from
orthogonal basis by satisfying the condition as
a0  2 and b0  1 . This requirement invites us to use
multiresolution analysis (MRA), which is also known as
multiresolution wavelet method (MWM). In this method
original signal xt  is decomposed into different scales
resolutions
and
the
mother
wavelet
function

ψt   2  d n  2t  n  is
To formulate a numerical model for transient signal’s
waveform generation, the resulting transient voltage is
considered to be consisted of two components, normal
power system voltage, and additive transient voltage.
Therefore, following relation is implemented to generate
power system transient event waveform [6-7].
VResultingwaveform  VPower system  VTransient (4)
4.1.1.1 Oscillatory Transient
dt  


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chosen
with
V  sin(2ft )  u.a. sin(2f osct1 ).e ( decay factor).t1 (5)
The second term in Eq. (4.2) models the transient
oscillations having frequency fosc. The transient element is
superimposed on the supply voltage at any required instant
of time with the help of unit step function u as defined in Eq.
(6).
1 : t if t - t 1  0
u
0 : t if t - t 1  0
4.1.1.2 IMPULSIVE TRANSIENT
V  sin(2f t )  [u.a.(e t1  e  t1 )]
Table 1: IEEE standards for power system transient signals
S. No.
Categories
1
Transients
1.1
n  
 t   2  c n 2t  n  known as scaling function, where
n  
d n and c n are squared sum able sequences [21-22].
3. METHODOLOGY
4.1
Transient Waveform Generation
MATLAB software is used to simulate the power system
transient disturbances numerically.
4.1.1
Numerical models
(7)
4.1.2
Standard adopted for transient signal generation
All the simulations comply with the IEEE 1159 standard
guidelines in terms of magnitude and spectral contents like
rise, fall and duration.
Table 1 provides information regarding typical spectral
content, duration, and magnitude where appropriate for each
category of electromagnetic phenomena [1-3].
4.1.3
Matlab implementation of numerical models
A user friendly GUI is designed in the Layout editor and
programmed in M-file editor of MATLAB. The GUI is
shown in Fig 2. By this GUI user can first simulate the
transient signals with an option of variety of spectral
contents.
function

(6)
Impulsive
1.1.1
Nanosecond
1.1.2
Microsecond
1.1.3
Millisecond
1.2.1
Oscillatory
Low
frequency
Medium
1.2
1.2.2
1.2.3
frequency
High
frequency
Typical
spectral
content
Typical
duration
5-ns
rise
1- s rise
0.1-ms
rise
<50 ns
50 ns–1
ms
>1 ms
---
<5 kHz
5–500
kHz
0.5–
0.3–50
ms
20μs
0–4 pu
5μs
0–4 pu
5MHz
Typical
voltage
magnitude
-----
0–8 pu
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3.3
CLASSIFICATION OF PSTD BY FEATURE
EXTRACTION
To extract the features from various coefficients of wavelet
transform of the signals at different levels, the total number
of decomposition levels is the first thing to know.
The number of levels is found by Eq. (8)
J  log 2 N
Fig. 02: Graphical User Interface (GUI)
The basic functions of the GUI are:
 Generation of transient signals
 Saving the generated signals on hard drive
 Performing time frequency analysis by initializing the
wavelet toolbox
4.2 SUITABLE
WAVELET
FUNCTION
FOR
DETECTION OF PSTD
Four wavelet functions are found to be frequently used in the
area of power system transients, namely; db4, coif4, bior3.1
and sym5. These mostly used wavelet functions are assessed
on the basis of perfect reconstruction algorithm, for their
suitability for accurate detection of PSTD. As shown in Fig.
(3), in this algorithm the signal after reconstruction is
compared with the signal before decomposition in order to
investigate the suitability of wavelet function to be used.
(8)
Where the signals to be decomposed has ‘N’ samples.
The following features are calculated at different
decomposition levels to classify the transients.
 Percentage Energy at each decomposition level.
 RMS value of detail components of wavelet coefficient
at maximum decomposition level.
4.3.1
Energy feature vector
The energy of the signal can be related to the energy in each
of the wavelet resolution levels by ‘Parseval’s theorem’, as
shown in Eq. (9)

2
2

2
j 0 k  
(9)
The energy carried by a signal at some decomposition
level is found by calculating the norm of the wavelet
coefficient obtained at that level. The feature vector of
energy at a decomposition level is formed as shown below
in Eq. (10)
ESignal  [ cAJ
2
2
cDJ
2
2
cD1
2
2
........... cDJ 1
(10)
2 T
2
]
Where

cAJ
1/ 2
2
 [  cA J ]
2
 [  cD J ]
2
K - 

cD J
Fig. 03: Decomposition and reconstruction by filters of wavelet
transform

f (t ) dt  k  a(k )    d j (k )
1/ 2
2
K - 
4.3.2
RMS feature vector
Root mean square value of voltage can be calculated as:
T
Vrms 
1 2
v dt 
T 0
E Signal
T
(11)
Since the energy at some decomposition level is nothing but
the norm of wavelet coefficient at that level, the Eq. (10) can
be again utilized to find the RMS values of individual
wavelet coefficients.
Fig. 04: Steps involved in selection of suitable wavelet function
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Fig. 5: Some selected waveforms from simulations
5
RESULTS
5.1 SIMULATION RESULTS
A total of 32 signals have been simulated for various
categories of power system transient, sixteen of which are
impulsive and remaining are oscillatory.
5.2
SUITABLE WAVELET FUNCTION
The Table 2 shows points that are observed related to
performance of each wavelet function.
5.3
RESULTS OF DETECTION OF PSTD BY
MRA
Multiresolution analysis of simulated PSTD signals reveals
sub-band frequency coefficients along with the time
information of the disturbances also. These coefficients are
outputs of high pass filters of wavelet transform, give an
indication of PSTD.
As shown in fig 6, a high frequency element is successfully
extracted from the signal ‘s’ at first level ‘d 1’ but its
localization in time is not good, i.e. the end point of
disturbance is not prominent. Furthermore, MRA gives a
wide range of coefficient values, and at the time of transient
event peak coefficient value is
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Fig. 6
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: Low frequency oscillatory transient and five levels of
decomposition by sym5
observed at a particular level, which is sufficient to detect
the PSTD, as in fig 6 it is observed at third level ‘d3’.
Similarly, at higher decomposition levels, the value of detail
coefficient becomes unusable due to very poor localization
of high frequency elements, i.e. high frequency elements
starts spreading over entire time axis, as in fig 6 it is
observed in 5th level ‘d5’. Table 3 presents the required
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sampling frequency to detect different categories of PSTD
with the help of MRA of DWT.
All categories of PSTD with different sampling rates are
simulated and hence when analyzed by MRA algorithm,
they produce wavelet transform sub-band of different
frequency ranges. The required sampling rate for detection is
found by Nyquist theorem.
5.4
CLASSIFICATION
BY
EXTRACED
FEATURES
The RMS and percent energy values of each PSTD are
plotted, considering RMS and percent energy values in yaxis and number of decomposition levels in x-axis.
5.4.1
Low frequency oscillatory transient
The simulated PSTD of this kind ranges from 500 Hz to
4250 Hz. The RMS and energy feature vectors are extracted
and plotted across the 11
levels as shown in fig 7, 8 There is a noticeable trend
common to all low frequency transient signals from 5 th level
to 11th level. For low frequency transient signal we get the
highest RMS and percentage energy values at 7th level.
5.4.2
Medium frequency oscillatory transient
The simulated PSTD of this kind ranges from 50000 Hz to
450000 Hz. The RMS and energy feature vectors are
extracted and plotted across the 14 levels as shown in fig 9,
10. There is a noticeable trend common to all medium
frequency transient signals from 11th to 14th level. For
medium frequency transient signal we get the highest RMS
and percent energy values at 14th level.
Table 2: Reconstruction performance of different wavelet functions
Impulsive
Wavelet Function
Minimum error
Db4
2.22×10
Bior3.1
0
Coif4
2.22×10
Sym5
0
-16
-16
Oscillatory
Better reconstruction results
Minimum error
Medium/Fast
3.33×10
Fast
0
Medium/Fast
8.88×10
Slow/Medium/Fast
0
-16
Better reconstruction results
Medium/Fast
Medium/Fast
-16
Medium/Fast
Slow/Medium/ Fast
Table 3: Detection results by MRA of various categories of PSTD
Transient Type
Oscillatory Transient
Impulsive transient
Highest value coefficient
Frequency range
Sampling frequency for detection
Low
d3
0.62kHz – 1.25kHz
2.5kHz
Medium
d3
62.5kHz – 0.125MHz
0.25MHz
High
d1
1MHz-2MHz
4MHz
Milliseconds
d2
1.25KHz-2.5KHz
5kHz
Microseconds
d3
(0.31 – 0.62)MHz
1.24MHz
Nanoseconds
d3
15.62MHz – 31.2 MHz
62.5MHz
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Fig 7:
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RMS Pattern for signal with low frequency oscillatory
transients
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Fig. 10: Energy Pattern for signal with medium frequency
oscillatory transients
5.4.3
High frequency oscillatory transient
The simulated PSTD of this kind ranges from 500000 Hz to
2750000 Hz. The RMS and energy feature vectors are
extracted and plotted across the 16 levels as shown in fig 11,
12. There is a noticeable trend common to all high frequency
transient signals from 13th to 16th level. For high frequency
transient signals we get the highest RMS and percent energy
values at 16th level.
Fig 8:
Energy Pattern for signal with low frequency oscillatory
transients
Fig. 11: RMS Pattern for signal with high frequency oscillatory
transients
Fig. 9: RMS Pattern for signal with medium frequency oscillatory
transients
Fig. 12: Energy Pattern for signal with high frequency oscillatory
transients
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5.4.4
Millisecond impulsive transient
The simulated PSTD of this kind ranges from rise time of
0.1 msec and duration of 6 msec to a rise time of 1 msec
with duration of 2 msec. The RMS and energy feature
vectors are extracted and plotted across the 11 levels as
shown in fig 13, 14. There is a noticeable trend common to
all millisecond impulsive transient signals from 5th to 11th
levels. For millisecond transient signals we get the highest
RMS and percent energy values at 11th level and 7th level
respectively.
Fig. 15: RMS Pattern for signal with microsecond impulsive
transients
Fig. 13: RMS Pattern for signal with milliseconds impulsive
transients
Fig. 16: Energy Pattern for signal with microsecond impulsive
transients
vectors are extracted and plotted across the 14 levels as
shown in fig 17, 18. There is a noticeable trend common to
all microsecond impulsive transient signals from 6 th to 16th
level. For microsecond transient signals we get the highest
RMS and percent energy values at 15th level.
Fig. 14: Energy Pattern for signal with milliseconds impulsive
transients
5.4.5
Microsecond impulsive transient
The simulated PSTD of this kind ranges from rise time of
100 µsec and duration of 700 µsec to a rise time of 1 µsec
with duration of 50 µsec. The RMS and energy feature
vectors are extracted and plotted across the 14 levels as
shown in fig 15, 16. There is a noticeable trend common to
all microsecond impulsive transient signals from 7th to 14th
level. For microsecond transient signals we get the highest
RMS and percent energy values at 14th level and 11th level
respectively.
5.4.6
Nanosecond impulsive transient
The simulated PSTD of this kind ranges from rise time of
100 µsec and duration of 700 µsec to a rise time of 1 µsec
with duration of 50 µsec. The RMS and energy feature
Fig. 17: RMS Pattern for signal with Nanoseconds impulsive
transients
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Fig. 18: Energy Pattern for signal with nanoseconds impulsive
transients
6.
CONCLUSIONS
This research work presents investigation of wavelet
analysis to detect and classify power system transients. The
investigation relies on MRA algorithm of DWT, in which
transient signals are decomposed into various timefrequency resolution levels. First of all the PSTD have been
simulated using numerical models, complying with all the
spectral constraints given by IEEE-1159 standards. Before
applying MRA, the question about selecting a particular
wavelet function (mother wavelet) for the wavelet analysis
has been taken into consideration. A suitable wavelet
function is then used in MRA of DWT, in which the
transient disturbance in the power system voltage is detected
at a certain resolution level in the detail component of DWT
coefficient, where as approximate component of DWT
coefficient shows low frequency power system voltage. This
research work reveals the fact that for identifying the type of
transient disturbance the values of a certain extracted feature
at a particular resolution level is not sufficient to distinguish
one kind of disturbance from the other.
Numerical models assist the validation of power transient
events characterization tool in the proposed method, and can
be utilized to contribute to the development of power
transient waveform simulation. Proposed MATLAB based
GUI of Power transient simulator is flexible because it can
be used to generate and save the PSTD data. The following
points are noted in the simulation of PSTD:
 By using step-function, the occurrence of transient
disturbances can be manipulated over the entire length
of the power system voltage.
 Numerical model for oscillatory transient consists of
single exponential for controlling the decay time of
ringing/oscillations , while that of impulsive transient
contains double exponential; one for manipulating the
rise of impulse, and second for deciding the decaying
duration of the impulse.
 For fast transient of duration in microseconds and
nanoseconds, increasing the simulation period increases
the number of samples (data points) and hence increases
the computational complexity and time of wavelet
analysis then after.
Symlet 5 (Sym5) is found to be more adequate as a mother
wavelet for detection of power system transients. A perfect
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reconstruction criterion of filters is adopted to compare db4,
coif, bior3.1, and sym5 wavelet functions, because wavelet
transformation is considered as passing the given signal
from a set of conjugate quadrature mirror high pass and low
pass filters. Sym5 gives least error between RMS values of
signal before decomposition and after reconstruction. The
following points are noted in this investigation:
 Db4 is efficient in medium and high frequency
disturbances.
 Bior3.1 is efficient in high frequency disturbances.
 Coiflet is efficient in medium and high frequency
disturbances.
 Sym5 is efficient in low medium and high frequency
disturbances.
For the accurate detection of PST, the frequency bands of
each decomposed coefficient of DWT are crucial. Keeping
in view, the magnitude and localization of disturbance
captured at a certain detail coefficient of DWT, it is
concluded that:
 Waveforms of level 1 to 3 detail coefficients can be
analyzed for detection of PSTD.
 To detect oscillatory transient of low frequency to high
frequency range, a sampling frequency of 2.5 kHz – 4
MHz is required respectively.
 To detect impulsive transient of milliseconds duration to
nanoseconds duration range, a sampling frequency of 5
kHz – 62.5 MHz is required respectively.
For classification of PSTD, energy and RMS values of
signals are calculated at various resolution levels and
following conclusive points are noted:
 For identifying the type of transient disturbance the
values of a certain extracted feature at a particular
resolution level is not sufficient to distinguish one kind
of disturbance from the other.
 From energy and RMS profile it is evident that for
classification of PSTD, the level 5 to 16 can be used.
REFERENCES
[1] M. H. J. Bollen, IEEE Industry Applications Society,
IEEE Power Electronics Society, and IEEE Power
Engineering Society, “Understanding Power Quality
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