Automatic
C
lassification of
S
ingle
P
ower
Q
uality
D
isturbances based on
M
odified
S

T
ransform
and Artificial Intelligence
Heman Shamachurn, Robert T. F. Ah King
*
and Harry C. S. Rughooputh
Department of Electrical and Electronic Engineering, Faculty of Engin
eering, University of Mauritius
,
Reduit, Mauritius
*
Email: r.ahking@uom.ac.mu
Abstract
This work
present
s
an
approach to
automatic power quality (PQ) disturbance
classification
based on a modified
version of S

transform
(ST)
and
Artificial Intelligence (AI
).
The proposed method involves time

frequency
analysis, feature extraction and pattern classification.
It is shown
here
that ST can be used
to provide
suitable
screen outputs
for visual classification of PQ disturbance signals.
ST
is an advanced signal p
rocessing technique
which
is used to extract essential features of PQ disturbance signals.
These features are then used to
train a
Probabilistic Neural Network (PNN)
classifier.
Eight classes
of PQ dis
turbance signals and
the normal
signal
are considered f
or classification.
The simulation results show that a combination of
modified
ST and PNN
provides an effective classification of PQ
distu
rbance signals
.
Keywords
: Power Quality, Disturbance Classification, S

Transform, Probabilistic Neural Network.
1.
Intr
oduction
Electric PQ
is a term that has
gained
much importance over the years
.
The
increasing use of sensitive and non

linear loads
, the deregulation of utilities,
and the
increased interconnections in power systems has led to
an
increased need to solve an
d prevent PQ problems (Kennedy, 2000)
.
Dugan et al. (1996, p.3) defined PQ as
“Any power problem manifested in voltage, current, or frequency deviations that results in failure or
malfunction of customer equipment.”
PQ
results in equipment malfunction and
premature failure and has
financial consequences
on
utilities, their customers and suppliers of load equipment
(Dugan, 2004)
.
Thus,
m
onitoring PQ
has become a necessity
fo
r
fast
identification and correction
PQ
problems
.
Signal processing
methods for PQ an
alysis comprise Fourier Transform (FT),
Park’s V
ector Approach, Kalman filters
and time

frequency analysis methods such as
Short Time Fou
rier Transform (STFT), Wavelet Transform (
WT)
,
and
Stockwell Transform (ST).
The traditional method
s
for PQ monitoring
are costly and inefficient.
As such
v
arious methods for
automatic
recognition and
classification of commonly occu
r
ring PQ disturbances such as
voltage sag,
swell,
transients and harmonics
involving the use of
signal processing techniques, power systems
kno
wledge and Artificial Intelligence (AI)
have
been proposed over the years
:
ST
and fuzzy logic
was
by
Chikuri and Dash
(2004)
,
HS

Transform and
Radial Basis Function Neural Network (RBFNN)
by Samantaray
et al. (2006)
, ST
and fuzzy neural network by
Dash et
al. (2007)
,
a combination of Windowed Discrete Fourier
Transform (WDFT) and ST
with Adaptive
Neuro

Fuzzy Inference System (ANFIS)
by Nguyen and Liao
(2009)
, Support Vector Regression (SVM) and
ST by
Faisal et al. (2009),
ST and RBFNN was proposed by
Jayasr
ee et al. (
2009),
ST
and
PNN by
Mishra et al. (2007a,
2007b
)
,
ST and
Support Vector Machine (SVM)
by
Panigrahi et al. (2008
)
, Panigrahi et al. (2009)
and eventually
ST and
Multi

layer Perceptrons Neural
Network
(MLPNN)
by
Uyar et al. (2008
)
.
Moreover,
Ngu
yen and Liao (2009)
mentioned that Pradhan et al.
(2006), He and Starzyk (2006) and
Santoso et al. (2000) worked on a
combination of
WT
and neural network
(NN)
systems.
Mishra et al.
(2008
a, 2008b
) cited that Gaing (2004)
used wavelets and PNN to classify
seven
types of PQ events.
Stationary signals
(George, 2009)
are those whose statistical properties
do not change with time while the
characteristics
of non

stationary signals vary with time
.
FT determines the spectral components of a signal
without providi
ng the times at which the different frequency components occurred.
FT produces a time

averaged spectrum which is
inadequate to track the changes in signal magnitude, frequency and phase with
time
.
Thus, non

stationary signals are better processed in the ti
me

frequency plane by using techniques like
STFT,
WT
and ST
.
For
non

stationary signals
like PQ disturbance signals
, where the frequency
content
change with time, STFT
has got a fixed resolution over the time

frequency plane and
does not recognize the sign
al dynamics properly
due to the limitation of a fixed window width
chosen a priory
(
Chikuri and Dash 2004;
Samantaray et al.
2006
)
.
WT
is incapable of providing
accurate results under noise conditions
(Samantaray et al. 2006). Moreover,
if
an
important d
isturbance
frequency component is not
precisely extracted by the WT,
the classification ac
curacy
using AI may be limited (Chikuri and Dash, 2004).
Also, there is an absence of phase information
in WT
and
t
he time

scale plots
provided by WT are difficult to
interpret
(George, 2009).
Therefore,
ST
which combines the
elements of STFT and WT
and
which performs multiresolution time

frequency analysis is a be
tter candidate for
PQ analysis.
2.
Standard
S

Transform
(ST)
ST
,
developed
by Stockwell
(
1996
)
, is a
power
ful time

frequency
m
u
lti

resolution
analysis signal processing
tool
.
ST provides a time

frequency representation (TFR) with a frequency dependent resolution.
The window
width varies inversely with frequency and thus,
ST produces high time resolution at hig
h frequency and
high
frequency resolution at low frequency.
It can be viewed as
a frequency dependent STFT or a phase corrected
WT (
George, 2009).
The PQ dis
turbance signals are sampled before processing by
Discrete ST
(DST)
.
Details
about the derivation o
f
Continuous
ST
(CST) and DST
can be found in
Stockwell et al. (1996
)
. The standard ST
of a signal
is defined as
(1)
Where th
e window function is a scalable
Gaussian Window
(2)
And
(3)
Hence,
(4)
2.1
Th
e Generalized ST
In
the standard ST, the Gaussian window has no parameter to allow its width in time or frequency to be
adjusted. Hence, Pinnegar and Mansinha (
2003
)
introduced a generalized ST which has a greater control over
the window function.
The gene
ralized ST is given by
(5)
Where
the window is
function of the ST and
denotes the set of parameters that determine the shape
and
property of
the
window function
. ST windows must
satisfy
the normalized condition
(6)
2.1
The Modified ST
As one example
,
(cited in
George 2009
)
the
Gaussian window
as modified by
Mansinha et al.
, 1997
is
(6)
Where
is
the only parameter in
and it controls
the width of the window.
Geo
rge (2009)
retain
ed the Gaussian window function, but
modified the
parameter
so that it becomes a linear
fu
nction of freque
ncy
(7)
Where
is the slope and
is the
intercept. The resolution in time and in frequency
depends on both
and
.
The modified ST then becomes
(8)
Where
,
the window
function of the modified ST
is
(9)
And this window also satisfies the normalization condition
(10)
Hence,
(11)
Fig.
1. Variation of window width
with
If
is too small,
frequency resolution degrades at higher frequencies and
if
is too large, the time resolution
degrade at lower frequencies. There is an optimum value of
for which
the trade

off between frequency and
time resolutions
is reduced.
Typical values (George, 2009)
of
is
0.25

0.
5 and
is 0.5

3.
The value of
and
need to be selected depending on the type and nature of the signal under
consideration
.
In this work it was
found that
and
provides accurate results fo
r PQ classification despite the fact that
i
s an
extreme value.
The PQ disturbance signal can be stated in a discrete form
(Mishra et al., 2008)
as
where
is the
sampling interval
and
is the time index
,
where N is the total n
umber of samples in the
signal.
The Discrete FT (DFT)
of
is
(12)
Where
and the
inverse DFT is
(13)
The ST of a discrete time series is given by Stockwell et al. (1996)
(14)
Where
=
is the Gaussian function and
By takin
g
the
advantage of the efficiency of the FFT and convolution theorem
, the following steps are adapted
for computing the DST
(cited in
Mishra et al., 2008)
:
1)
Perform the DFT of the sampled signal
(with
points and sampling
interval
) to get
using the FFT routine.
This is computed only once.
2)
Calculate the localizing Gaussian
for the required
frequency
.
3)
Shift the spectrum
to
for the frequency n/NT.
4)
Multipl
y
by
to get
5)
Inverse FT of
to give the row of
corresponding to the
frequency
.
6)
Repeat steps 3, 4, and 5 until all the rows of
corresponding to all discrete freq
uencies
have
been defined.
The above mentioned steps also apply to the modified
ST
. The
output
of the modified ST is
an
matrix
called the S

matrix whose rows
corresponds to frequency and columns to time
index
.
Thus, each row is
called
a
voice
of frequency
and each column is called
local spectra
as it gives all the frequency components present at
that time index (Stockwell, 1999).
Each element of the S

matrix is complex valued.
2.3
Performance of modified ST by visual inspection
ST can be used to recognize PQ disturbances by visual inspection (Reddy et al.,2004).
From the
S

matrix, the S

Transform Amplitude (STA) matrix can be obtained by finding the
absolute value of
each element of the S

matrix.
(15)
From
the STA, the
time

frequency, time

amplitude and
frequency

amplitude
plots can easily be obtained
. These
plots enable the detection, localization and visual classification of PQ disturbances.
In this
work, eight single
commonly occurring
PQ disturbances namely voltage sag, swell, notch, transient,
flicker, spike,
harmonics and interruptions
as well as the pure si
nusoidal waveform are considered.
The
following plots show some of the essential informatio
n that can be obtained from
the modified ST.
In Figures 2

10(a), the disturbance signals are shown
for eight cycles
.
Per unit values are considered in this work.
Figures 2

10(b) show the time

frequency contours
for each class of disturbance signals
, clearl
y providing a clue about the
type of disturbance that occurred.
Figure 2(b) shows that the S

contours are straight lines and therefore indicate
clearly that there are no harmonics present in the waveform.
Figure 3(b) shows that the S contours clearly revea
l
a 100% voltage drop
during approximately the same time interval as the disturbance waveform in the time
domain.
The color of the plot and the color bar are of great importance for the visualization purpose.
Figure 4(b)
shows that
the S

contours have a ma
gnitude reduction during the disturbance similar to the voltage sag signal in
the time

domain.
Figure 5(b) shows that the S

contours clearly
depict
an increase in magnitude during the
disturbance, and this is supported by the time

domain signal.
Figures 6

9(b)
clearly
show the presence of other
frequency components
.
Figure 10(b) shows an amplitude variation resembling a voltage flicker in the time
domain.
Figures 2

10(c) show the
maximum magnitude of ST at each time index
.
For example, in figures 3
, 4, 5
(c)
, it
can be concluded that the disturbances occurred are
momentary interruptions,
instantaneous sag and swells
respectively.
Figures 2

10(d) show
the amplitude spectrum of the signals.
For example,
figure
6(d) clearly
shows three peaks, implying that
th
e d
isturbance signal is a voltag
e harmonic.
The
highest frequency considered
being
9
50Hz which occurs during an oscillatory transient,
a sampling frequency of 3200Hz is used
in
accordance with Shannon’s Theorem.
The signals considered have a fundamental frequ
ency component
of
50Hz.
The frequencies have been normalized with respect to the sampling frequency, i.e.
.
Therefore, each cycle being represented by 64 points, 8 cycles of signals
corresponding to
512 points are considered.
Fig.
2
.
Pure
sine wave and its feature waveforms
Fig.
3
. Momentary Interruption and its feature waveforms
Fig.4
. Instantaneous voltage sag and its feature waveforms
Fig.5
. Instantaneous voltage swell and its feature waveforms
Fig.6. Voltage harmonics and its fe
ature waveforms
Fig.7
. Voltage Notch and its feature waveforms
Fig.8.
Voltage spike and its feature waveforms
Fig.9. Low frequency oscillatory transient and its feature waveforms
Fig.10. Voltage flicker
3.
S

Transform based
Feature Extraction
and P
NN
3.1
Feature Extraction
The features required for
PQ disturbance classification are
extracted from the S

matrix and STA

matrix
.
The
features extracted are used to train a pattern recognition neural network and test it.
“Many features such as
amplitude,
slope (or gradient) of amplitude, time of occurrence, mean, standard deviation and energy of the
transformed signal are widely used for proper classification” (Mishra et al., 2008
(b)
, p.281
).
In this work,
five
features are extracted and they are
(Mishra e
t al. 2008
a, 2008b
; Panigrahi et al.
,
2008; Uyar et al.,
2008
;
Jayashree et al., 2009
):
1)
Standard deviation (SD) of the data set
comprising
the elements
of maximum magnitude fro
m each
column of the STA

matrix,
i.e. the SD of the ST

amplitude v/s time index
contour.
2)
Energy of the data set comprising the elements of maximum magnitude fro
m each column of the
STA

matrix, i.e. energy of the ST

amplitude v/s time index contour.
3)
SD of the
data set consisting of the elements of
maximum magnitude from each row of the
STA

matrix
, i.e.
SD of the amplitude spectrum.
4)
SD of the
stationary
phase contour
.
5)
Mean of the data set constituting the elements of maximum magnitude from each row of the STA

matrix
, i.e. mean of the amplitude spectrum.
A large gap between input
feature
values to the PNN may tend to affect the performance of the PNN.
Thus, all the feature values are normalized as shown below so that the features take values between 0
and 1.
(16)
Where
i
s the
normalized feature value,
is the
maximum value of a given feature set
and
is
any value in the same
feature
set
where
.
Considering 150 feature vectors
wi
th 100
used
for training and 50
used
for testin
g for each type of
disturbance,
the following
ten
3

D maps
and 25 2

D maps
are presented to show the suitability of the
extracted features for classification.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
Fig.10.
(a)

(j)
3

D plots of the 5 features used for the classification
, (k) 2

D plots
3.2
Classification of PQ disturbances using Probabilistic Neural Network
Artificial
Neural Network (ANN) is made up of many interconnected neurons.
Present
ed by Specht in 1988,
Probabilistic neural networks
(PNN)
are forward feed networks built with three layers
a
s shown in figure
11
(Wang et al., 2009)
.
A probabilistic neural network is a pattern classiﬁcation network based on the classical
Bayes classiﬁer, which is statistically an optimal classiﬁer that seeks to minimize the risk of misclassiﬁcations.
The PNN was developed
to construct the probability d
ensity functions
(PDF) required by Bayes’ theory. Since
the network architecture’s learning speed is very fast and it is indispensable to have tolerance of making
information mistake,
it
is
suitable for signal classification in real

time
(Wang et al., 2009
).
They train quickly
since the training is done in one pass of each training vector, rather than several.
P
robabilistic neural networks
estimate the probability density function for each
class based on the training samples using Parzen or a similar
probab
ility density function. This is calculated for each test vector. Usually a spherical Gaussian basis function
is used, although many other functions work equally well. Vectors must be normalized prior to input into the
network. There is an input unit for ea
ch dimension in the vector. The input layer is fully connected to the hidden
layer. The hidden layer has a
n
ode for each classification. Each hidden node calculates the dot product of the
input vector with a test vector,
subtracts 1 from it and divides the
result by the standard deviation
s
quared. The
output layer has a node for each pattern classi
fi
cation. The sum for each hidden node is sent to the output layer
and the highest values wins. The Probabilistic neural network trains immediately but execution
time is slow and
it requires a large amoun
t of space in memory. It
only works for data
classification
. The training set must be a
thorough representation of the data. Probabilistic neural networks handle data that has points outside the
norm
better than ot
her neural nets.
Mathematical details for Bayes
theory and Parzen estimator
are provided in Bishop
(1995).
Fig.11.
Architecture of PNN
4.
Simulation and results
4.1
Waveform generation
The simulations were carried out In MATLAB 2008a environment.
The w
aveforms were
generated by
parametric equations
in such a way so that they closely
resemble
real waveforms occurring
on the power
system.
The equations for the disturbance signals are
provided by Uyar (2008) and the parameters were
varied
within the ranges
specified by the IEEE
standard 1159
(
IEEE
1995)
.
Table 1 provides the waveform equati
ons
and their parameter’s range
.
The values for the times corr
espond to the number of points. The waveforms are
represented for a length of 8 cycles
with
64 points per cy
c
le
.
Considering a fundamental frequency of 50Hz,
64
points
thus
corresponds to 20msec. As such, the number of points corresponding to
the
duration of
the
events
could be
calculated before simulating the waveforms.
4.2
PNN Classification
The classification
results for standard ST as well as modified ST are
sh
own in the
tables
2, 3, 4, and 5.
The
parameters of the waveforms were kept in the same ranges for all the different cases.
About two third of the
data generated were used for training and the remaining
one third was used for testing, implying that out of 150
waveforms generated, 100 feature vectors were used to train the PNN and 50 vectors were used or testing.
Similarly out of 300 PQ disturbance signals generated, 200 were used for training and 100 for
testing the
proposed system. Thus, the data used during the testing phase were not used during training.
From Tables 2 and 4, standard ST provided an overall accuracy of only 92% for 150 waveforms generated as
compared to modified ST which produced an ov
erall accuracy of 97.33% for exactly the same waveforms
generated. Similarly, from Tables 3 and 5, doubling the number of data for training as well as for testing
produced an overall accuracy of only 95.33% for standard ST while modified ST provided an ove
rall accuracy
of 99.44% for exactly the same waveforms generated. Thus, in both cases, modified ST provided more
interesting results than standard ST.
These presented accuracy values clearly reveal that modified ST is more accurate in the extraction of the
same
features as compared to standard ST for PQ analysis.
To support the 3

D feature plots, the performance of PNN with different features was tested and the results are
shown in Table 6 for 150 waveforms generated. As can be observed, PNN works satisfact
orily even with three
or four features are used.
Table 1: Signal equations and variations of parameters
PQ disturbance
Class Symbol
Equation
Parameter range
Swell
C1
Sag
C2
Spike
C3
Notch
C4
Interruption
C5
Flicker
C6
Harmonics
C7
Transient
C8
Sine
C9
PNN classification results for
standard
ST
Table 2
:
PNN classification with 1
00 trai
n
samples and 5
0 test samples
PQ disturbances
Number of
disturbances
Number of cases
correctly identified
Number of cases
misclassified
Correct
identification
(%)
Swell
50
50
0
100
Sag
50
37
13
74
Spike
50
50
0
100
Notch
50
50
0
100
Interruption
50
43
7
86
Flicker
50
34
16
68
Harmonics
50
50
0
100
Transient
50
50
0
100
Sine
50
50
0
100
Sum
450
414
36
92
.00
Table 3
: PNN classification with 200 train samples and 100 test samples
PQ disturbances
Number of
disturbances
Number of cases
correctly ide
ntified
Number of cases
misclassified
Correct
identification
(%)
Swell
100
100
0
100
Sag
100
89
11
89
Spike
100
100
0
100
Notch
100
100
0
100
Interruption
100
86
14
86
Flicker
100
83
17
83
Harmonics
100
100
0
100
Transient
100
100
0
100
Sine
100
1
00
0
100
Sum
900
858
42
95.33
PNN classification results for modified ST
Table
4
: PNN classification with 100 train samples and 50 test samples
PQ disturbances
Number of
disturbances
Number of cases
correctly identified
Number of cases
misclassified
Co
rrect
identification
(%)
Swell
50
46
4
92.00
Sag
50
46
4
92.00
Spike
50
50
0
100
Notch
50
50
0
100
Interruption
50
48
2
96.00
Flicker
50
48
2
96.00
Harmonics
50
50
0
100
Transient
50
50
0
100
Sine
50
50
0
100
Sum
450
438
12
97.33
Table 5
: PNN c
lassification with 200 train samples and 100 test samples
PQ disturbances
Number of
disturbances
Number of cases
correctly identified
Number of cases
misclassified
Correct
identification
(%)
Swell
100
100
0
100
Sag
100
100
0
100
Spike
100
100
0
100
Not
ch
100
100
0
100
Interruption
100
95
5
95
Flicker
100
100
0
100
Harmonics
100
100
0
100
Transient
100
100
0
100
Sine
100
100
0
100
Sum
900
895
5
99.44
Table 6:
Comparison of accuracies for different combinations of features
Feature Combination
Ove
rall Classification Accuracy (%)
F1, F2, F3
91.56
F1, F2, F4
88.22
F1, F2, F5
92
F2, F3, F4
91.11
F2, F3, F5
86.67
F3, F4, F5
80
F1, F3, F4
87.78
F1, F3, F5
84.89
F2, F4, F5
91.56
F1, F4, F5
70.89
F1, F2, F3, F4
96.22
F1, F2, F3, F5
92.67
F1,
F2, F4, F5
96.67
F1, F3, F4, F5
88.22
F2, F3, F4, F5
94.22
F1, F2, F3, F4, F5
97.33
5.
Conclusion
In this work, an ST

based PNN classification process is proposed for the automatic classification
of PQ
disturbances.
The proposed system performs essen
tially four tasks: waveform generation, feature extraction,
fe
ature normalization and
training as well as testing of PNN.
It has been shown that the 5
simple
features
extracted are efficient to allow a PNN distinguish clearly between different classes of P
Q events.
The PNN has
got a very fast training and testing time
; 0.6 sec for 150 data generated and
2.35
sec
for 300 data generated
for
modified ST.
Thus it is suitable for an online
PQ
disturbance
classification
system
where a very large number of
wavefor
ms can be captured and analysed
in a very short time interval. Eventually, it can be concluded that
modified ST alone can provide very good results for PQ analysis.
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