Automatic Classification of Single Power Quality Disturbances based on Modified S-

jamaicacooperativeAI and Robotics

Oct 17, 2013 (3 years and 9 months ago)

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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.


References


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-
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-
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CHIKURI, M.V. and DASH, P.K., 2004.
Multiresolution S
-
Transform
-
Based Fuzzy Recognition System for
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