Classification of power quality disturbances
using time-frequency ambiguity plane and
neural networks
Min Wang
IEEE Student Member
Piotr Ochenkowski
Alexander Mamishev
IEEE Member
SEAL (Sensors, Energy, and Automation Laboratory)
Department of Electrical Engineering
University of Washington
Box 352500, Seattle, WA 98195
Abstract – Identification and classification of voltage and current
disturbances in power systems is an important task in power
system monitoring and protection, This paper presents a new
approach for classifying the events that represent or lead to the
degradation of power quality. The concept of ambiguity plane
together with modified Fisher’s Discriminant Ratio Kernel is used
A neural network with feedforward
for feature extraction.
structure is chosen as the classifier. The results of extensive
simulations confirm the feasibility of the proposed algorithm. This
novel combination of methods shows promise for further
development of a fully automated power quality monitoring
system. The potential of developing a more powerful fuzzy
classification method based on this algorithm is also discussed.
Keywords
-- Power Quality Disturbances,
Classification,
Ambiguity Plane, Modified Fisher’s Discriminant Ratio Kernel,
Neural Network
I. INTRODUCTION
of highly sensitive
computerized
The proliferation
equipment places increasingly more stringent demands on
the quality of electric power supplied to the customer. Not
only must the power be supplied without interruption, but
also the voltage and current waveforms must maintain
nearly sinusoidal shape, constant frequency, and amplitude
at all times to ensure continuous equipment operation. Low
power quality can cause serious problems for the affected
loads, such as short lifetime, malfunctions, instabilities,
interruption, and etc. The key reason for our increasingly
keen interests in power quality lies in the great economic
value directly associated with those disturbances.
Poor power quality is normally characterized by the
presence of disturbances such as harmonics distortion,
capacitor switching, high impedance faults, transformer
inrush currents, lightning pulses, and motor starting
transients. In order to improve the quality of service,
electrical utilities must provide real-time monitoring
systems that are able to identify the signatures of different
events and make proper decisions for switching and
maintenance.
Existing methods for detection and classification of power
system disturbances are laborious since they are primary
based on visual inspection of waveforms [1]. Recent
advances in signal processing and pattern recognition have
led to the development of several new classification
approaches, which are based on discrete wavelet transform,
multiresolution
signal
decomposition,
polynomial
approximation,
and bispectra analysis [1-4]. The new
method presented in this paper is based on employing timefrequency ambiguity plane, modified Fisher’s Discriminant
Ratio Kernel, and artificial neural network. It shows very
good classification
performance
on 6 categories of
simulated disturbance signals. This novel combination of
methods also brings up the possibility of discriminating
transient type disturbances automatically and accurately.
II. POWERQUALITYDISTURBANCECLASSES
There are various types of events that can degrade power
quality, which makes the identification problems often
elusive and difficult. In this paper we develop our
classification algorithm based on disturbance events from
six major categories, which are harmonics, capacitor high
frequency switching, capacitor low frequency switching,
voltage sudden sag, voltage gradual sag, and voltage swell,
Figure 1 shows the example waveforms of these events,
Figure 1(a) represents the waveform affected by harmonics.
To some, harmonics distortion is still the most significant
power quality problem [5]. Because of the increased
popularity of electronic and other non-linear loads, such as
adjustable-speed
drives, arc furnaces, and induction
0-7803-7031-7/01/$10.00 (C) 2001 IEEE
furnaces, perfect sinusoid waveforms quite often become
distorted in this way. Current harmonics causes increased
losses in the customer’s and utility’s power system
components, while voltage harmonics affects not only
sensitive electronic loads but also electric motors and
capacitor banks.
“Ir’Lrum
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———–—r
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20
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III. BACKGROUND
In pattern recognition applications, features are often
extracted some form of time-frequency representations
(TFRs). Among the class of correlative TFRs, ambiguity
plane plays an important role. It has been used extensively
in the fields
of radar,
sonar, radio
astronomy,
communications and optics [7],
80
~w
-20
Figure 1(f) shows the signal affected by voltage swell.
Swells are often caused by faults, capacitor ener.gization,
and load switching.
(a)
2°
0
can cause the whole plant to shut down. These industries
plastics,
include
petrochemicals,
textiles,
paper,
semiconductor, and rubber [6].
60
80
..—–~
60
‘-” 40--”Time(ms)
80
Figure 1. Sample disturbance
signals: a) harmonics, b) fast
switching transient, c) slow switching transient, d) sudden voltage
sag, e) graduate voltage sag, f) voltage swell.
Transients caused by capacitor switching are one of the
most common sources of degradation in utility systems [5].
Two sample signals that correspond to capacitor high and
low frequency switching are shown on Figure l(b) and 1(c),
respectively. The frequency of a transient is determined by
capacitance and inductance of the system. Although
capacitors have the drawback of producing the oscillatory
transients when switched, they are still used in power
systems to correct the power factor.
A momentary voltage dip that lasts for a few seconds or less
is classified as voltage sag. It is caused by faults on the
power system or the start of large loads, such as motors,
Figure 1(d) shows an example of voltage sudden sag. Also a
voltage gradual decay sag signal is given on Figure 1(e).
Process industry equipment can be particularly susceptible
to problems with voltage sags because the equipment is
interconnected and a trip of any component in the process
To achieve good classification results, the feature extraction
scheme should be based on some TFR that is optimal for the
classification task. The spectrogram is traditionally used
with an underground assumption that a spectrogram is
appropriate for the classification task. This assumption
might not be appropriate and potentially degrade the
classification performance, because the objective of a
spectrogram is to describe the energy density of a signal
simultaneously in time and frequency accurately, while the
goal for classification is generating a TFR that maximizes
the separability of TFRs from different classes. So it is
desirable to design TFRs that specifically emphasize the
differences between classes [8]. Gillespie and Atlas showed
that a certain class of quadratic TFRs always provides best
classification performance [9]. This class of ambiguity
plane based TFRs discard any redundant information and
retain only that information
which is essential for
classification. Gillespie and Atlas have successfully applied
this technique on tool-wear monitoring and radar transmitter
identification [9, 10].
Here in our algorithm for classifying power quality
disturbances, the concept of ambiguity plane together with
modified Fisher’s Discriminant Ratio Kernel is used for
feature extraction, essentially looking for certain form of
TFR that fits the classification goal best. A neural network
with feed forward structure is chosen as the classifier.
IV. CLASSIFICATION
ALGORITHM
The diagram in Figure 2 shows the complete classification
algorithm we proposed. (The transient signal picture in this
figure is taken from the website of Electrotek Inc.)
In our study, each voltage signal to be identified consists of
five cycles of voltage waveform sampled 256 times per
added randomly generated noise.
cycle, with up to 0.5
The target of the feature extraction is to generate a N-point
feature vector from the original 1280-point voltage signal.
The feature vectors are the inputs of the neural network for
classification.
0-7803-7031-7/01/$10.00 (C) 2001 IEEE
YO
m
!R[Yt,r] = x * [n]x[((l’z
+ T))N ]
(1)
If we express an example voltage signal as,
V=[Vl V2 V3... V2Vn_lvfi]i]
(2)
The instantaneous autocorrelation function (IAF) will be,
2
Instantaneous
Autocorrelation Function
2
h
IAF =
v,
r+
V2.
V,.
V3
V2V4
V3
V2.
v
““”
‘n-1
‘n
‘n
‘n–1
‘1
‘n
n
Z=()
‘‘1
(3)
‘2
‘=2
“.’.
. .
1
v.-,
V,
v
n–l
‘r=l
.
~l.vn
v.-,
[ v, V.
2
2
“’”
.
v,
Time-Frequency
Ambiguity Plane
V2
v.-,
.
v.–)
Vu-2
v“
V*.2
vfl
vn.,
~=~–z
1
‘r=~-l
In our case, n is equal to 160.
I
1
Modified Fisher’s
Discriminant Ratio
Kernel
I
I
C. Ambiguity Plane
(a)
*
F==l
I
Figure 2.
I
Classification Algorithm
(c)
A. Lowpass Filtering and Resampling
As depicted in Figure 2, the first step is to pass the original
signal through a Lowpass filter and resample the signal with
a downsampling rate 8. By downsampling, the signal
dimension has been reduced greatly, which leads to a
dramatic reduction of the computation complexity. In
addition, electrical noise has also been attenuated. Using
Lowpass filter is to avoid aliasing during downsampling.
After this step, a new 160-point signal that keeps the
signature of the original signal is obtained.
B. Instantaneous Autocorrelation
Function
Now we calculate the instantaneous autocorrelation
R/n, t]for the signal x,
function
(e)
Figure 3. Ambiguity Planes for Different PQ Events
a) Harmonics; b) Capacitor fast switching; c) Capacitor slow
switching; d) Sudden sag; e) Gradual sag decay; f,) Swell.
Here the horizontal and vertical axes are discrete Doppler q
and lag ~.
The time-frequency
ambiguity plane of the original
can be obtained by taking inverse Fourier transform
IAF as follows,
0-7803-7031-7/01/$10.00 (C) 2001 IEEE
signal
on the
~~w,
Iz(i)[q,z]--x(’)
Here q and ~ are discrete Doppler and lag respectively.
Ambiguity plane is a very important concept of our feature
extraction process. We will construct the TFR optimal for
our classification task by smoothing the ambiguity plane
with a class-dependant kernel. Here the dimension of
ambiguity plane is 160*160. Basically we will directly
select N points from this plane as our feature vector.
A4FDK[q,r] = ‘“ ‘“
(5)
~(a(’’[q,zq)’
,=1
Where,
dc)[q, z]=+~1
A;;)[q, r] 12 -1 Z(’) [q, r] 1’
D. Modified Fisher’s Discriminant Ratio Kernel
There is a distinct ambiguity plane for each disturbance
signal. We want to determine N locations from the 160*160
ambiguity plane, such that values in these locations are very
similar for signals from the same class, while they vary
significantly for signals from different classes.
(y+ \
wzl
ap31
A.
ap12 ““ ““”
q)22
ap32
.
.
. .
.
. ...
wl,,,-l
Wjn-l
ap3,n_,
43,,
Here A:) [q, ~] is the value at a particular
apn-,,2
~”
““
W}l+l+
belongs to class c. ~(’)[q, r]
point in ~ and r on
to example signal y, that
is the average
value at a
particular point for a class i. The weight for distance
between class i and class j is ~,, . There are normally two or
three classes that are really similar. We specify big weights
for their distances to make them easier to discriminate. And
cd’)[q, T] is the estimated standard deviation at a particular
point for the 1 training examples from class c. MFDR is
maximized when the separation between means of the class
clusters is large, and the within class variance is small, The
MFDR designed by a large number of training examples is
still a 160*160 plane. We transform it into a binary matrix
by replacing the maximum N points with 1‘s and the other
points with 0’s.
By multiplying the binary form of MFDR with certain
signal’s ambiguity plane, we will find N feature points for
this signal. We put them into a vector as its feature vector,
as shown in Figure 4 (We take N = 6 here).
E, Classification By Neural Network
W2[,
w3.
“.”.
atkl,l
(6)
r-1
the ambiguity plane corresponding
Before we describe how to select features vectors, let’s look
at the ambiguity planes corresponding to different classes of
signals in Figure 3 and get some intuitions about it. We find
the ambiguity planes corresponding to different classes
show different patterns. The ambiguity plane has very
desirable properties
for classification.
An individual
location in this plane captures “global” information about
the time frequency structure of the signal. Points on the axis
q=O result in time-frequency structure that is stationary in
time. Similarly, points on the ~=0 axis correspond to a timefrequency structure that is stationary in frequency [7].
[q,z] 1’
aPn-l,n
We choose an artificial neural network (ANN) with a 3layered feedforward structure as the classifier. The inputs of
the ANN are features extracted by the scheme presented in
the last section. The outputs of the ANN determine which
class the disturbance event belongs to.
V. NMULATIONEXPERIMENTS
The classification experiments were done with power
quality disturbance signals simulated by MatLab. The
classes include harmonics,
capacitor
fast switching
transients, capacitor slow switching transients, voltage
sudden sag, voltage gradual decay sag, and voltage swell.
‘4=
Figure 4. Apply MFDK onto AP to get feature vector
We design and use a Modified Fisher’s Discriminant
Ratio
kernel (MFDR) to get those N locations. Here the MFDR
kernel is designed by Z training example signals from each
class with the equation as follows,
Each example signal consists of five cycles of a voltage
waveform sampled 256 times per cycle, with up to 0.570
added randomly generated noise. We use totally 6000
examples (1000 examples per class) to design the modified
Fisher’s Discriminant
Kernel and train the 3-layer
feedforward neural network. Totally 1800 examples (300
examples per class) are used to test the classification
method. All the example events are generated in a random
way. The starting time, duration, and distortion magnitude
of each training and testing event are all random. This
0-7803-7031-7/01/$10.00 (C) 2001 IEEE
makes the testing results more reliable, because none of
these are fixed for real power system disturbance events.
Substantial computer simulations have been conducted to
optimize the feature extraction algorithm and neural
network structure. The input layer of ANN has 13 neurons,
hidden layer 8 neurons, and output layer 6 neurons. The 13
inputs to the ANN include 12 feature points extracted from
the ambiguity plane and one bias. The 6-point output vector
determines which category the disturbance event belongs to.
The results for a 6-class classification are competitive and
shown in table I.
Class
l,HM
Correct
(%)
I Ml I M2 I M3
(%)
(%)
(%)
0
1
99
2,CHST
0
2
98
3.CLST
0
9.7
85.3
4.VSS
0
0
1.3
98
5.VGD
0
0
0
100
6,VSW
0
0
0
100
Table I. Results of a 6-class PQ event
M41M5)M6
(%)
(%)
(%)
0
0
4.3
0
0
0
0
0.7
0
0
-
0
0
0
0.7
0
classification
(Here
HM-harmonics,
CHST-capacitor
high frequency
switching transients, CLST-capacitor
low frequency switching
transients, VSS-voltage sudden sag, VSW-voltage swell; Correctpercentage of correct identification,
Mi-percentage of mistake
identification to class i,)
VI. FuzzY CLASSIFICATION
APPROACH
We have proposed a new classification algorithm for power
quality disturbance signals. However, the philosophy behind
this algorithm is to take in a disturbance signal and classify
the signal to one of the disturbance classes. We call it the
crisp classification approach. That means we always assume
that there is only one type of disturbance in a 5-cycle
waveform.
In some cases, however, there are multiple types of
disturbances happening at the same time, The crisp
classification strategy does not work very well for these
combined events, Based on the same feature extraction
scheme, we are exploring a fuzzy classification approach
that will provide us more accurate, more comprehensive,
and more useful information for the power system under our
monitoring. The basic idea is as follows. For a given piece
of 5-cycle disturbance waveform, we will give a soft
evaluation of the disturbance component in this waveform.
Specifically, we will determine the grade (i.e. membership
function) corresponding to each disturbance class. The
grade of an arbitrary class A will show us to what extent the
waveform includes the disturbance of class A. For example,
if we input a 5-cycle disturbance waveform, we may get an
output like this -- “Harmonics 2.5, Capacitor fast switching
7.5, Capacitor slow switching 5.5, Sudden sag 0.5, Sag
gradual decay 3, Swell 0.5”. Thus we know this short
duration disturbance is mostly capacitor switching event.
But it also has slight harmonics and sag gradual decay
components. This strategy serves better the goal of
monitoring, analyzing, and evaluating the power quality of a
given power system. We are exploring the details of the
fuzzy classification idea. Multiple neural networks and
statistical signal processing techniques are employed.
VII.
CONCLUSIONS
Identification and classification of voltage and current
disturbances in power systems is an important task in power
system monitoring and protection, A new classification
algorithm for power quality disturbances have been
proposed and tested in this paper. This algorithm is based
on time-frequency
ambiguity plane concept, Fisher’s
Discriminant kernel, and artificial neural network. It shows
very high classification performance in the simulation
experiments. This novel combination of methods shows
promise for future development
of fully automated
monitoring systems with classification ability. The potential
of developing a fuzzy classification method based on this
algorithm is also discussed, Power system monitoring
becomes more powerful by including the ability of
classifying disturbed signals automatically.
VIII.
This project
Technologies
Washington.
ACKNOWLEDGEMENTS
is supported by the Advanced Power
University
of
(APT)
Center
at the
The APT
ESCA, CESI,
Electric Corp.
LG
Center
Industrial
is supported
Systems
by ALSTOM
and
Mitsubishi
IX. REFERENCES
[1]
S. Santoso, E. J. Powers, W. M. Grady, A. C.
Parsons, “Power quality disturbance waveform
recognition using wavelet-based neural classifier. I.
Theoretical foundation,” IEEE Transactions on
Power Delivery, Vol. 15, pp. 222-228, Jan. 2000.
[2]
B. Perunicic, M. Mallini, Z. Wang, Y. Liu, “Power
quality disturbance detection and classification
using wavelets and artificial neural networks, ” 8th
International
Conference
On Harmonics and
Quali~ of Power Proceedings, Vol. 1, pp. 77-82,
1998.
[3]
A. M. Gaoudaj M, M, A, Salama, M. R, Sultan, A,
Y. Chikhani,
“Power quality detection and
classification using wavelet-multiresolution signal
IEEE Transactions On Power
decomposition,”
Delivery, Vol. 144, pp. 1469-1476, Oct. 1999.
[4]
J. S. Lee, C. H. Lee, J. O. Kim, S. W. Namj
“Classification of power quality disturbances using
approximation
and
orthogonal
polynomial
0-7803-7031-7/01/$10.00 (C) 2001 IEEE
bispectra,” Electronics Letters,
1522-1524, Aug. 1997.
Vol. 33 18, pp.
X. BIOGRAPHIES
[5]
R. C. Dugan, Electrical Power Systems Quality,
New York: McGraw-Hill, 1996.
[6]
D. Mueller, M, McGranaghan, “Effects of voltage
process
industry
applications,”
sags
in
nct,elcctrotek. corn/pGnet/main/backg
rnd/tutorial/sag/paper/paper.htm.
[7]
F. Hlawatsch, G. F. Boudreaux-Bartels,
“Linear
and
quadratic
time-frequency
signal
IEEE
Processing
representations, ”
Signal
Magazine, Apr. 1992.
[8]
J. McLaughlin, J. Droppo, L. Atlas, “Classdependent, discrete time-frequency distributions
via
theory,”
IEEE
International
operator
Conference on Acoustics, Speech, and Signal
Processing, 1997.
[9]
B. W. Gillespie, L.E. Atlas, “Data-Driven TimeFrequency Classification Techniques Applied To
Tool-Wear Monitoring,” Proceedings of the 2000
IEEE ICASSP, 2000.
[10]
B. W. Gillespie, L.E. Atlas, “Optimization of Time
and Frequency Resolution for Radar Transmitter
Identification,” Proceedings of the 1999 IEEE
ICASSP, vol.3, pp. 1341-4, 1999.
Min Wang received his B.S. degree from Tsinghua University,
Beijing, China, in 1999. Currently, he is pursuing his M.S. degree
in the Department of Electrical Engineering,
University of
Washington. He also works as a research assistant with Professor
Alexander Mamishev. His research and study interests include
signal processing, power quality, and software engineering. He is
a student member of IEEE and the PES.
Piotr Ochenkowski received his B.S. and M.S. degrees from
the University of Washington in 1999 and 2000, respectively, both
in Electrical Engineering. His area of interests included Digital
Signal Processing for communications application. He is currently
with Boeing Space and Communication Group as an embedded
software engineer.
Alexander Mamishev received an equivalent of B.S. degree
from the Kiev Polytechnic Institute, Ukraine, in 1992, M.S. degree
from Texas A&M University in 1994, and a Ph. D, degree from
MIT in 1999, all in electrical engineering. Currently he is an
Assistant Professor and Director of SEAL (Sensors, Energy, and
Automation
Laboratory)
in the Department
of Electrical
Engineering, University of Washington, Seattle. Dr. Mamishev is
an author of about 40 journal and conference papers, and one
book chapter. His research interests include sensor design and
integration,
dielectrometry,
electric
power
and electrical
electromagnetic,
insulation,
bioengineering,
MEMS,
optimization, and inverse problem theory.
He serves as a
reviewer for IEEE Transactions on Power Delivery and IEEE
Transactions on Dielectrics and Electrical Insulation.
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