th
The 5 Student Conference on Research and Development –SCOReD 2007
11-12 December 2007, Malaysia
Detection and Classification of Power Quality
Disturbances Using Time-Frequency Analysis
Technique
Abdul Rahim Abdullah, Ahmad Zuri Sha’ameri, Abd Rahim Mat Sidek and
Mohammad Razman Shaari
Abstract--This paper presents the detection and classifications
of power quality disturbances using time-frequency signal
analysis. The method used is based on the pattern recognition
approach. It consists of parameter estimation followed
classification. Based on the spectrogram time-frequency analysis,
a set of signal parameters are estimated as input to a classifier
network. The power quality events that are analyzed are swell,
sag, interruption, harmonic, interharmonic, transient, notching
and normal voltage. The parameter estimation is characterized
by voltage signal in rms per unit, waveform distortion, harmonic
distortion and interharmonic distortion. A rule based system is
developed to detect and classify the various types of power
quality disturbances. The system has been tested with 100 data
for each power quality event at SNR from 0dB to 50dB to verify
its performance. The results show that the system gives 100
percent accuracy of power quality signals at 30dB of SNR.
Index Terms-- Spectrogram, pattern classification, power
quality, time-frequency analysis, Signal to Noise Ratio (SNR).
W
I. INTRODUCTION
ith the rapid advance in industrial applications that rely
on sophisticated electronic devices, a demand for power
quality and reliability has become a great concern because the
smallest interruption of power quality event can cause
equipment failure, data loss and loss revenue. Voltage
disturbances are the most frequent cause of a broad range of
disruption in industrial and commercial power supply systems.
These disturbances often referred to as power quality
problems, which significantly affect many industries [1].
Major causes of power quality related revenue losses are
interrupted manufacturing processes and computer network
downtime.
The examples abound in semiconductor industry, chemical
industry, automobile industry, paper manufacturing, and ecommerce. A report by Consortium for Electric Infrastructure
to Support a Digital Society (CEIDS) [2] shows that the U.S.
economy is losing between $104 billion and $164 billion a
year due to outages and another $15 billion to $24 billion due
to power quality phenomena. The conventional methods
Abdul Rahim Abdullah is a student at the Faculty of Electrical
Engineering, Universiti Teknologi Malaysia - (email: [email protected])
Ahmad Zuri Sha’ameri is with the Faculty of Electrical Engineering,
Universiti Teknologi Malaysia - (email: [email protected])
currently used by utilities for power quality monitoring are
primarily based on visual inspection of voltage and current
waveforms [2]. Therefore, a highly automated monitoring
software and hardware is needed in order to provide adequate
coverage of the entire system, understand the causes of these
disturbances, resolve existing problems, and predict future
problems.
This paper looks at the use of time-frequency
representation in the interpretation of power quality
disturbances. Spectrogram distribution is performed to detect
and classify the power quality events. By using its timefrequency characteristics, each of the disturbance signal’s
features is distinguished
for the classification of the
respective types of power quality problems.
II. POWER QUALITY PHENOMENA
The term power quality refers to a wide variety of
electromagnetic phenomena that characterize the voltage and
current at a given time and at a given location on the power
system. According to the International Electrotechnical
Commission (IEC), electromagnetic phenomena are classified
into several groups as shown in Table 1 [3], [4]. This paper
focused on seven types of power quality problems: voltage
swell, voltage sag, interruption, harmonic, interharmonic,
transient and notching.
A. Voltage Swell
A swell is defined as an increase in rms voltage at the
power frequency for durations from 0.5 cycles to 1 minute.
Typical magnitudes are between 1.1 and 1.8pu.
B. Voltage Sag
Voltage sag is a decrease to between 0.1 to 0.9pu in rms
voltage at the power frequency for duration of 0.5 cycles to 1
minute.
C. Interruption
An interruption occurs when the supply voltage or load
current decreases to less than 0.1pu for a period of time not
exceeding 1 minute.
D. Harmonic
Harmonics are sinusoidal voltages or currents having
frequencies that are integer multiples of the frequency at
which the supply system is designed to operate (50Hz for
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Malaysia). Harmonics combine with the fundamental voltage
or current and produce waveform distortion [10].
transient if frequency component less than 5 kHz and duration
from 0.3 to 50 ms.
E. Interharmonics
Interharmonics are signal components at frequencies that are
not integer multiples of the power system frequency. For
example, a 190 Hz component in a 50 Hz system [1]. To
correctly measure an interharmonic component requires a
measurement window which is also an integer multiple of the
interharmonic cycle length.
G. Notching
Notching is a switching or other disturbance of the normal
power voltage waveform, lasting less than 0.5 cycles which is
initially of opposite polarity than the waveform and is thus
subtracted from the normal waveform in terms of the peak
value of the disturbance voltage. This includes complete loss
of voltage for up to 0.5 cycles [4]. Notching is caused by the
normal operation of power electronics devices when current is
commutated from one phase to another.
TABLE I
CATEGORIES AND TYPICAL CHARACTERISTICS OF POWER SYSTEM
ELECTROMAGNETIC PHENOMENA
III.
Typical
spectral
content
Typical
duration
1.0 Transients
1.1 Impulsive
1.2 Nanosecond
1.3 Millsecond
5 ns rise
1 ms rise
0.1 ms rise
< 50 ns
50 ns-1 ms
> 1 ms
1.2 Oscillatory
1.2.1 Low frequency
1.2.2 Medium frequency
1.2.3 High frequency
< 5 kHz
5-500 kHz
0.5-5 MHz
0.3-50 ms
20 ms
5 ms
0-4 pu
0-8 pu
0-4 pu
0.5-30 cycles
0.5-30 cycles
0.1-0.9 pu
1.1-1.8 pu
0.5 cycles -3
s
30 cycles-3 s
30 cycles-3 s
< 0.1 pu
0.1-0.9 pu
1.1-1.4 pu
Categories
2.0 Short duration variations
2.1 Instantaneous
2.1.1 Sag
2.1.2 Swell
2.2 Momentary
2.2.1 Interruption
2.2.2 Sag
2.2.3 Swell
2.3 Temporary
2.3.1 Interruption
2.3.2 Sag
2.3.3 Swell
3 s-1 min
3 s-1 min
3 s-1 min
3.0 Long duration variations
3.1 Interruption, sustained
3.2 Undervoltages
3.3 Overvoltages
4.0 Voltage imbalance
0.0 pu
0.8-0.9 pu
1.1-1.2 pu
steady state
0.5-2%
0-0.1%
0-20%
0-2%
0.1-7%
broad-band
steady state
steady state
steady state
steady state
steady state
6.0 Voltage fluctuations
< 25 Hz
Intermittent
7.0 Power frequency variations
< 0.1 pu
0.1-0.9 pu
1.1-1.2 pu
> 1 min
> 1 min
> 1 min
5.0 Waveform distortion
5.1 DC offset
5.2 Harmonics
5.3 Interharmonics
5.4 Notching
5.5 Noise
0-100th H
0-6 kHz
Typical voltage
magnitude
0-1%
< 10 s
F. Transient
The term transient has been used in the analysis of power
system variations for a long time. Transient can be classified
into two categories: impulse and oscillatory. Impulsive
transients are normally characterized by their rise and decay
times. These phenomena can also be described by their
spectral content. For example, a 1.2/50µs 2000V impulsive
transient rises to its peak value of 2000 V in 1.2 us and decays
to half its peak value in 50µs. Oscillatory transients with a
primary frequency component greater than 500 kHz and a
typical duration measured in microseconds are considered
high-frequency oscillatory transient. A transient with a
primary frequency component between 5 and 500 kHz with
duration measured in tens microseconds is termed a mediumfrequency transient and considered as a low-frequency
TIME-FREQUENCY ANALYSIS
Time-frequency analysis is motivated by the analysis of
non-stationary signals whose spectral characteristics change in
time [4]. Spectrogram is one of the time-frequency analysis
techniques and it represents a three-dimensional plot of the
signal energy with respect to time and frequency [9]. The
spectrogram is the result of calculating the frequency spectrum
of windowed frames of a compound signal. Usually,
spectrograms are calculated from the time signal using the
short-time Fourier transform (STFT). In practice, the STFT is
computed at a finite set of discrete values of ω . Moreover,
due to the finite length of the windowed sequence, the STFT is
accurately represented by its frequency sample as long as the
number of frequency samples is greater than the window
length [6], [7]. For an arbitrary discrete-time waveform of
length N, the spectrogram time-frequency representation is
calculated as follows:
1
Px (n, k ) =
M
M −1
∑ x(m) w(m − n) e
−j
m =0
2πkm
M
2
(1)
0 ≤ n ≤ N − 1 and 0 ≤ k ≤ M − 1
x(n) is the input signal, w(n) is the window function, N is the
number of samples and M is the windows length.
Analysis results based on the spectrogram were made by
simulation using MATLAB. Fig. 1 and 2 show the simulation
results for swell and transient signal. For each time-frequency
distribution, the corresponding time series data and spectrum
are provided. Fig. 1a and 2a are the time series data that
generates corresponding time-frequency distribution function
in Fig. 1b and 2b. The amplitude of the distribution is
expressed as the color intensity of the plot. The highest power
is represent as red color while the lowest power by blue color.
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IV.
Power Quality Signal
1.5
1
Amplitude(Vpu)
0.5
0
-0.5
-1
-1.5
0
50
100
150
200
Time (msec)
250
300
350
Fig. 1a. Swell voltage in time representation
Normal voltage
Swell
SYSTEM DESIGN
The time-frequency distribution function is used as a tool to
extract the most salient features that represent the power
quality phenomenon [5]. Before the application of this
transform, a pre-processing of the signals is required to
normalize them, because they are collected from various
voltage levels in the distribution system. The time-frequency
distribution is employed to generate a set of parameters which
are used in classification process. The parameters are voltage
(rms), harmonic distortion, interharmonic distortion, wave
distortion and voltage pulse. The flow chart for analysis and
classification of the power quality events is depicted in Fig. 3.
Normal voltage
Fig. 1b. Swell voltage in time-frequency representation
Power Quality Signal
1.5
Amplitude (Vpu)
1
0.5
0
-0.5
-1
0
50
100
150
200
Time (msec)
250
300
350
Fig. 2a. Transient voltage in time representation
Fig. 3. Flow chart for analysis and classification of power quality events.
The rms (root mean square) is one of the parameters of the
signal. From the spectrogram time-frequency distribution (1),
the rms can be defined as below;
Transient
X (n) rms =
Normal voltage
M −1
∑ P (n, k )
x
k =0
0 ≤ n ≤ N −1
0 ≤ k ≤ M −1
Fig. 2b. Transient voltage in time-frequency representation
N is the number of samples and M is the windows length.
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(2)
Information of the harmonic distortion is needed especially
to detect harmonic in power quality signal. When the
waveform is nonsinusoidal but periodic with a period of one
cycle (of the power system frequency, about 50 or 60 Hz),
current and voltage waveforms can be decomposed into a sum
of harmonic components [3]. The equation below is used to
detect maximum power of harmonic distortion (HD)
frequency component.
PHD (n) = max[Px (n, h )]
h
0 ≤ n ≤ N −1
(3)
th
2 ≤ h ≤ 100 harmonic
Besides that, voltage often contains interharmonic
components that are not a multiple integer of the power
system frequency [10]. For example, a 50 Hz signal distorted
with a 155 Hz interharmonic. So, the parameter of
interharmonic is required to classify interharmonic signal. The
maximum power of interharmonic distortion (IhD) frequency
component is defined as below.
PIhD (n) = max[Px (n, h )]
h
0 ≤ n ≤ N −1
(4)
th
h interharmonic
Rule 8: if WD=No and Vpu < 1.1pu and Vrms > 0.9pu
THEN Normal
VI. RESULTS
Analysis results were made based on the several parameter
estimations obtained from the time-frequency distribution of
power quality signals. The parameter estimations are voltage
in rms per unit (Vrmspu), maximum value of waveform
distortion (WD) frequency component, maximum value of
harmonic distortion (HD) frequency component and maximum
value of interharmonic distortion (IhD) frequency component.
Fig. 4 and 5 show the transient signal and its respective
analysis results. The transient voltage can be characterized by
a voltage pulse in the Vrmspu as shown in Fig. 5a, while Fig.
5b indicates that the transient frequency components exist in
the WD signal. The frequency components consist of
harmonic HD and IhD as shown in Fig. 5c and Fig. 5d.
Fig. 6 and 7 show the harmonic signal and its parameter
estimation results. From the Vrmspu, the magnitude level of
voltage signal increases more than its threshold value as
shown in Fig. 7a. Its frequency distortion is observed in the
WD in Fig. 7b. The harmonic signal is characterized by the
presents of HD in Fig. 7c and IhD is zero as shown in Fig. 7d.
From the characterization, a simple rule base system can be
developed for the classification process of power quality
events.
Waveform distortion includes all deviations of the voltage
waveform from the ideal sine wave [8]. The distortion can
consists all the following possibilities: harmonic and,
interharmonic distortion. The following equation is used to
present the maximum power of waveform distortion (WD)
frequency component in a power quality signal.
if PHD (n) >= PIhD (n)
= PIhD (n)
if PIhD (n) >= PHD (n)
1
Amplitude(Vpu)
PWD (n) = PHD (n)
Power Quality Signal
1.5
(5)
0.5
0
-0.5
0 ≤ n ≤ N −1
-1
0
50
100
V. RULE-BASE FOR CLASSIFICATION OF POWER QUALITY
300
350
a) Voltage Signal (Vrms pu)
Vrms pu
1.0004
1.0002
1
0.9998
0
50
150
200
250
Time (msec)
b) Maximum Value of WD Frequency Component
-4
4
x 10
100
300
3
Power
Rule 1: if Vpu < 0.1pu and Duration > 10ms THEN
Interruption
Rule 2: if Vpu ≥0.1pu and Vpu ≤0.9pu and Duration > 10ms
THEN Sag
Rule 3: if Vpu ≥1.1pu and Vpu ≤1.4pu and Duration > 10ms
THEN Swell
Rule 4: if HD=Yes and IhD=No and Vpu > VThreshold
THEN Harmonic
Rule 5: if HD=No and IhD=Yes and Vpu > VThreshold
THEN Interharmonic
Rule 6: if WD=Yes and Vpu < VThreshold
THEN Notching
Rule 7: if WD=Yes and Vpulse=1
THEN Transient
250
Fig. 4. Transient signal
EVENTS
To formulate rules, strict threshold values are set by a
comprehensive analysis and comparison of derived features
from each category of power quality event. The rules based to
classify the power quality events are listed below:
150
200
Time (msec)
2
1
0
0
500
1000
1500
2000
Time (msec)
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2500
3000
3500
-4
c) Maximum Value of HD Frequency Component
1
0
0
500
-4
4
x 10
1000
1500
2000
2500
3000
Time (msec)
d) Maximum Value of IhD Frequency Component
-4
c) Maximum Value of HD Frequency Component
10
8
6
3500
0
500
0
500
1000
1500
2000
2500
3000
Time (msec)
d) Maximum Value of IhD Frequency Component
3500
1
0.5
Power
3
Power
x 10
12
Power
Power
x 10
2
0
-0.5
1
0
0
500
1000
1500
2000
Time (msec)
2500
3000
-1
3500
Fig. 5. Analysis results for transient.
1000
1500
2000
Time (msec)
2500
3000
3500
Fig. 7. Analysis results for harmonic
In order to measure the distortion amount independent from
the scale of the original signal, we used the signal to noise
ratio, SNR which is defined as
Power Quality Signal
1.5
1
Amplitude(Vpu)
0.5
SNRdB = 10 log
0
Px
Pnoise
(6)
-0.5
-1
-1.5
0
50
100
150
200
Time (msec )
250
300
350
Fig. 6. Harmonic signal
a) Voltage Signal (Vrms pu)
1.0019
Vrms pu
1.0019
1.0019
1.0019
1.0019
12
0
x 10
50
150
200
250
Time (msec)
b) Maximum Value of WD Frequency Component
-4
100
300
where Px and Pnoise corresponds to the original signal and noise
power [8]. The SNR measurement is important because
normally the power quality signals are having noise.
By simulation, the system has been tested by using 100 data
of each power quality event. The SNR measurement is tested
from 0 to 50dB. Fig. 8 shows the performance evaluation of
this system in terms of the accuracy the data versus SNR for
each power quality events. The result shows the system gives
the correct classification for all power quality events starting
point at 30dB. Voltage swell gives the best performance
amongst the other events. It gives 100% accuracy at SNR of
2.5dB. For a normal event, it gives the 100% accuracy at the
noise level SNR of 27.5dB.
Swell
100
Normal
8
6
0
500
1000
1500
2000
Time (msec)
2500
3000
3500
Number of Data
Power
120
10
Sag
80
Notching
60
Interharmonic
40
Harmonic
Interruption
Transient
Normal
Swell
Sag
Interruption
Harmonic
Transient
Notching
Interharmonic
20
25
27
.5
30
32
.5
35
37
.5
40
42
.5
45
47
.5
50
5
7.
5
10
12
.5
15
17
.5
20
22
.5
2.
5
0
0
SNR dB
Fig. 8. SNR for each power quality event
VII. CONCLUSION
In short, the detection and classification system is developed
by using the spectrogram time-frequency analysis technique. It
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performs the extraction of the required time information, rms
measurement, harmonic, interharmonic and waveform
distortion of power quality signals. The performance of the
rule-based classifier is demonstrated and verified by a set of
simulated disturbance waveforms. In addition, each power
quality signals have been tested by using 100 data with SNR
from 0dB to 50dB. The result is the power quality signals give
100 percent accuracy at 30dB of SNR.
VIII. REFERENCES
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H.J.Bollen, Y.H. Gu, Signal Processing of Power Quality Disturbances.
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[2] A. Kusko, T. Thompson, Power Quality in Electrical Systems. McGraw
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