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Detection and Classification of Multiple
Power-Quality Disturbances With
Wavelet Multiclass SVM
Whei-Min Lin, Member, IEEE, Chien-Hsien Wu, Chia-Hung Lin, and Fu-Sheng Cheng
Abstract—This paper presents an integrated model for recognizing power-quality disturbances (PQD) using a novel wavelet
multiclass support vector machine (WMSVM). The so-called
support vector machine (SVM) is an effective classification tool.
It is deemed to process binary classification problems. This paper
combined linear SVM and the disturbances-versus-normal approach to form the multiclass SVM which is capable of processing
multiple classification problems. Various disturbance events were
tested for WMSVM and the wavelet-based multilayer-perceptron
neural network was used for comparison. A simplified network
architecture and shortened processing time can be seen for
WMSVM.
Index Terms—Disturbances-versus-normal (DVN) approach,
power-quality disturbances (PQD), support vector machine
(SVM), wavelet multiclass support vector machine (WMSVM).
I. INTRODUCTION
T
HE POWER-QUALITY (PQ) study has become a more
important subject lately. Harmonics, voltage swell,
voltage sag, and the power interruption could downgrade the
service quality. In recent years, the high-speed railway (HSR)
and massive rapid transit (MRT) system have been rapidly
developed, with the applications of widespread semiconductor
technologies in the autotraction system. The harmonic distortion level worsens due to the increased use of electronic
equipment and nonlinear loads. To ensure the PQ, power disturbances detection becomes important as well to further detect
the location and disturbance types.
Traditionally, PQ was judged by visual inspection of the
disturbance waveforms, so the engineer’s knowledge plays
a critical role. As always, the PQ engineer is inundated with
an enormous amount of data for inspection. It is desirable
to develop automatic methods for detecting, identifying, and
analyzing various disturbances [1]–[4]. Fast Fourier transformation (FFT) [2] has been applied to the steady-state
phenomenon but short-time duration disturbances require the
Manuscript received November 30, 2006; revised November 27, 2007. First
published July 9, 2008; current version published September 24, 2008. Paper
no. TPWRD-00780-2006.
W.-M. Lin and C.-H. Wu are with the Department of Electrical Engineering,
National Sun Yat-Sen University, Kaohsiung 80424, Taiwan, R.O.C. (e-mail:
[email protected]).
C.-H. Lin is with the Department of Electrical Engineering, Kao-Yuan University, Kaohsiung 821, Taiwan, R.O.C. (e-mail: [email protected]).
F.-S. Cheng is with the Department of Electrical Engineering, Cheng-Shiu
University, Kaohsiung 833, Taiwan, R.O.C. (e-mail: [email protected].
tw).
Digital Object Identifier 10.1109/TPWRD.2008.923463
short-time Fourier transformer (STFT) to aid in the analysis.
The choices for sizes of the time window affect the frequency
and time resolution when using STFT. In order to improve
these limitations, wavelet theory [5]–[7] has been applied to
model several short-term events. It allows for the convenient
reconstruction of short duration with a tool to examine the
effects of the short-term transient effects on the power system.
For this reason, a method based on wavelet transformation
(WT) for PQ analysis has been presented [1]. This method uses
multiresolution signal decomposition and reconstruction by
means of the discrete wavelet transform (DWT).
In order to improve the processing time for detection, [3]
and [4] applied a multilayer-perceptron neural network (MLP)
to detect the harmonics. MLP is well known for its learning
and recognition ability. However, MLP has difficulties in determining a proper architecture, such as the number of hidden
layers and nodes. Training MLP is time-consuming and very
slow without a guaranteed global minimum [8]. In [3], a partial connecting network was proposed to detect harmonics, but
the training process is still very slow. Applying MLP to detect
tasks from distorted waves, it is necessary to sample an input
amplitude for each input node of MLP. Accuracy will be affected by the limited number of samples. Considering these limitations, the support vector machine (SVM) [9]–[13] with strong
classification capability was studied and proposed in this paper.
The standard SVM often adopts the one-versus-one (OVO) approach or one-versus-rest (OVR) approach to solve the multiclass problems [11], [13], but these multiclass SVM (MSVM)
methods may have problems with the network size, heuristic solution scheme, or complicated training data preparation. To improve the structure, we present the disturbances-versus-normal
(DVN) approach for MSVM and then integrate WT to form the
wavelet multiclass support vector machine (WMSVM). First,
WT is used to extract the characteristic features from disturbances, and then MSVM performs on the multiclass problems,
such as PQD. With selected locations for measurements, the
proposed WMSVM can not only identify the type but also the
location of a disturbance. The WMSVM can simplify the design architecture and reduce the processing time for detection.
Furthermore, the simple architecture can be effectively used for
multiple disturbances detection, which is not easily attainable
with other methods. A sample power system will be studied for
example. Computer simulations will show test results and the
comparisons with wavelet MLP (WMLP).
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 4, OCTOBER 2008
for non-SVs. Using the SVs,
margin can be calculated as
and
of Fig. 1 and (2), the
(4)
is equivalent to minimizing
Maximizing
(5)
Fig. 1. Maximum margin classifier.
subject to
(6)
II. FUNDAMENTAL THEORY
A. Support Vector Machine (SVM)
SVM is a new universal learning machine of one output, and
can deal with linear and nonlinearly separable models based on
theoretical results from the statistical learning theory [11]. This
structural risk minimization (SRM) framework formally generalizes the empirical risk minimization principle that is usually
applied for neural-network (NN) training [12]. The number of
hidden units is equal to the number of the so-called support vectors (SVs) which are the learning data points, closest to the separating hyperplane. As a result, the classification becomes very
effective. Once a case exists which does not belong to either of
the binary classes, a “relatively” closer one with minimal error
will be chosen.
, where
is
Consider a training set
a real valued -dimensional input vector (i.e.,
) and
is a label that determines the class of . The
SVMs employed for two-class problems are based on hyperplanes to separate the data, as the example shown in Fig. 1 [10],
[14]. The hyperplane indicated by the dotted line in Fig. 1(a)
and a bias , which
is determined by an orthogonal vector
. By finding a hyidentifies the points that satisfy
perplane that maximizes the margin of separation , it is intuitively expected that the classifier will have better generalization
ability. The hyperplane with the largest margin on the training
set can be completely determined by the closest points to the hyand
in Fig. 1(b), and they
perplane. Two such points are
are called SVs because the hyperplane (i.e., the classifier) depends entirely on them. In its simplest form, SVMs learn linear
decision rules by
is an inner product.
where
Minimization of the cost function (5) and constrain (6) leads
to a simple quadratic optimization problem with a unique solution. In this paper, linear SVM is proposed to solve the nonlinear
PQD problem. Instead of solving (5) and (6) directly, it is much
easier to solve the dual problem (7) with (8) in terms of the Laby maximizing [11]
grange multipliers
(7)
subject to
and
(8)
This optimization problem can be expressed in the matrix notation by maximizing [10]
(9)
subject to
and
(10)
,
where
denotes the Hessian matrix (
is a unit vector
. If
can solve the problem, the training points
are the SVs, and (7) depends entirely on them.
), and
with
Then we have
(1)
(11)
are determined to correctly classify the training
so that
examples and to maximize .
To show the reasons for doing this, consider the fact that it is
always possible to scale and so that
And
can be calculated using (2) to obtain
(12)
(2)
The optimal discriminate function is thus given by
for the SVs, and with
(13)
(3)
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LIN et al.: DETECTION AND CLASSIFICATION OF MULTIPLE PQ DISTURBANCES
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In the simplest form, SVMs learn decision rules as
(14)
In [11] and [14], SVMs can be represented as a feedforward
multilayer network. For highly complicated data, the SVM
can be extended to work in the high dimensional feature space
formed by the nonlinear mapping of the -dimensional input
vector into a -dimensional feature space
through
instead of the inner
the use of a kernel function
[10], [11]. Linear SVM is used in this paper.
product
B. Wavelet Transformation (WT)
WT functions as a filter which provides good resolution at
both the high and low frequencies. For computer implementation, DWT was used for analysis. DWT has a finite number of
wavelet parameters depending on the dilation and translation
. The mother wavelet function has the form [6], [7], [16] of
Fig. 2. Structure of the proposed WMSVM.
TABLE I
CLASSIFICATION FUNCTION AND OUTPUT PATTERN
(15)
,
, and
. In
this paper, wavelet functions are chosen as Gaussian wavelets,
which act as a preprocessor for distortion detection and feature
extraction. For problems of finite energy signals as the ones
discussed in this paper, Gaussian functions are optimal in terms
of the time–frequency localization [6], [16]. The localization
property can be controlled by using the dilation and translation
parameters to measure the content of unknown signals in a
certain frequency band within a certain time interval. The
features will be constructed from various patterns, including
harmonics and voltage disturbances.
where
III. PROPOSED DESIGN ARCHITECTURE
A. DVN Approach and WMSVM
The architecture of the proposed WMSVM is shown in Fig. 2.
The activation functions in the wavelet layer can be derived from
the mother wavelet [6] as
(16)
is a common and effective term [6] used
where
to adjust the dilation and translation. Equation (16) possesses
superior localization performance in the time and frequency domain [16]. That is, the activation function of the th wavelet
node has the form of
(17)
(18)
(19)
where
dilation parameters
here;
translation parameters;
continuous-time fundamental wave;
sequence of samples obtained from an unknown
signal ;
number of sampling points;
sampling period.
Note that the node number of the wavelet layer is equal
to the number of sampling points . The property of (17)
would act as a filter, and is used to eliminate the fundamental
wave. Sequence activation functions as a preprocessor for
feature extraction and can construct various patterns for disturbances. The input vector
is connected to the wavelet layer, and inputs are the sampled
data from the distorted wave. Then, the enhance features
transformed
by WT would be fed to the MSVM.
In our design, MSVM is built by the use of basic SVM elements with the DVN approach. Each linear SVM’s input vector
is , and is designed by comparing a preselected disturbance
event with the normal condition as shown in Table I. It only
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 4, OCTOBER 2008
Fig. 4. SVM unit training for a known disturbance.
Fig. 3. Architecture of the WMSVM-based DEDS.
needs four binary linear SVM classifiers to form MSVM for the
nonlinear PQD problem, and there will be four elements in the
. It has to be noted that
output vector
the binary classifier provides a “relative” comparison (i.e., if an
event does not belong to either of the two classes), a “relatively
near” class of the two will be chosen.
B. Disturbance Events Detection System (DEDS)
The architecture of the proposed WMSVM-based DEDS is
shown in Fig. 3. DEDS is capable of dealing with detecting various disturbances at the chosen “observation locations (OLs)”.
, bus voltage records are taken from
At OLthe data acquisition (DA) and each full cycle of a distorted wave
, where
is used for detection by WMSVMis the number of OLs. Every OL has the same WMSVM architecture. In each WMSVM, the sampled data are provided
in time-domain, the wavelet layer enhances the voltage feature
with WT, and MSVM will perform the pattern recognition.
C. Training Patterns Creation
In this paper, four single disturbances plus the normal condition and two more complex disturbances comprised “seven disturbance events.” According to [17], the disturbance events can
be summarized as:
• harmonics: existing harmonic sources with total harmonic
;
voltage distortion
• voltage sag: a sudden voltage drop with 10 90% nominal,
lasting from 0.5 cycles to several seconds;
• voltage swells: a voltage rise above 110% nominal with a
duration of 0.5 cycles to 1 min;
• voltage normal: a voltage between 95 105% nominal;
• voltage interruption: an event with either a severe voltage
sag or complete blackout for not exceeding 1 min;
• complex event 1: voltage sag involving harmonics;
• complex event 2: voltage swell involving harmonics.
In order for WMSVM to detect disturbances from distorted
voltage waves, it is necessary to create all aforementioned
training patterns for WMSVM. Voltage sag/swell training data
can be created easily by decreasing/increasing the nominal
voltage at certain percentage intervals for all OLs. Voltage
normal and interruption can be created similarly. For harmonics, the harmonic power flow (HPF) [18] was used in this
paper. For a particular harmonic disturbance, the HPF voltages
will be collected at each OL, and then be sampled with a
chosen rate . Every set of input samples, together with the
known disturbance, is used for training and is called a “training
are
set.” Elements of output patterns
displayed by using signal “1” for “Abnormal” and “ 1” for
“Normal.”
D. SVM Training Procedure
According to Section II, SVM training has become a simple
quadratic optimization problem to be solved by using the
quadratic-programming (QP) technique. Since the DVN approach is adopted; only four SVMs are needed for the four
basic disturbances (i.e., harmonics, sag, swell, and interruption). Fig. 4 shows the training of one SVM for its related
disturbance at an OL, where contains all of the training sets
of “a disturbance” plus the “normal” data and has elements
.
Note that although SVM is a relatively complex concept, its
application can become so simple as a QP problem. The same
SVM architecture can be built in portable devices, and a field
crew can collect various data at various OLs for training. Besides harmonics, the sag, swell, and interruption data can be
predefined to train the related SVM. Furthermore, the untrained
disturbances could be continually added for training such a sag
rung between 0.1 and 0.7 p.u., voltage flicker, and oscillatory
transients. The detection can only work after SVM training with
a known disturbance.
IV. CONFIGURATION OF THE TEST EXAMPLE
A 14-bus system is used, for example, as shown in Fig. 5.
The system has five generator buses, 15 lines, five transformers,
and eight nonlinear devices as shown in Table II. The bus and
line data are provided in [19]. Most harmonics are related to
power rectifiers or converters with constant harmonic current
modes. Buses are defined as the “locations” in this paper
and the buses with harmonic sources are the interested buses
with measurements for “observation,” and there are eight
“OLs” in two electrically distant areas in this example. In this
system, voltage sags are 70 90% nominal voltage, swells are
110 130% nominal voltages, voltage interruptions and complex disturbances are also considered. In a power system, the
harmonic source also causes voltage distortion for neighboring
buses. In this example, we also consider various harmonic load
combinations, work durations, and intermittence loads such
as dc motors. With HPF, we can simulate harmonic voltages
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LIN et al.: DETECTION AND CLASSIFICATION OF MULTIPLE PQ DISTURBANCES
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TABLE III
ARCHITECTURE OF THE WMSVM
Note: W (I)-S-O: Wavelet (input) layer-SVM layer-output layer
TABLE IV
ARCHITECTURE OF THE WMLP
Fig. 5. IEEE 14-bus system.
TABLE II
TEST CASE FOR SAMPLE POWER SYSTEM
Note: SFC: Static frequency converter; TCR: Thyristor-controlled reactor
Fig. 6. Harmonic voltage spectrum with various nonlinear loads.
at these selected OLs. Fig. 6 shows the harmonic voltages
used for HPF training for various devices, and the harmonics
with
between 1.2% 5.2% were used for various tests
in the next section. The Nyquist sampling theorem requires a
double frequency for effective sampling [20]. Since the highest
harmonic order is 25 (1.5 kHz) in the test, a suitable sampling
rate greater than 3 kHz is needed. However, to show the strong
classification capability of WMSVM, three sampling rates
including both the lower and higher rates were considered for
tests as:
• Type I: 30 samples with a sampling rate of 1.8 kHz;
• Type II: 60 samples with a sampling rate of 3.6 kHz;
• Type III: 90 samples with a sampling rate of 5.4 kHz.
Note: W (I)-H-O: wavelet (input) layer-hidden layer-output layer
V. SIMULATION RESULTS
At each observing location, five disturbance events (four
single disturbances plus the normal condition) with 41 sets
of training data were first used. Bus 12 of Area 2 is used for
example, and Area 1 is considered too remote to be effective.
We have:
• harmonics: harmonic load combinations with seven sets of
training data. For example, combinations {Bus 12}, {Bus
12, Bus 6}, {Bus 12, Bus 11}, {Bus 12, Bus 13}, {Bus 12,
Bus 6, Bus 11}, {Bus 12, Bus 6, Bus 13}, {Bus 12, Bus 11,
Bus 13} at observing location Bus 12;
• voltage sag: 70 90% nominal voltage with 11 sets of
training data, 2% voltage change each set;
• voltage swell: 110 130% nominal voltage with 11 sets of
training data, 2% voltage change each set;
• voltage interruption: voltage magnitude of less than 10% of
nominal voltage with six sets of training data, 2% voltage
change each set;
• voltage normal: 95 105% nominal voltage with six sets of
training data, 2% voltage change each set.
Another two complex disturbance events are:
1) voltage sag involving harmonics: with 11 sets of training
data containing different sags with the most serious harmonic combinations simultaneously;
2) voltage swell involving harmonics: with 11 sets of training
data containing different swells with the most serious harmonic combinations simultaneously.
There are a total of 63 sets of training data. The 41 and 63 sets
of training data were used for various tests.
The DEDS was designed on a Pentium IV PC with 256-MB
RAM and Matlab software. Three sampling types of WMSVMs
for each OL are shown in Table III. For comparison purposes,
WMLP was also developed with the combination of WT and
MLP for tests. Table IV shows the architecture of WMLP which
consists of three layers. The first layer contains wavelet nodes
(i.e., input nodes) with the same activation functions as in
(17)–(19). A traditional network is used for training with a
back-propagation learning algorithm [5], [21]. WMLP has the
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Fig. 8. (a) Time-domain waves at Bus 12. (b) WT patterns at Bus 12.
Fig. 7. Detection results of Bus 12.
TABLE V
DETECTION OF THE DISTURBANCE AND LOCATION
+
Note: (1) “ ”: Disturbance Event; “
(2)
: Bus k output
O
0”: Normal
same number of input and output nodes as WMSVM. As in general cases, one hidden layer is used [10], [11] and the number
of hidden nodes is determined by the experience formulas in
[21] (i.e., the square root of the number of input nodes times the
output nodes). In our method, the SVM layer also functions as
a hidden layer. The output vectors indicate the possible disturbance events at the OL with signal “1” for “Abnormal” and “0”
for “Normal.” To avoid the effect of overfitting or underfitting
[9], [11], a suitable range of learning rate (Lr) for WMLP
training was determined by the cross validation [9], [11] and a
tested
tedious trial-and-error procedure with
in this paper. All weights are frozen when a satisfactory mean
square error (MSE) is reached. Through various tests,
yields the best result and is chosen in this paper. To show
the effectiveness, many tests were conducted and a few case
studies were chosen for demonstration. Note that only the 41
sets of training data with the lowest sampling rate (Type I) are
used to show the strong classification capability of WMSVM
in Sections V-A, B, and D.
A. Study Case 1: Single Even
With a single harmonic source at Bus 12, sampled data were
applied to each WMSVM for detection. Time-domain analysis
was conducted to detect the distorted waves with 30 cycles
(0.5 s), and harmonics
were detected after 20
cycles as shown in Fig. 7. In Table V, the results also show the
detected event and location of Bus 12, with normal conditions
at all of the other buses.
B. Study Case 2: Multiple Harmonics Involving the Complex
Event
With multiple harmonic sources already detected at Bus 6,
Bus 9, Bus 12, and Bus 13, an additional voltage sag event
occurred from heavy motor loads at Bus 12 after 20 cycles.
Fig. 9. Detection results of Bus 12.
TABLE VI
DETECTION OF THE DISTURBANCE AND LOCATION
Sampled data were then applied to each WMSVM for detection. Time-domain analysis was conducted to detect the distorted waves with 30 cycles (0.5 s). For Bus 12, Fig. 8(a) and (b)
shows the time-domain waves and WT patterns. When voltage
sag suddenly dropped 13%, periodic sampling was performed
in the data processor. Fig. 9 shows the results of Bus 12. Other
buses can be detected similarly. Table VI shows the detection
results for the locations and events. This confirms that the proposed models have the capability for distinguishing the periodic
and nonperiodic voltage variances.
C. Detection Accuracies Test
Both the 41 and 63 sets of training data with various sampling
rates were used to test the accuracies of the proposed method.
Combinations of 395 sets of various disturbance data were
tested. Loc-11 with a six-pluse rectifier is used for example.
Fig. 10 shows the detection accuracies, and other locations have
similar results. For a simulated disturbance at a given location,
the accuracy of WMSVM is higher than the WMLP. From the
tests, it can be seen that it is confident enough for WMSVM
with 41 training sets and 30 input nodes. It shows the strong
classification capability of the proposed method. Reducing the
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TABLE VII
COMPARISON OF WMSVM AND WMLP
E. Performances Test
Fig. 10. Accuracies of detection for WMSVM and WMLP.
2
Note: (1) Accuracy (%) = (N =N ) 100%
(2) N : the number of successful sets in identification; N : total number
of test sets, N = 395 here.
Table VII compares the learning performance of MSVM and
WMLP for sampling Type I at Loc-12.
is chosen
for WMLP training. With various tests, we can see that the
training time of WMSVM substantially outperformed WMLP
by a great scale, with the testing time very close to each other.
WMSVM has a fast learning process with neither estimation for
the number of layers nor hidden nodes. With the same training
data, the proposed WMSVM shows better overall performance.
VI. CONCLUSION
Fig. 11. Output value against voltage magnitude variances.
input nodes from 90 to 30, the data storage can be substantially
reduced without losing originalities. We can minimize data
storage, shorten preprocessing needs, and reduce the network
size. However, it is difficult for WMLP to use 41 training sets,
because it cannot classify the complex disturbances unless
these disturbances are specifically trained. It can also be seen
that the accuracy of WMLP increases significantly with 63 sets
of training data.
D. Robustness Tests
In order to test the robustness of the proposed method, the
41 sets of training data and sampling Type I were used for
WMSVM at Loc-7.
Testing data were produced with voltage magnitudes varying
and then Gaussian
from 0 to 1.7 p.u., where
noises were further added randomly to the voltage with zero
mean and 10% variance. Fig. 11 shows the output value
against the voltage magnitude variances for testing data, including interruption, sag, normal, and swell. With a specific
sag range between 0.7 and 0.9 p.u. for ”voltage sag” training,
voltages between 0.44 and 0.95 p.u. were strongly identified
as “sag events.” The same results can also be observed for
the “voltage swell” between 1.05 and 1.7 p.u. The voltage
interruption was gradually identified with the magnitude below
0.44 p.u. This confirms that the proposed method has a better
capability for enhancing the classification performance and is
very robust.
DEDS with WMSVMs was developed in this paper.
WMSVMs were designed with a simple network architecture
to shorten the processing time. The proposed architecture could
effectively detect information from distorted waves using WT
and MSVM techniques. In a real power system, where DA is
not available, training data could be periodically collected by
portable recording instruments placed at measurement points.
The special patterns could also be extracted from real-world
monitors at measurement points including oscillatory transients, sag rung between 0.1 and 0.7 p.u., and voltage flicker.
Some advantages of the WMSVM-based DEDS are that:
• WMSVM has a fast processing procedure;
• WMSVM has a strong classification capability with less
sampling rates;
• WMSVM uses the simple QP technique to produce a
unique optimal solution;
• a minimum-sized network can be built using simple
learning algorithms with minimal training data;
• the DVN approach and linear SVM are used to solve the
nonlinearly separable problems, such as PQD;
• WMSVM can work either with existing DA interface or
portable recorders;
• WMSVM could detect multiple harmonics and voltage disturbances simultaneously at each observation location;
• WMSVM has good classification performance, detection
accuracy, and robustness.
Computer simulation shows that WMSVM-based DEDS are
precise, easy to work with, and are very effective and robust.
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Whei-Min Lin (M’87) was born in 1954. He
received the B.S. degree in electrical engineering
from the National Chao-Tung University, Hsin-Chu,
Taiwan, R.O.C., the M.S. degree in electrical engineering from the University of Connecticut, Storrs,
and the Ph.D. degree in electrical engineering from
the University of Texas at Arlington in 1985.
Currently, he is with National Sun Yat-Sen University, Taiwan, R.O.C., where he has been since 1991.
He was a Visiting Researcher with Chung-Hwa
Institute for Economic Research, Taiwan, in 1985.
He joined Control Data Corp., Minneapolis, MN, in 1986 and was with Control
Data Asia, Taipei, in 1989. His main interests are geographic information
systems (GIS), distribution system, supervisory control and data acquisition
(SCADA), and the automatic control system.
Dr. Lin is a member of Tau Beta Pi.
Chien-Hsien Wu was born in 1970. He received
the B.S. degree in electrical engineering from the
National Taiwan University of Science and Technology, Taipei, Taiwan, R.O.C., in 1994, the M.S.
degree in electrical engineering from the National
Sun Yat-Sen University, Kaohsiung, Taiwan, in
2001, and is currently pursuing his Ph.D. degree at
National Sun Yat-Sen University, Kaohsiung.
His research interests include fault diagnosis
in power systems, applications of soft computing
in power systems, power system operation, and
harmonic analysis.
Chia-Hung Lin was born in 1974. He received the
B.S. degree in electrical engineering from the Tatung
Institute of Technology, Taipei, Taiwan, R.O.C., in
1998, the M.S. degree in electrical engineering from
the National Sun Yat-Sen University, Kaohsiung,
Taiwan, in 2000, and the Ph.D. degree in electrical
engineering from National Sun Yat-Sen University,
Kaohsiung, in 2004.
Currently, he is Assistant Professor in the Department of Electrical Engineering, Kao-Yuan
University, Kaohsiung, Taiwan, where he has been
since 2004. His research interests include fault diagnosis in power systems,
neural network computing, and harmonic analysis.
Fu-Sheng Cheng received the Ph.D. degree from
the National Sun Yat-Sen University, Kaohsiung,
Taiwan, R.O.C., in 2001.
He has been with the Department of Electrical Engineering of Cheng-Shiu University, Taiwan, since
1990. He is interested in AI applications on power
system operation.
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