Engineering, 2009, 1, 211-215
doi:10.4236/eng.2009.13025 Published Online November 2009 (http://www.scirp.org/journal/eng).
Applications of Data Mining Theory in Electrical
Engineering
Yagang ZHANG, Jing MA, Jinfang ZHANG, Zengping WANG
Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control under Ministry of
Education, North China Electric Power University, Baoding, China
Received January 10, 2009; revised February 21, 2009; accepted February 23, 2009
Abstract
In this paper, we adopt a novel applied approach to fault analysis based on data mining theory. In our re-
searches, global information will be introduced into the electric power system, we are using mainly cluster
analysis technology of data mining theory to resolve quickly and exactly detection of fault components and
fault sections, and finally accomplish fault analysis. The main technical contributions and innovations in this
paper include, introducing global information into electrical engineering, developing a new application to
fault analysis in electrical engineering. Data mining theory is defined as the process of automatically ex-
tracting valid, novel, potentially useful and ultimately comprehensive information from large databases. It
has been widely utilized in both academic and applied scientific researches in which the data sets are gener-
ated by experiments. Data mining theory will contribute a lot in the study of electrical engineering.
Keywords: Fault Analysis, Data Mining Theory, Classification, Electrical Engineering
1. Introduction
Data mining is the efficient discovery of valuable,
non-obvious information from a large collection of data.
It is also referred to as exploratory data analysis, deals
with extraction of knowledge from data. Data mining is
the process of discovering interesting knowledge, such as
patterns, associations, changes, anomalies and significant
structures, from large amounts of data stored in databases,
data warehouses, or other information repositories [1].
And data mining is usually used for very large databases,
where it is normally not possible to comprehend or ana-
lyze the data because of the complexity and the immen-
sity of the size of database. It aims at the discovery of
useful information from these large databases, and it is
also popularly referred to as knowledge discovery in da-
tabases (KDD). Data mining involves an integration of
techniques from multiple disciplines such as database
technology, statistics, machine learning, high-perform-
ance computing, pattern recognition, neural networks,
data visualization, information retrieval, etc [2–4]. A
common problem in data mining is to find associations
among attributes of the data.
Data mining tasks have the following categories: [5]
 Class description;
 Association analysis;
 Cluster analysis;
 Outlier analysis;
 Evolution analysis.
A fault is defined as a departure from an acceptable
range of an observed variable or calculated parameter
associated with equipments, that is, a fault is a process
abnormality or symptom. In general, faults are deviations
from the normal behavior in the plant or its instrumenta-
tion. They may arise in the basic technological equipment
or in its measurement and control instruments, and may
represent performance deterioration, partial malfunctions
or total breakdowns [6]. The analysis procedure locates
the process or unit malfunction that caused the symptoms.
The goal of fault analysis is to ensure the success of the
planned operations by recognizing anomalies of system
behavior. As a result of proper process monitoring, down-
time is minimized, safety of plant operations is improved,
and manufacturing costs are reduced. Generally speaking,
the process of fault analysis can be divided into three
main steps: alarm, identification, evaluation.
Electric power system is one of the most complex arti-
ficial systems in this world, which safe, steady, economi-
cal and reliable operation plays a very important part in
guaranteeing socioeconomic development, even in safe-

Y. G. ZHANG ET AL. 212
guarding social stability. In order to resolve this difficult
problem, some methods and technologies that can reflect
modern science and technology level have been intro-
duced into this domain. Of course, no matter what kind of
new analytical method or technical means we adopt, we
must have a distinct recognition of electric power system
itself and its complexity, and increase continuously
analysis, operation and control level [7–11].
When electric power system operates from normal state
to failure or abnormal operates, its electric quantities may
change significantly. Relay protection is just using the
sudden changes of electric to distinguish whether the
power system is failure or abnormal operation. After con-
trasting the electric variational measurements with the
electric parameters of normal system, we can detect fault
types and fault locations. Furthermore, we can implement
selective failure removal. In our researches, global infor-
mation will be introduced into the backup protection sys-
tem. After some accidents, utilizing real-time measure-
ments of phasor measurement unit (PMU), we will seek
after for characters of electrical quantities’ marked chan-
ges. Then we can carry out quickly and exactly analysis
of fault components and fault sections, finally, we can
accomplish fault isolation. Basing on statistical theory,
we have carried out large numbers of basic researches in
nonlinear complex systems [12–14]. In this paper, we are
using mainly cluster analysis technology of data mining
theory to resolve fault detection problem in electrical en-
gineering.
2. Electric Circuit Principle
We consider a circuit with resistors(R), inductors (L), and
capacitors(C) [15]. The simplest circuit has one element of
each connected in a loop. The part of the circuit containing
one element is called a branch. The points where the
branches connect are called nodes. In this simplest exam-
ple, there are three branches and nodes. See Figure 1.
We let
R
i,and be the current in the resistor, indu-
ctor and capacitor respectively. Similarly let ,
and be the voltage drop across the three branches of
the circuit. If we think of water flowing through pipes,
then the current is like the rate of flow of water, and the
voltage is like water pressure. Kirchhoff’s current law
states that the total current flowing into a node must
equal the current flowing out of that node. In the circuit
L
iC i
R
vL v
C
v
Figure 1. RLC electric circuit.
being discussed, this means that
R
LC
iiiwith the
correct choice of signs. We orient the branches in the
direction given in Figure.1, so,
R
LC
iii i

.
Kirchhoff’s voltage law states that the sum of the
voltage drops around any loop is zero. For the present
example, this just means that,
0
RLC
vvv


Next, we need to describe the properties of the ele-
ments and the laws that determine how the variables
change. A resistor is determined by a relationship betw-
een the current and voltage. In the present sec-
tion, we consider only a linear resistor given by
R
iR v
R
R
vRi

where is a constant. This is Ohm’s law. In further
discussions, we consider as a nonlinear function of
or as a nonlinear function of.
0R
R
i
R
v
R
iR v
An inductor is characterized by giving the time deriva-
tive of the current
L
di
dt
, in terms of the voltage : Fara-
day’s law has proved that
C
v
L
L
di
Lv
dt 
where the constant is called the inductance.
Classically, an inductor was constructed by making a coil
of wire. Then, the magnetic field induced by the change
of current in the coil creates a voltage drop across the
coil.
0L
A capacitor is characterized by giving the time deriva-
tive of the voltageC
dv
dt
, in terms of the current ,
C
i
C
C
dv
Ci
dt 
where the constant is called the capacitance.
0C
3. Classification in the Data Mining
Classification is one of the classical topics in the data
mining field. Clustering is the process of grouping data
objects into a set of disjoint classes, called clusters, so
that objects within a class have high similarity to each
other, while objects in separate classes are more dissimi-
lar. Clustering is an example of unsupervised classifica-
tion. “Classification” refers to a procedure that assigns
data objects to a set of classes. “Unsupervised” means
that clustering does not rely on predefined classes and
training examples while classifying the data objects.
Theories of classification come from philosophy,

Y. G. ZHANG ET AL.213
)m
mathematics, statistics, psychology, computer science,
linguistics, biology, medicine, and other areas. Cluster
analysis encompasses the methods used to:
1) Identify the clusters in the original data;
2) Determine the number of clusters in the original
data;
3) Validate the clusters found in the original data.
Cluster analysis has great strength in data analysis and
has been applied successfully to the researches of various
fields.
Suppose there are samples, each sample has
indexes, the observation data can be expressed as
n
1,
m
(1,,, ,
ij inj


ij
d
()i

. The most commonly used
measurement that describes the degree of relationship is
distance, is usually denoted the distance between
samples

and ()j

. The distance definitions in
common use include:
a. Minkovski distance
1
1
()[] (,1,2,,)
mqq
ijit jt
t
dqij n 

 
.
b. Lance distance(0
ij

)
1
1
(), (,1,2,,)
()
mitjt
ij
titjt
dLijn
m






.
c. Mahalanobis distance
1
()()()( )
()()() (,1,2,,)
ijij ij
dMSij n  

  
Hereinto, is an inverses matrix of samples’ co-
variance matrix.
1
S
d. Oblique space distance
In order to overcome the influence of relativity be-
tween variables, one can define the distance of oblique
space:
1
2
2
11
1
[()() ]
(,1,2,,)
mm
ijikjkiljl kl
kl
dm
ij n






Hereinto, kl

is the correlation coefficient between
k

and l

.
4. Fault Analysis Based on Data Mining
Now let us consider IEEE9-Bus system, Figure 2 is its
electric diagram. In the structure of electric power net-
work, Bus1 appears single-phase to ground fault. By
BPA programs, the vector-valued of corresponding vari-
ables is only exported one times in each period. Using
these actual measurement data of corresponding variable,
1Gen
2Gen
3Gen
1
B
us
2
B
us
3Bus
BusA
BusB BusC
Figure 2. Electric diagram of IEEE 9-Bus system.
we can carry through fault analysis of fault component
and non-fault component (fault section and non-fault
section).
4.1. Fault Diagnosis Based on Node Phase
Voltage
After computing IEEE9-Bus system, we can get node
phase voltages at 1
T

, (Fault), ,and five times,
see Table 1. Figure 3 is the dendrogram of cluster analy-
sis based on node phase voltage. The entire cluster
analysis process is carried out according to the principle
of similarity from high to low (distance from near to far),
the order is,
0
T1
T2
T3 T
Steps 1: BusC combines with BusB and forms the new
BusB;
Steps 2: Bus3 combines with Bus2 and forms the new
Bus2;
Steps 3: BusA combines with Bus2 and forms the new
Bus2;
Steps 4: Bus2 combines with Gen1 and forms the new
Gen1;
Steps 5: Gen3 combines with Gen2 and forms the new
Gen2;
Steps 6: Gen2 combines with Gen1 and forms the new
Gen1;
Steps 7: BusB combines with Bus1 and forms the new
Bus1;
Steps 8: Bus1 combines with Gen1 and forms the new
Gen1.
It can be found easily out from Figure 3 that Bus1 has
remarkable difference with other buses, and the fault
characteristic is obvious. These results are entirely iden-
tical to the fault location set in advance, so we can con-
firm exactly fault location by the cluster analysis based
on node phase voltage.
4.2. Fault Diagnosis Based on Node Negative
Sequence Voltage
By BPA programs, we can get node negative sequence
voltage at 1
T

,(Fault), ,and five times, see Ta
0
T1
T2
T3 T
ble 2. Figure 4 is the dendrogram of cluster analysis based
on negative sequence voltage.

Y. G. ZHANG ET AL. 214
Let us explain the entire process of cluster analysis in
detail. The entire cluster analysis process is still carried
out according to the principle of similarity from high to
low (distance from near to far), the order is,
Steps 1: BusA combines with Bus2 and forms the new
Bus2;
Steps 2: Bus3 combines with Bus2 and forms the new
Bus2;
Steps 3: BusC combines with BusB and forms the new
BusB;
Steps 4: Bus2 combines with Gen1 and forms the new
Gen1;
Steps 5: Gen3 combines with Gen2 and forms the new
Gen2;
Steps 6: Gen2 combines with Gen1 and forms the new
Gen1;
Steps 7: BusB combines with Bus1 and forms the new
Bus1;
Steps 8: Bus1 combines with Gen1 and forms the new
Gen1.
From the entire hierarchical cluster process analysis,
Bus1 has the lowest similarity to other nodes (the farthest
distance to other nodes). Figure.4 shows that the differ-
ence of Bus-1 and other Buses is more distinct by cluster
analysis based on node negative sequence voltage. So, it
can also identify effectively fault location that using
cluster analysis based on node negative sequence volt-
age.
These instances have fully proven that the analysis of
fault component (fault section) can be performed by data
mining theory.
5. Conclusions and Discussions
In the control of electric power systems, especially in the
wide area backup protection of electric power systems,
the prerequisite of protection device’s accurate, fast and
Table 1. The node phase voltages a ,(Fault),1
T,and
1
T0
T2 T
3 five times.
T
Bus
Time T-1
T0
(Fault) T1
T2 T3
Gen1 1.0100 0.7275 0.6924 0.6814 0.6747
Gen2 1.0100 0.8762 0.8476 0.8327 0.8134
Gen3 1.0100 0.8449 0.8071 0.7909 0.7710
Bus1 1.0388 0 0 0 0
Bus2 1.0430 0.7622 0.7350 0.7217 0.7049
Bus3 1.0534 0.7600 0.7275 0.7134 0.6960
BusA 1.0319 0.7540 0.7248 0.7114 0.6944
BusB 1.0222 0.2512 0.2404 0.2356 0.2294
BusC 1.0061 0.2470 0.2381 0.2336 0.2276
Table 2. The node negative sequence voltages at
1
T

,(Fault),1
T,and five times.
0
T2
T3
T
Bus
Time
T-1 T0
(Fault) T1
T2 T3
Gen1 0 0.1330 0.1270 0.1247 0.1227
Gen2 0 0.0556 0.0530 0.0521 0.0512
Gen3 0 0.0742 0.0708 0.0696 0.0684
Bus1 0 0.3408 0.3252 0.3196 0.3142
Bus2 0 0.1058 0.1009 0.0992 0.0975
Bus3 0 0.1168 0.1115 0.1096 0.1077
BusA 0 0.1027 0.0980 0.0963 0.0947
BusB 0 0.2419 0.2309 0.2269 0.2231
BusC 0 0.2287 0.2182 0.2144 0.2108
Figure 3. The dendrogram of cluster analysis based on node
phase voltage.
Figure 4. The dendrogram of cluster analysis based on node
negative sequence voltage.
reliable performance is its corresponding fault type and
fault location can be discriminated quickly and defined
exactly. In our researches, global information has been
introduced into the backup protection system. Based on
data mining theory, we are using mainly cluster analysis
technology to seek after for the characters of electrical
quantities’ marked changes. Then, we carry out fast and
exact identification of faulty components and faulty sec-
tions, and finally accomplish fault analysis. The main
technical contributions and innovations in this paper in-
clude, introducing global information into electrical en-

Y. G. ZHANG ET AL. 215
gineering, developing a new application to fault analysis
in electrical engineering.
Data mining is defined as the process of automatically
extracting valid, novel, potentially useful and ultimately
comprehensive information from large databases. It has
been widely utilized in both academic and applied scien-
tific researches in which the data sets are generated by
experiments. The most important characteristic of data
mining theory is its interdisciplinarity and universality.
Data mining is largely connected with machine learning
in which scientists develop algorithms and techniques to
find and describe potential laws in data. Generally speak-
ing, data mining adds useful techniques to many other
fields such as information processing, pattern recognition
and artificial intelligence etc.
6. Acknowledgment
This research was supported partly by Key Program
of National Natural Science Foundation of China
(50837002, 50907021) and the Science Foundation for
the Doctors of NCEPU.
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