Energy and Power Engineering, 2009, 21-27
doi:10.4236/epe.2009.11004 Published Online August 2009 (http://www.scirp.org/journal/epe)
Fault Detection Based on Hierarchical Cluster Analysis
in Wide Area Backup Protection System
Yagang ZHANG, Jinfang ZHANG, Jing MA, 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
Abstract: In wide area backup protection of electric power systems, the prerequisite of protection device’s
accurate, fast and reliable performance is its corresponding fault type and fault location can be discriminated
quickly and defined exactly. In our study, global information will be introduced into the backup protection
system. By analyzing and computing real-time PMU measurements, basing on cluster analysis theory, we are
using mainly hierarchical cluster analysis to search after the statistical laws of electrical quantities’ marked
changes. Then we carry out fast and exact detection of fault components and fault sections, and finally ac-
complish fault isolation. The facts show that the fault detection of fault component (fault section) can be per-
formed successfully by hierarchical cluster analysis and calculation. The results of hierarchical cluster analy-
sis are accurate and reliable, and the dendrograms of hierarchical cluster analysis are in intuition.
Keywords: wide area backup protection, phasor measurement unit, PMU, wide area measurement system,
WAMS, fault detection, cluster analysis
1 Introduction
Electric power system is one of the most complex artifi-
cial systems in this world, which safe, steady, economi-
cal and reliable operation plays a very important part in
guaranteeing socioeconomic development, even in safe-
guarding social stability. In early 2008, the infrequent
disaster of snow and ice that occurred in the south of
China had confirmed it again. The complexity of electric
power system is determined by its characteristics about
constitution, configuration, operation, organization, etc.,
which has caused many disastrous accidents, such as the
large-scale blackout of America-Canada electric power
system on August 14, 2003, the large-scale blackout of
Chinese Hainan electricity grid on September 26, 2005.
In order to resolve this difficult problem, some methods
and technologies that can reflect modern science and
technology level have been introduced into this domain,
such as computer and communication technology, con-
trol technology, superconduct and new materials tech-
nology and so on. Obviously, no matter what we adopt
new analytical method or technical means, we must have
a distinct recognition of electric power system itself and
its complexity, and increase continuously analysis, op-
eration and control level [1-3].
Relay protection is the first line of guaranteeing large-
scale electricity grid’s safety. The faults in electric power
system are inevitable. If protection devices can operate
rightly, quickly and reliably, the deterioration of system
status will be checked effectively, then it will play a de-
cisive role to protect electricity grid’s safe operation.
Otherwise, it will accelerate system crashes, as a result,
large-scale and long-time power blackout will continue.
After counting seventeen years accident data in electric
power system, North American Electric Reliability
Council (NERC) has found: 63% accidents in electric
power system are concerned with the incorrect operation
of relay protection. The large-scale power blackouts oc-
curred in China and other countries of the last thirty
years have also indicated: the large-scale power blackout
accidents are often raised from the improper cooperation

Y. ZHANG, J. F. ZHANG, J. MA, Z. P. WANG
22
or chain reaction of protection devices. The large-scale
blackout of America-Canada electric power system was
just because the removal of four connection lines be-
tween Akron and Cleveland in northern Ohio by backup
protection for overload, and the accident spread rapidly.
The backup protection in current electricity grid is only
reflecting the information of protection installation posi-
tion, which will be affected by topological connecting
relations and operation modes. In order to guarantee its
reliability, we can only carry through configuration and
setting according to the most rigorous condition. In order
to guarantee its selectivity, we have to sacrifice the ra-
pidity and sensitivity of backup protection [4][5]. In re-
cent years, the appearance of wide area measurement
system (WAMS) affords the possibility for introducing
system information into backup protection system.
WAMS can obtain synchronously electrical measure-
ments in the whole power system, and realize power
system dynamic process monitoring and control. It can
also decrease the update speed of measurements from
seconds to tens of millisecond, and create condition to
realize power system dynamic process control, which
will help us carry through backup protection design
based on global optimal angles of electricity grid, and
afford the possibility for resolving dynamic security
monitoring, control and protection of complex large-
scale electricity grid.
When electric power system operates from normal
state to failure or abnormal operates, its electric quanti-
ties (current magnitude, voltage magnitude and their
angles, etc.) may change significantly. In our researches,
global information will be introduced into the backup
protection system. After some accidents, utilizing
real-time measurements of phasor measurement unit
(PMU) [6-10], basing on multivariate statistical analysis
theory [11-13], we are using mainly cluster analysis
technology [14-19], and seeking after for statistical laws
of electrical quantities’ marked changes. Then we can
carry out fast and exact detection of fault components
and fault sections, and hereby ascertain protection com-
ponents associated with them. Finally we can accomplish
fast and exact fault isolation.
The cluster analysis theory is one of multivariate sta-
tistical analysis theory, which is a synthetical analysis
theory. In recent years, as the development of computer
application technology and the demand of scientific re-
search and production, multivariate statistical analysis
theory has been applied successfully to many researches
of various fields, such as geology, weather, hydrology,
iatrology, industry, agriculture, and economy, etc. It has
been an efficient theory that can resolve different kinds
of complex problems. Basing on statistical theory, we
have carried out large numbers of basic researches in
nonlinear dynamical systems [20-22]. In this paper, we
are using mainly cluster analysis of multivariate statisti-
cal analysis theory to resolve fault detection problem in
wide area backup protection of electric power systems.
2 Cluster Analysis Theory
Theories of classification come from philosophy, mathe-
matics, statistics, psychology, computer science, linguis-
tics, biology, medicine, and other areas. Cluster analysis
can also be named classification, which is concerned
with researching the relationships within a group of ob-
jects in order to establish whether or not the data can be
summarized validly by a small number of clusters of
similar objects. That is, cluster analysis encompasses the
methods used to:
 Identify the clusters in the original data;
 Determine the number of clusters in the original
data;
 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 (variables), the observation data can be
expressed as,
n m
(1,,, 1,,)
ij
x
injm



Y. ZHANG, J. F. ZHANG, J. MA, Z. P. WANG
23
In these data, the definition of mean is:
1
1 (1,2,,
n
jtj
t
)
x
xj m
n


the definition of standard deviation is:
2
1
1() (1,2,,
1
n
jtjj
t
Sxxj
n

)m
.
2.1 The Distance and Similar Coefficient
Between Samples
The most commonly used measurement that describes the
degree of relationship is distance, is usually denoted
the distance between samples
ij
d
()i
X
and ()j
X
, the general
demands are:
(1). 0,
ij
d for arbitrary ,ij , and
()( )j
X
;
0
ij i
dX
(2). ,
ij ji
dd for arbitrary ,ij ;
(3). , for arbitrary ,,ijk(Triangle
inequality).
ijik kj
ddd
The distance definitions in common use include:
1) Minkovski distance
1
1
()[]
( ,1,2,,)
mqq
ijit jt
t
dqx x
ij n





.
2) Lance distance () 0
ij
x
1
1
(),
()
( ,1,2,,)
mit jt
ij
tit jt
xx
dL mxx
ij n






.
This is a measure without dimension, and it is insensi-
tive to big singular values.
3) Mahalanobis distance
1
()()()()
()()()
(,1,2,,)
iji ji j
dMX XSX X
ij n


 

.
Hereinto, is an inverses matrix of samples’ co-
variance matrix.
1
S
4) 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
dxxxx
m
ij n





] r
.
Hereinto, is the correlation coefficient between
kl
r
k
X
and l
X
.
2.2 The Similar Coefficient and Distance
Between Variables
Suppose can be expressed as the similar coefficient
between
ij
C
i
X
and
j
X
, the general demands are:
(1). 0,1 (
iji j
CXaXa

 constant);
(2). 1,
ij
C

for arbitrary ,ij;
(3). ,
ij ji
CC

for arbitrary ,ij.
ij
C close to one means that i
X
and
j
X
have near
relationship, otherwise, close to zero means that
they have distant relationship. The similar coefficients in
common use are included angle Cosine and correlation
coefficient.
ij
C
1) Included angle Cosine
These observed values ( n12 ,,,
ii ni
x
xx) of i
X
can be regarded as vectors in -dimensional space, and
the angle
n
ij

’s Cosine ofi
X
and
j
X
is called simi-
lar coefficient of these two variables, namely
1
22
11
(1)[ ]
(,1,2,,)
n
ti tj
t
ijij nn
ti tj
tt
xx
CCos
x
x
ij m








.
2) Correlation coefficient
The correlation coefficient is just the included angle
Cosine after the data have been standardized. is ex-
pressed in common use the correlation coefficient of
ij
r
i
X
and
j
X
, here we define it as , (2)
ij
C
1
22
11
()( )
(2)
()( )
( ,1,2,,)
n
tii tjj
t
ij nn
ti itjj
tt
xxxx
C
xx xx
ij m









.

Y. ZHANG, J. F. ZHANG, J. MA, Z. P. WANG
24
3 Fault Detection Based on Hierarchical
Cluster Analysis
Cluster analysis is commonly applied for statistical
analyses of large amounts of experimental data exhibit-
ing some kind of redundancy, which allows for compres-
sion of data to amount feasible for further exploration.
Most common clustering algorithm choices are hierar-
chical cluster analysis.
The hierarchical cluster analysis does not require us to
specify the desired number of clusters
K
, instead af-
fording a cluster dendrogram. In practice, the choice can
be based on some domain specific and often have sub-
jective components. There are three steps to hierarchical
cluster analysis. First, we must identify an appropriate
proximity measure, for there are many metric methods,
such as Minkovski distance, Lance distance, Mahalano-
bis distance, Oblique space distance and the similar co-
efficients, which is the best one? Second, we need to
identify the appropriate cluster method for the data, in-
clude Between-groups linkage, Within-groups linkage,
Nearest neighbor, Furthest neighbor, Centroid, Median
and Ward's method, and so on. Finally, an appropriate
stopping criterion is needed to identify the number of
clusters in the hierarchy. According to the result of clas-
sification, how many clusters should we divide? The
distance or similarity metric used in cluster is crucial for
the success of the cluster method. Euclidean distance and
Pearson correlation are among the most frequently used.
Firstly, let us consider IEEE9-Bus system, Figure 1 is
its electric diagram. In the structure of electricity grid,
Bus-1 appears single-phase to ground fault. By BPA
programs, the vector-valued of corresponding variables
is only exported one times in each period. Using these
actual measurement data of corresponding variables, we
can carry through hierarchical cluster analysis of fault
component and non-fault component (fault section and
non-fault section).
3.1 Fault Detection of IEEE9-Bus System Based
on Node Positive Sequence Voltage
After computing IEEE9-Bus system, we can get node po-
Figure 1. Electric diagram of IEEE 9-Bus system
Figure 2. The dendrogram of hierarchical cluster analysis based on
node positive sequence voltage
sitive sequence voltages at ,(Fault) and three
times. (The reason that we only choose three times data
is because it must satisfy the actual sampling-rate of
PMU and the control time of the wide area backup pro-
tection system.) Figure 2 is the dendrogram of hierarchi-
cal cluster analysis based on node positive sequence
voltage.
1
T0 T1 T
It can be found easily out from Figure 2 that Bus-1 has
remarkable difference with other buses, and the fault
characteristic is obvious. Because Bus-A and Bus-B are
directly connected with Bus-1, Bus-A, Bus-B and Bus-1
can be regarded as a cluster. In fact Bus-1, Bus-A and
Bus-B have constituted accurately the fault section.
These results are entirely identical with the fault location

Y. ZHANG, J. F. ZHANG, J. MA, Z. P. WANG
25
set in advance, so we can confirm exactly fault location
by the hierarchical cluster analysis based on node posi-
tive sequence voltage.
3.2 Fault Detection of IEEE9-Bus System Based
on Node Negative Sequence Voltage
By BPA programs, we can also get node negative se-
quence voltages at ,(Fault) and three times.
Figure 3 is the dendrogram of hierarchical cluster analy-
sis based on node negative sequence voltage.
1
T0 T1 T
Figure 3 shows that the difference of Bus-1 and other
Buses is more distinct by hierarchical cluster analysis
based on node negative sequence voltage. At the same
time, Bus-A, Bus-B and Bus-1 can still be regarded as a
cluster, of course, they have also constituted accurately
the fault section. These results of fault detection based on
node negative sequence voltage are identical with the
results of fault detection based on node positive se-
quence voltage, and both of them are fitting completely
the fault location set in advance. So, it can also identify
effectively fault location that using hierarchical cluster
analysis based on node negative sequence voltage.
Now let us further consider IEEE39-Bus system, Fig-
ure 4 is its electric diagram. In the structure of electricity
grid, Bus-18 appears three-phase short-circuit to ground
fault. By BPA programs, the vector-valued of corre-
sponding variables are only exported one time in each
period. Using these actual measurement data of corres-
ponding variables, we can carry through hierarchical
Figure 3. The dendrogram of hierarchical cluster analysis based on
node negative sequence voltage
Figure 4. Electric diagram of IEEE 39-Bus system
Figure 5. The dendrogram of hierarchical cluster analysis based on
node positive sequence voltage

Y. ZHANG, J. F. ZHANG, J. MA, Z. P. WANG
26
Figure 6. Branch set around BUS-18 fault node
cluster analysis of fault component and non-fault com-
ponent (fault section and non-fault section).
3.3 Fault Detection of IEEE39-Bus System Based
on Node Positive Sequence Voltage
Likewise, we calculate the node positive sequence volt-
age at ,(Fault) and three times. Figure 5 is the
dendrogram of hierarchical cluster analysis based on
node positive sequence voltage.
1
T0 T1 T
In the hierarchical cluster analysis based on node posi-
tive sequence voltage, the fault characteristic of Bus-18
is very obvious. Bus-18, Bus-3 and Bus-17 can be re-
garded as a cluster. For Bus-3 and Bus-17 are directly
connected with Bus-18, the fault of Bus-18 will un-
doubtedly affect its adjacent nodes, as the case stands,
Bus-18, Bus-3 and Bus-17 have also constituted accu-
rately the fault section. Figure 6 is the branch set around
Bus-18 fault node. So, in accordance with three-phase
short-circuit to ground fault, based on node positive se-
quence voltage, the fault location can be detected exactly
by the hierarchical cluster analysis.
These instances have fully proven that fault detection
of fault component (fault section) can be performed by
hierarchical cluster analysis and calculation. The results
of hierarchical cluster analysis are accurate and reliable,
and the dendrograms of hierarchical cluster analysis are
in intuition.
4 Conclusions and Discussion
In wide area backup protection of electric power systems,
the prerequisite of protection device’s accurate, fast and
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, basing on
cluster analysis theory, we are using mainly hierarchical
cluster analysis technology, and seeking after for statis-
tical laws of electrical quantities’ marked changes by
analyzing and computing real-time PMU measurements,
thereby we carry out fast and exact detection of fault
components and fault sections, and finally accomplish
fault isolation.
Multivariate statistical analysis theory is an efficient
theory that can resolve different kinds of complex prob-
lems. It has been applied successfully to many researches
of various fields, and can analyze statistical law con-
tained within subject, even multi-object and multi-index
are associated together. In this paper, we are using
mainly hierarchical cluster analysis of multivariate statis-
tical analysis theory to resolve fault detection problem in
wide area backup protection of electric power systems,
and have got some ideal results. In the study of electric
power systems, multivariate statistical analysis theory
must also have a good prospect of application.
Acknowledgements
This research was supported partly by Key Program of
National Natural Science Foundation of China
(50837002) and the Science Foundation for the Doctors
of NCEPU.
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