Energy and Power En gi neering, 2011, 3, 34-42
doi:10.4236/epe.2011.31006 Published Online February 2011 (http://www.SciRP.org/journal/epe)
Wavelet Entropy Based Algorithm for Fault Detection and
Classification in FACTS Compensated Transmission Line
Amany M. El-Zonkoly, Hussein Desouki
Department of Electri c & Control Engineering, Collage of Engineering & Technology,
Arab Academy for Science & Technology, Alexandria, Egypt
Received November 3, 2010; revised December 10, 2010; accepted December 15, 2010
Abstract
Distance protection of transmission lines including advanced flexible AC transmission system (FACTS) de-
vices has been a very challenging task. FACTS devices of interest in this paper are static synchronous series
compensators (SSSC) and unified power flow controller (UPFC). In this paper, a new algorithm is proposed
to detect and classify the fault and identify the fault position in a transmission line with respect to a FACTS
device placed in the midpoint of the transmission line. Discrete wavelet transformation and wavelet entropy
calculations are used to analyze during fault current and voltage signals of the compensated transmission line.
The proposed algorithm is very simple and accurate in fault detection and classification. A variety of fault
cases and simulation results are introduced to show the effectiveness of such algorithm.
Keywords: FACTS, SSSC, UPFC, Wavelet Transform, Entropy Calculation
1. Introduction
In recent years, it has become more difficult to construct
new generation facilities and transmission lines due to
energy and environmental problems. Hence, it is required
to enhance the power transfer capability of existing
transmission lines instead of constructing new ones. Be-
cause of all that, it became more important to control the
power flow along the transmission lines to meet the
needs of power transfer. On the other hand, FACTS de-
vices have received more attention in transmission sys-
tem operations as they can be utilized to alter power sys-
tem parameters in order to control power flow. With
FACTS technology, such as static var compensators
(SVCs), static synchronous compensators (STATCOMs),
static synchronous series compensators (SSSCs) and
unified power flow controllers (UPFCs), etc., bus volt-
ages, line impedances and phase angles in the power
system can be flexibly and rapidly regulated. In addition,
the FACTS devices have the capability of increasing
transmission capabilities, decrease the generation cost
and improve the security and stability of power system
[1,2]. During fault, the presence of compensating devices
affects steady-state and transient components of current
and voltage signals which create problems with relay
functionality [3,4].
Fault classification and section identification in a
transmission line with FACTS devices is a very chal-
lenging task. Some researchers used current and voltage
signals to determine the fault location and fault resis-
tance only without attempting to find the fault type and
phase involved [5]. Earlier an adaptive Kalman filtering
approach has been proposed for protection of uncom-
pensated power distribution networks [6] and compen-
sated transmission system employing an advanced series
compensator [7]. However, the Kalman filtering ap-
proach finds its limitation, as fault resistance cannot be
modeled and further it requires a number of different
filters to accomplish the task. Different types of neural
networks (NN) based pattern recognition procedures [7-9]
were proposed which large training need set generation,
large training time and design of a new neural network
for each transmission line. Different attempts have been
made for fault location and classification using numerical
methods, wavelet transform, S-transform, TT-transform,
fuzzy logic systems and support vector machines [3-15].
Most of these attempts were trying to classify the fault
and identify the faulted section in a transmission line
compensated either by series capacitor protected by
metal-oxide varistor (MOV) or compensated by thyris-
tor-controlled series compensators (TCSCs) protected by
MOV or compensated by both.

A. M. El-ZONKOLY ET AL.35
In [5], authors took advantage of the post-fault voltage
and current samples taken synchronously from both ends
of the line to build a recursive optimization algorithm to
find the distance to fault in a transmission line compen-
sated with a series FACTS device. The proposed algo-
rithm in [5] is independent of the FACTS device model.
However, it aimed only to the location of fault without
trying to find its type.
In this paper, we are interested in two of the most im-
portant FACTS devices; the SSSC and the UPFC. The
SSSCs are FACTS devices for power transmission line
series compensation. It is a power electronic-based volt-
age source converter (VSC) that generates a nearly sinu-
soidal three-phase voltage which is in quadrature with
the line current. The SSSC converter block is connected
in series with the transmission line by series coupling
transformer. The SSSC can provide either capacitive or
inductive series compensation independent of the line
current [16]. The UPFC, which has been recognized as
one of the best featured FACTS devices, is capable of
providing simultaneous active and reactive power flow
control, as well as, voltage magnitude control. The UPFC
is a combination of STATCOM and SSSC which are
connected via a common DC link, to allow bidirectional
flow of real power between series output terminals of
SSSC and the shunt terminals of the STATCOM [2].
These two devices are suggested due to some problems
encountered in case of lines compensated with conven-
tional compensators such as fixed series capacitor or
TCSC. Problems encountered in case of series compen-
sated lines are as follows [12]:
1) The steady state current is increased significantly
with series compensation and it may be greater than the
line-to-ground fault current towards the boundary of the
line.
2) In a typical series compensation arrangement, the
metal oxide varistor (MOV) is used to protect the ca-
pacitor from over-voltages during a fault. However, it
acts non-linearly during faults and increases the com-
plexity of the protection problem.
3) Voltage and current inversions.
4) The voltage and current signals produced on the
transmission line contain different frequency components
such as non fundamental decaying as well as decaying
DC components due to resonance between the system
inductance and series capacitor, odd harmonics due to
MOV conduction during faults, sub-synchronous fre-
quencies having frequency components varying around
half the fundamental frequency value, high frequency
components caused by resonance between line capaci-
tance and line inductance and fundamental components
of the steady state fault current.
The proposed algorithm is more general it uses voltage
and current signals recorded at one end of the line with
no need for synchronization and is independent of modes
of operation of FACTS devices. The proposed algorithm
is simple and applied to both symmetrical and unsym-
metrical faults with no need for pre-trained NN.
For the purpose of fault identification and classifica-
tion, the wavelet entropy theory is applied to produce a
simple and accurate algorithm. Wavelet transform (WT)
has good time-frequency localization ability so it par-
ticularly adapted to analyze the singular signals caused
by fault. Wavelet transform provides theory basis for
fault detection. The most effective method for fault de-
tection is using a universal applicable quantity (UAQ) to
describe the system and detect the fault. Shannon entropy
is such a UAQ, and wavelet entropy (WE) is formed by
combining WT and Shannon entropy together [17]. A
combination of wavelet and entropy, could exploit the
advantages of both methods to describe the characteris-
tics of a signal. This is because wavelet meets the de-
mands of transient signal analysis and entropy is ideal for
the measurement of uncertainty.
In [18], the proposed algorithm was applied to a
non-compensated transmission line. Therefore, current
waveforms only are used. In this paper due to the pres-
ence of FACTS devices the steady-state and transient
components of current and voltage signals are much af-
fected which create problems with fault detection, classi-
fication and phase selection. The faulted phase couldn’t
be determined using current waveforms coefficients only.
For this reason, the three phase voltages waveforms are
also needed to determine the phase included in fault in
case of SLG fault after the compensating device. That is
why the proposed algorithm in this paper, although it is
simple, it is more detailed and complicated than that in-
troduced in [18].
In this paper, a test system is built using SIMULINK.
The resulting data under different fault types and posi-
tion with respect to the compensating device are ana-
lyzed using the modified WE algorithm than that in [18]
to consider the system compensation. The test results
show the effectiveness of the proposed algorithm.
2. Wavelet Transform and Entropy
Calculations
Lots of fault information is included in the transient
components. So it can be used to identify the fault or
abnormity of equipments or power system. It can also be
used to deal with the fault and analyze its reason. This
way the reliability of the power system will be consid-
erably improved.
Transient signals have some characteristics such as
high frequency and instant break. Wavelet transform is

A. M. El-ZONKOLY ET AL. 36
m
capable of revealing aspects of data that other signal
analysis techniques miss and it satisfies the analysis need
of electric transient signals. Usually, wavelet transform
of transient signal is expressed by multi-revolution de-
composition fast algorithm which utilizes the orthogonal
wavelet bases to decompose the signal to components
under different scales. It is equal to recursively filtering
the signal with a high-pass and low-pass filter pair. The
approximations are the high-scale, low-frequency com-
ponents of the signal produced by filtering the signal by
a low-pass filter. The details are the low-scale, high-
frequency components of the signal produced by filtering
the signal by a high-pass filter. The band width of these
two filters is equal. After each level of decomposition,
the sampling frequency is reduced by half. Then recur-
sively decompose the low-pass filter outputs (approxi-
mations) to produce the components of the next stage
[19,20].
Given a discrete signal x(n), being fast transformed at
instant k and scale j, it has a high-frequency component
coefficient Dj(k) and a low-frequency component coeffi-
cient Aj(k). The frequency band of the information con-
tained in signal components Dj(k) and Aj(k), obtained by
reconstruction are as follows [21].





1
1
:2 ,2
1, 2,,
:0,2
jj
jss
j
js
Dkff j
Ak f
 


 




 (1)
Where, fs is the sampling frequency.
The original signal sequence x(n) can be represented
by the sum of all components as follows [21].
 




 
1112 2
1
J
jJ
j
x
nDnAnDnDnAn
Dn An



 (2)
Various wavelet entropy measures were defined in
[19]. In this paper, the nonnormalized Shannon entropy
will be used. The definition of nonnormalized Shannon
entropy is as follows [21].
log
j
jk jk
k
EE
E (3)
Where Ejk is the wavelet energy spectrum at scale j
and instant k and it is defined as follows.

2
jk j
EDk (4)
3. Proposed Algorithm for Transmission
Line Fault Detection and Identification
During fault, the amplitude and frequency of the test
signal will change significantly as the system change
from normal state to fault. The Shannon entropy will
change accordingly. It becomes incapable of dealing
with some abnormal signals while wavelet can. Wavelet
combined entropy can make full use of localized feature
at time-frequency domains. Wavelet analysis deals with
unsteady signal while information entropy expresses
information of the signal. That is why wavelet entropy
can analyze fault signals more efficiently [17,19,20].
The proposed algorithm detects if there is a fault or the
compensated system is under normal conditions. It also
determines the position of the fault if it is after or before
the compensating device. In addition, the algorithm de-
termines the type of fault if it is a single line to ground
(SLG) fault, line to line (L-L) fault, double line to
ground (DLG) fault or a three line to ground (3LG) fault.
Finally, the algorithm selects the phases involved in the
fault.
The transient signals of the three phase currents and
voltages are produced using the simulation model built
with the power block set of the SIMULINK. A discrete
wavelet transformation is performed using two level
symmetric wavelet for the three phase current signals (ia,
ib and ic) and the ground current ig, where
g
abc
iiii

 (5)
The entropy of each coefficient of the four currents is
then calculated. The sum of absolute entropies of such
coefficients for each current is then calculated (suma,
sumb, sumc and sumg). The sums related to the three
phase currents are then arranged to determine the maxi-
mum sum (max1) the minimum sum (min1) and the in-
termidiate sum (max2).
The wavelet and entropy calculation are performed
also for the three phase voltages in case the algorithm
detected a single line to ground fault after the compen-
sating device. The entropy sums of the three phase volt-
ages are used to determine which phase is included in the
fault.
The proposed algorithm is applied in three main steps.
First, the fault is detected then its type and position with
respect to the compensating device are determined. Fi-
nally, the phases included in the fault are identified. A
detailed flow chart of the proposed algorithm is shown in
Figure 1 which proceeds as follows:
 If sumg < th1 a No Fault condition is declared.
 If sumg > th1 and sumg < 1 then check on max1
If max1 < th2 a No Fault condition is declared
Else if max1 > th2 then it is a LL Fault. Further
check max1 to determine the fault position with
respect to the FACTS device where,
If max1 < th3 then the fault is after the FACTS
device
Else the fault is before.

A. M. El-ZONKOLY ET AL. 37
Figure 1. Flow chart of the proposed algorithm.

A. M. El-ZONKOLY ET AL. 38
 If sumg > th1 but sumg > 1 then check sumg again
where,
If sumg > 1000 then the fault is before the
FACTS device
Else the fault is after.
 To determine the fault type whether it is after or
before the FACTS device proceed as in the fol-
lowing steps.
 For a fault before the FACTS device,
If sumg < th5 then it is a 3LG Fault
Else if sumg > th5 then check
if sumg > max2 then it is a SLG Fault
else if sumg < min1 then it is a DLG Fault.
 For a fault after the FACTS device,
If sumg < th6 then it is a 3LG Fault
Else if sumg > th6 then check
If max1 > th7 then it is a DLG Fault
Else it is a SLG Fault.
 Finally, after determining the location and type of
each fault, the phases involved in each fault is de-
termined as follows,
- for a LL fault the phases involved in the fault
will be PP1 and PP2.
- for a DLG fault the phases involved in the fault
will be PP1 and PP2 in addition to ground.
- for a SLG fault before the FACTS device the
phase involved in the fault will be PP1.
- for a SLG fault after the FACTS device the se-
lection of the phase included in fault was not
possible using sum of currents entropies. There-
fore, the sum of entropies of the coefficients of
each of the phase voltages were calculated and
the phase with the minimum sum was consid-
ered as the faulted phase.
4. Test System
Using the power system blockset (PSB) and the SIMU-
LINK software, the test system is simulated. The test
system is shown in Figure 2 and its data are listed in the
Appendix.
5. Simulation Results
As mentioned before the test system was compensated
by two different FACTS devices, SSSC and UPFC. In
the following the simulation results of the system with
the SSSC are given first then the results with the UPFC
are given next. The simulation frequency was 10 kHz.
5.1. System Compensated with SSSC
For different fault types before and after the SSSC the
FACTS
Device
Vdc


Area 1 Area 2
L 1
L 2 L 3
L 4
L 5
S
Trans 1
Trans 2
T.L. 1 T.L. 2
B1
B2
B3
B4
B5
Figure 2. Power system model.
sum of absolute entropies of the coefficients of each cur-
rent is given in Table 1.
As shown in Table 1, in case of no fault or in case of
connecting extra load (L5) to the system, sumg was less
than th1which is equal to 1 × 10−8 for faults either before
or after the FACTS device. It was also noticed that in
case of SLG fault after the SSSC the selection of the
phase included in fault was not possible using sum of
currents entropies as it is in case of fault before the SSSC.
For example, for an AG fault before the SSSC, suma is
greater than sumb and sumc. However, for an AG fault
after the SSSC, suma is greater than sumb but not sumc.
Therefore, the sum of entropies of the coefficients of
each of the phase voltages were calculated and the phase
with the minimum sum was considered as the faulted
phase. The sum of entropies of the coefficients of the
phase voltages in case of a SLG fault after SSSC are
given in Table 2. As shown in Table 2, for an AG fault
after the SSSC, suma is less than sumb and sumc.
As a sample, the waveforms of the three phase cur-
rents in case of 3 LG fault before the SSSC are shown in
Figure 3. The wavelet coefficients (approximate A2,
level 1 detail D1 and level 2 detail D2) of phase A cur-
rent are shown in Figure 4. In the same way, the wave-
forms of the three phase currents in case of 3 LG fault
after the SSSC and the wavelet coefficients of phase A
current are shown in Figure 5 and Figure 6.
5.2. System Compensated with UPFC
For different fault types before and after the UPFC the
sum of absolute entropies of the coefficients of each cur-
rent is given in Table 3.
As shown in Table 3, in case that sumg was greater
than th1which is equal to 1 × 10-8, greater than 1, but less
than 1000, there will be a fault located after the FACTS
device. It was also noticed that in case of SLG fault after
the UPFC the selection of the phase included in fault was
not possible using sum of currents entropies as it is in
case of fault before the UPFC. For example, for a BG

A. M. El-ZONKOLY ET AL. 39
Table 1. The sum of absolute entropies of the coefficients of each current before and after SSSC.
Before × 106 After × 106
Fault Type suma sumb sumc sumg suma sumb sumc Sumg × 10−6
AG 1.48 1.18 1.06 2.09 1.05 0.94 1.15 26.2
BG 0.98 1.34 1.24 1.75 1.04 1.03 0.99 22.34
CG 1.15 1.02 1.45 1.88 0.89 1.08 1.09 24.57
AB 5.5 4.86 0.99 0.045 × 10−6 2.29 1.94 0.93 0.17
BC 0.91 3.6 2.96 0.043 × 10−6 0.88 1.88 1.54 0.15
CA 5.27 0.94 6.04 0.0517 × 10−6 2.01 0.85 2.48 0.14
ABG 5.91 4.61 1.06 0.59 2.24 1.84 0.89 20.73
BCG 0.98 3.77 2.99 0.74 0.86 1.72 1.43 21.77
CAG 5.39 1.01 6.03 0.60 1.95 0.78 2.33 21.67
3LG 8.20 4.64 5.3 0.33 2.93 3.17 2.18 9.78
Loading 0.99 1.02 1.08 0 0.99 1.03 1.08 0.3
No Fault 0.98 1.02 1.07 0 0.98 1.02 1.07 0
Figure 3. Three phase current waveforms during 3LG fault
before the SSSC.
Figure 5. Three phase current waveforms during 3LG fault
after the SSSC.
Figure 6. Approx. and details of phase A current during
3LG fault after SSSC.
Figure 4. Approx. and details of phase A current during
3LG fault before SSSC.

A. M. El-ZONKOLY ET AL. 40
Table 2. The sum of entropies of the coefficients of the
phase voltages in case of a SLG fault after SSSC.
Fault Type sum a sum b sum c
AG 3.4885 × 103 3.5568 × 103 3.5539 × 103
BG 3.5476 × 103 3.5149 × 103 3.5551 × 103
CG 3.5418 × 103 3.5631 × 103 3.5022 × 103
fault before the UPFC, sumb is greater than suma and
sumc. However, for an BG fault after the UPFC, sumb is
greater than sumc but not suma. For this reason, as i
lated and
the phase with the minimum sum was considered as the
faulted phase. The f entropthe coefficients of
the phase voltagaafe
given ible 4, fo
after tPFC,s thnd
As a sample,rmrer-
nts in case of 3LG fault before the UPFC are shown in
n
case of SSSC compensation, the phases included in a
SLG fault after the UPFC were determined using the
voltage entropies. The sum of entropies of the coeffi-
cients of each of the phase voltages were calcu
sum oies of
es in case of SLG fault ter UPFC ar
n Ta
he U
. As shown in
sumb is les
Table 4
an suma a
r a BG fault
sumc.
the wavefos of the the phase cu
re
Figure 7. The wavelet coefficients (approximate A2,
level 1 detail D1 and level 2 detail D2) of phase A cur-
rent are shown in Figure 8. In the same way, the wave
forms of the three phase currents in case of 3LG fault
after the UPFC and the wavelet coefficients of phase A
current are shown in Figure 9 and Figure 10.
Figure 7. Three phase current waveforms during 3LG fault
before the UPFC.
Figure 8. Approx. and details of phase A current during
3LG fault before UPFC.
Table 3. The sum of absolute entropies of the co
Before × 105
efficients of each current before and after UPFC.
After × 105
Fault Type suma sumb sumc sumg suma sumb sumc sumg × 10−5
AG 2.82 1.92 1.83 3.59 1.95 1.52 2.09 5.069
BG 1.59 2.52 2.23 2.
CG 1.98 1.58 2.93 3.13
AB 9.98 8.57 1.82 0.0746
BC 1.56 6.66 5.39 0.0321
CA 9.83 1.56 11.44
84 1.79 1.789 1.76 4.054
1.51 1.81 2.11 4.592
× 10−5 4.29 3.59 1.75 0.0024
× 10−5 1.51 3.49 3.042 0.0002
0.0773 × 10−5 3.98 1.48 4.92 0.0749
ABG 3.548
BCG 1.61 6.98 1.19 1.56 3.42 3.05 4.913
0.
3LG 15.1 8.7 10.35 0.289 5.535 3.75 4.504 2.288
Loading 1.69 1.69 1.95 0.047 × 10-5 1.69 1.69 1.95 0.047
No Fault 1.66 1.66 1.92 0 1.66 1.66 1.92 0
10.7 8.16 1.87 0.918 4.31 3.49 1.78
5.52
CAG 10.1 1.62 11.51 9564 4.015 1.52 4.79 3.762

A. M. El-ZONKOLY ET AL.41
Table 4. The sum ofopiese coets of the
phase voltages in case ofer UP
Fault Type sum a sum b sum c
entr
a SLG fault aft
of thfficien
FC.
AG 652.73 517 423 673.60673.
BG 666.51 674.0677
CG 663.866 661.2325
0345 662.10
4631 674.5
Figureree pht wavefo
after tPFC.
9. Th
he Uase currenrms during 3 LG fault
Figure 10. Approx. and details of phase A current during
3LG fault after U
erg
PFC.
6. Conclusion
As shown in the paper, the proposed algorithm was very
accurate and simple in the same time. The algorithm
succeeded in detecting the fault, determining its type and
position with respect to compensating device and id
fying the phases included in fault. Test results showed
the effectiveness of the proposed algorithm under any
type and position of fault.
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Voltage: 13.8 kV
Leakage Resistance: 0.002 pu
Leakage Reactance: 0.08 pu
ransformer 2 (Y/Y): Rated Voltage: 735/230 kV
Rated Power: 300 MVA
Leakage Resistance: 0.002 pu
Reactance: 0.0195 pu
d
s: 48 pulse
Series Coupling Transformer (Y/Y):
Rated Voltage: 138/147 kV
Rated Power: 100 MVA
Leakage Resistance: 0.002 pu
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Short Circuit Capacity: 21000 MVA
Area 2: Rated Voltage: 735 kV
Short Circuit Capacity: 30000 MVA
Transformer 1 (/Y): Rated Voltage: 13.8/735 kV
Rated Power: 2100 MVA
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Appendix
System Parameters of Figure 2 (Base MVA =
100)
Area 1: Rated
T
Leakage Reactance: 0.15 pu
Transmission Lines: Resistance: 0.001 pu
Loads: Loa 1: 100 MW
Ls 2 and 3: 1.32 MW, 330MoadVAR
Load 4: 250MW
Load 5: 300MW
SSSC: Rated Power: 100 MVA
Nominal DC Voltage: 20 kV
Nominal AC Voltage: 138 kV
Number of Pulses: 48 pulse
UPFC: SSSC and STATCOM each;
Rated power: 100 MVA
Nominal DC Voltage: 20 kV
Nominal AC Voltage: 138 kV
Number of Pulse
Leakage Reactance: 0.05 pu
Shunt Coupling Transformer (Y/Y):
Rated Voltage: 138/735 kV
Rated Power: 100 MVA
Leakage Resistance: 0.002 pu
Leakage Reactance: 0.02 pu