DISTANCE PROTECTION FOR SIX-PHASE TRANSMISSION LINES BASED
ON FAULT INDUCED HIGH FREQUENCY TRANSIENTS AND WAVELETS
M. M. Mansour
H. E. A. Talaat
S . 0. Faried
Ain Shams University
Cairo, E a p t
mmsmansour@ieee.org
King Saud University
Riyadh, Saudi Arabia
htalaat@kr;u.edu.sa
Universityof Saskatchewan
Saskatoon, Canada
sherif_of aried@engr.usask.ca
Ammar A. Hajjar
Tishreen University
Latakia, Syria
aahajjar@hotmail.com
Abstract
Six-phase transmission is an optimal solution for
increasing the power transmission capability of overhead
power transmission lines over existing rights-ofiway. This
new technology, however, causes some protection
problems. This paper introduces a new technique based on
wavelet transform for high-speed distance protection of
six-phase transmission lines. The technique utilizes a
wavelet to capture the fault induced high frequency
transient currents superimposed on the power Pequency
modal currents. The trip decision is based on the relative
arrival times of these high frequency signals at the
relaying point. The introduced technique is tested and
validated through simulation studies. The results show
that the technique is accurate and high-speed in fault
detection irrespective of the fault vpe, fault inception
angle, and fault resistance. Moreover, it is insensitive to
the line terminals and transposition.
Keywords: SLx-Phase Transmission Lines; Distance
Protection; High Frequency Transient; WaveletAnalysis.
1.
INTRODUCTION
Three-phase transmission system encounters some
problems such as increasing demand and restrictions on
rights-of-way (environmental laws). In this respect, sixphase transmission system is introduced as an optimal
solution for the aforementioned problems. The existing
double-circuit three-phase transmission line can be
successively converted to a singlecircuit six-phase line
[1,2]. In this context, the first empirical six-phase line in
the world was energized in USA in 1992 [2].
Therefor, there is a need to establish protection
schemes for six-phase transmission system because the
additional three-phases complicate the fault analysis and
consequently the required protection. In this respect, the
number of shunt faults is “120” in a six-phase system
whereas it is only “1 1” in a three-phase system [3].
So far, there is a few protection schemes dedicated for sixphase transmission lines [4-61. In this paper, a new
protection approach based on wavelet transform (WT) and
distance protection is presented.
The WT of a signal consists of measuring the similarity
between the signal and a set of translated and scaled
version of the basis function “mother wavelet”. The
mother wavelet is a chosen fast decaying oscillatory
function The WT maps a given nonstationary signal from
the time domain into time-frequency (scale) domain. The
main advantage of the WT is its ability to extract a tiny
discontinuity on a disturbed signal [7]. T h s feature is used
for detecting the abrupt disturbances such as faults in
transmission lines [8-lo].
In this paper, a useful application of the WT is
presented for distance protection of six-phase transmission
lines. The technique is based on fault induced high
frequencies (HF) transient modal currents captured using
wavelets and the travelling wave theory. Extensive
computer simulations of the proposed scheme show that
the technique is accurate and hgh-speed irrespective of
fault type, fault inception angle and fault resistance.
Moreover, it is unaffected by line terminals and line
transposition.
2.
WAVELET TRANSFORM
Wavelet transform is relatively a new mathematical
techmque for a nonstationary signal analysis. In this
respect, the WT ofa time dependent signalfor) consists of
finding a set of coefficients C/a,b) that measure the
similarity between the signal and a set of scaled
(compressed or dilated) and translated (shifted) versions of
a function y(t) called the mother wavelet that given by:
where “a” and “b” represent the time dilation and
translation respectively. The selection of the mother
wavelet depends on the application. The coefficients
C!a,b) , or the continuos wavelet transform, are defined
by the following inner product:
Proceedings of the 2002 IEEE Canadian Conference
on Electrical & Computer Engineering
0-7803-7514-9/02/%17.00 0 2002 IEEE
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The arrived phase signals are first transformed to their
modal signals. The first mode (mode 0) is frequency
dependent and refers to the ground mode that is usually
used to distinguish grounded faults. The other five modes
(model ...mode5) are frequency independent and refer to
the aerial modes that are present for any kind of fault.
Accordingly, the fault distance is determined based on the
aerial rnodes and their velocity.
I--
CWT(a,b)=
If
(t).;t,,dt).dt
(2)
-00
where “*” refers to complex conjugate.
Wavelet transform of a sampled signal can be obtained
by using the following discrete wavelet transform (DWT):
where, uom,k represent a time exponential dilation and’
time shift, respectively, n, k, a. are integers; % is some
selected spacing factor (usually chosen equal to “2” for
dyadic grid), and the dilation index (scaling) m is
0,1,2,3
,....
The DWT analysis involves successive pairs of lowpass and high-pass filters at each scaling stage of the WT.
The first scale covering a large frequency range at the high
frequency end of the spectrum with the highest time
resolution. The higher scales covering the lower end of the
frequency spectrum with progressively shorter bandwidths
with increasinglylonger time interval [7-91.
3. FAULT INDUCED TRANSIENTS AND
4a’WAVELET FOR SIX-PHASE LINES
DISTANCE PRQTECTION
The proposed approach uses wavelet transform as a
fault induced HF transient currents detector. For this
purpose, it is tuned to extract the HF currents
superimposed on the modal power frequency currents at
freque.ncy ranges between 50 and 100 IcHz. In this respect,
the so-called“D4” mother wavelet, which is more suitable
for transient analysis, time-frequency localizing, is used
[9]. The fault distance calculation is based on the
reflections times of the HF signals either from the fault
point only or from both the fault point and far-end bus.
This depends on the existence of a connection between the
fault and the ground.
MODAL TRANSFORM
4.1. Ungrounded Faults
When a fault occurs on a power transmission line, high
frequency transient signals of currents and voltages are
induced at the fault point. These HF signals travel toward
the line ends then they reflect back and forth between the
fault point and the line ends until the post fault steady state
is reached. However, these HF signals, which contain a
wealth information about the fault type, distance, and its
direction are superimposed on the power frequency signals
of the faulted and unfaulted phases due to the mutual
coupling between phases. Therefore,modal transformation
is used to decouple the phase signals into their respective
aerial and ground modes. The relation between the phase
currents and the modal currents given by:
Iphase = T
Imde
When the fault is ungrounded or symmetrical, the
reflection from the remote end is insignificant and the fault
distance x is determined by measuring the time interval
between the first two consecutive peaks of similar polarity
of the WT coefficients of the considered signal as follows:
x=- V .z
(6)
2
wherc: V is the wave velocity of the aerial mode and z is
the time interval between the two consecutive peaks of the
WT coefficients. On the other hand, if the first two
consecutive peaks are of opposite polarities, then fault is
considered out of protection zone.
(4)
where Tis the modal transformationmatrix and Iphme,Imode
are the phase and modal current vectors, respectively. In
this study, the six-phase transmission line is assumed
ideally transposed; therefore the Clarke’s constant and real
transformationmatrix is used [4]:
(5)
4.2. Grounded Faults
For a grounded fault the reflections from the fault point
and Rrom the remote end buses will be observed at the
sendhg end of the faulted line. Depending on the fault
distance, the reflections from the remote end buses may
arrive before or after those reflections from the fault point.
It c m be easily verified by using the lattice diagram
ill arrive
method, that the remote end bus reflections w
later than the fault reflections if the fault occurs within the
first half of the line. The opposite will be true if the fault
occurs in the second half of the line. Another problem
arises due to a ground connection is that the reflections
may be from the adjacent (faultedunfaulted) line.
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Therefor, a suitable algorithm is developed to distinguish
the faulted line and the fault distance as follows:
If the first two consecutive reflections are with
same polarity, the fault is in the first half of the line.
Moreover, if the time interval between these reflections
plus the time interval between the first one and the first
significant reflection of opposite polarity is equal to
twice the traveling time of the considered line, the fault
is on the considered line. Otherwise the fault is on the
adjacent line.
If the first two consecutive reflections are with
opposite polarities, the fault should be in the second
half of the line. Moreover, if the time interval between
these reflections plus the time interval between the first
one and the first significant reflection of same polarity
is equal to twice the traveling time of the considered
line, the fault is on the considered line. Otherwise the
fault is on the adjacent line.
0
If the two peaks of the WT coefficients are equal
this refers to coincidence between the reflected signals
from the fault and from the far-end bus.
Fig. 1 shows a schematic block diagram of the proposed
distance protection approach
5- SIMULATION RESULTS
A verification of the developed approach with practical
cases is carried out with the help of electromagnetic
transient program (PSCADEMTDC) [ 111. The algorithm
of the proposed approach is programmed under the
MATLAB environment and using its wavelet toolbox
[ 121. The study is conducted on a 230 kV six-phase power
transmission system shown in Fig. 2. The line parameters
are considered to be frequency dependent. The source’s
impedances Zsl, Zs2 and Zs3 are 20, 10 and 20 ohms
respectively. The arc resistance is included in the fault
model.
L1= 200 km
I L,2=1OOkm
I
Fig. 2. A one line diagram of a six-phase power transmission
system.
The system is simulated under various types of faults at
different locations, fault resistances, source configurations
and fault inception angles. Moreover, the line transposition
and untransposition are also considered. The relay is
located at bus 1. A sampling frequency of 200 kHz is used
and the CWT at scale 2 is used to capture the HF current
signal superimposedon the aerial modes.
5.1 Source Configuration
Transform
Wavelet
Transform
Ungrounded fault
A
Out of zone fault
Trip
decision
Fig. 1. A flowchart of the proposed distance protection approach.
Fig. 3 depicts the CWT coefficients of the modal current
signal corresponding to phase “a” to ground fault at 180
km from source S1 on line L1 for fault inception angle of
90” of phase “a”. Fig. 3.a corresponds to S1, S2, S3
impedances of 20, 10 and 20 i2 respectively, whereas Fig.
3.b corresponds to equal sources impedances of 20 R. As
shown in Fig. 3.a and 3.b, the first and second HF transient
signals arrive at busbar 1 with positive and negative
polarities at times tl = 5.122 ms, t 2 = 5.255 ms
respectively, this signifies that the fault is at the second
half of the line. The time interval z1between tl, t2 is 0.133
ms and the time interval z2between tl and tlois 1.2002 ms,
where tlois the arrival time of the first significant positive
reflection, tlo= 6.3222 ms. Hence, z = 21+22= 1.3332 ms
which correspond to the 399.98 km which equals to the
twice of the line length of L,. Therefore, the faulted line is
L1and the fault distance is 180.05 km.Accordingly a trip
decision from the relay near bus1 should be issued to the
dedicated circuit breaker. This assures that the technique is
insensitive to the system source configuration. This is due
to the busbar capacitances, which act as a short circuit at
the considered range of frequency.
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3-15
15
C
2 IO.
3
n
2
w-
0
0.15
I
a
L
L
2
m
+ +
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-a
-
O.O!j
1 '
-
-
w-
0
iv),-0.15
v)
e-10.
5
Time,ms
3-15L
I
k
-o.o!j -
-0.25
-
'tl
-1c
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Time,ms
5.4 Fault Types
5.2 Fault Resistance
Fig. 4 shows the WT coefficients of the modal transient
current for a single line to ground fault 'f-g' at 25 km from
busl for a 135' fault inception angle and 400 i2 fault
resistance. Despite the WTC magnitude reduction, the
wave shapes of the captured signals remain unchanged and
accurate fault distance is calculated as follows: tl = 4.6 ms,
tz = 4.764 ms and t4 = 5.772 ms, thus z 31-4. Hence, L1
is the faulted line and the fault distance is 24.6 lan. The
obtained result proves that the proposed approach is
insensitive to the fault resistance.
Fig. 6 shows the WT coefficients for symmetrical 3-phase
fault '"b-d-f' at 130 km of SI. Since WO= 0 and the first
two consecutive reflections are with similar polarities, the
fault is at L1and the fault distance is130.5 lan.
= In,
U)
Fig. 6 . A 3-phase "b-d-f' fault at 130 km of line Ll.
Fig. 7 shows the WT coefficients for a 4-phase fault "cdAlso, since (WO= 0) and the first two
e-f' at 60 km of L.
consecutive reflections are with opposite polarities the
fault is on the adjacent line and the relay will reset.
4.5
5
5.5
6
Fig. 4. A line-to-ground "f-g" fault at 25 km from S1 with
~p = 135" and Rf = 400 a.
5.5 Untransposed Line
Due to untransposition, mutual couplings arise between
the phases which consequently affect significantly the
ground mode signal, whereas the aerial mode signals are
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References
5.6
5.4
5.8
6
6.2
6.4
Fig. 7. A 4-phase “c-de-f” fault at 60 km of line L2.
slightly affected. Since the proposed method is based on
the aerial modes, the WT coefficients will not affected by
l i e untransposition as shown in Fig. 8, which corresponds
to a six-phase fault at 130 km of the untransposed line L1.
Therefore, the proposed approach is suitable and accurate
for both transposed and untransposed lines.
E 20‘
? 15.
-3 1 0 .
5.
t
tl
B -5.
-10.
3
-
-20
-D+
t3
L
o
$ -15.
J
+ c
-
v
4
1
Tme,ms
Fig. 8. A six-phase fault at 130 km fiom S1 of
untransposed line LI.
an
Finally, it is worth noting that the proposed distance
protection technique is complemented by the authors with
a fault classification and phase selection technique 161.
6- CONCLUSION
This paper presents a new distance protection technique
based on the WT and a fault induced HF transients to be
used for six-phase transmission. The technique utilizes the
WT for extracting the fault induced HF transient signals,
and the traveling waves theory for determining their
consecutive arrival times. Studies show that the technique
is high-speed and accurate irrespective of the fault type,
fault inception angle and fault resistance. Moreover, it is
not affected by the line tennmls and line transposition.
The accuracy of the technique is proportional to the
sampling frequency rate; however the error in determining
the fault distance in the worst case does not exceed 1.5
km. This accuracy could be improved either by increasing
the sampling frequency rate or by using a smoothing
algorithm
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