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Fault Line Selection Method of Small Current Grounding System Based on Wavelet Packet and Multi Frequency Band Analysis
Wang Xiaowei, Lu Yongfang, Hou Yaxiao
Fault Line Selection Method of Small Current Grounding System Based
on Wavelet Packet and Multi Frequency Band Analysis
Wang Xiaowei, 2Lu Yongfang, 1Hou Yaxiao
School of Electrical Engineering and Automation, Henan Polytechnic
University, Jiaozuo, 454000, Henan Province, China
E-mail: [email protected]
2
School of Mechanical and Electrical Engineering, Jiaozuo University, Jiaozuo 454000,
Henan Province, China
1
*1
Corresponding Author
Abstract
This paper puts forward a fault line selection method of multi-band correlation analysis based on
transient zero sequence current. The method first makes a decomposition of the transient zero sequence
current signals when fault occurs with the use of db10 wavelet packet to specify the characteristic
information of the feeders; then, according to the energy principle, the first and second largest
frequency bands are selected as the characteristic frequency bands (CFB) of transient zero sequence
current on each feeder; next, correlation analysis of the two characteristic frequency bands (CFB1 and
CFB2) is made respectively as well as the calculation of their integrated correlation coefficients and
average correlation coefficient; finally, the difference of the maximum and minimum average
correlation coefficients is compared with the threshold value to determine the fault line. A large
number of simulations show that the method can accurately determine the fault line whatever the fault
angle and grounding resistance is.
Keywords: Wavelet packet, Characteristic frequency bands, Fault line selection, Correlation
analysis
1. Introdution
The fault line selection problem of distribution networks has not been effectively resolved, needing
to be further researched. Nowadays the existing fault line selection methods mainly include line
selection based on steady-state signal and transient signal. Owing to the system will produce abundant
transient information after it has a single-phase ground fault. And the amplitude of the fault transient
volume is 10 times or even dozens of times greater than the steady-state volume. Therefore, many
scholars pay attention to the fault line selection based on the transient. Paper [1] gets the feature
frequency band and calculates relative energy to select circuit by making use of first half wave
transient information of the fault zero-sequence current. Paper [2] gets feature frequency band of fault
zero-sequence current and select circuit by comparing the non power frequency component polarity of
fault lines and not faults lines, with the help of feature frequency band that Hilbert-Huang transform
extracts fault zero-sequence current. Paper [3] extracts the fault signal transient by using the S
transform select circuit according to the line selection criterion that Shannon fuzzy entropy votes
mechanism to form.
On the basis of previous studies, this paper presents a novel fault line selection method which based
on wavelet packet and multi frequency band analysis. At the same time, it uses the circuit recluse to
monitor the possible fault current sequence circularly, which can improve the reliability of the results.
The simulation results show that the accuracy rate of the fault line selection method is high, and it can
be applied to the fault line selection of cable mixed in distribution networks.
2. The transient ground current
The transient ground current is determined by the transient capacitance current and the inductance
current linear superposition, its characteristic changes with both changing. Based on this analysis,
although their rC and rL have a very small difference, their frequency is quite different. So they can’t
International Journal of Digital Content Technology and its Applications(JDCTA)
Volume7,Number6,March 2013
doi:10.4156/jdcta.vol7.issue6.134
1176
Fault Line Selection Method of Small Current Grounding System Based on Wavelet Packet and Multi Frequency Band Analysis
Wang Xiaowei, Lu Yongfang, Hou Yaxiao
compensate each other. Thus, the residual current and detuning are no longer applicable concepts under
the condition in the analysis of transient problem. In initial stage of the transient process, transient
capacitance current characteristic play a major role to the transient grounding current. In order to
achieve the goal of balancing DC (Direct Current) component of the transient inductance current, it
needs to produce a DC component which is equal in size and opposite in direction during the transient
grounding current. Although it does not alter the polarity of the grounding current half wave, it has a
significantly impact in the amplitude of the ground current.
The mathematical expression of the transient ground current id is as follows.
id  iC  iL  ( I Cm  I Lm ) cos(t   )
t
t
(1)


f
 I Cm [ sin  sin t  cos  cos  f t ]e  C  I Lm cos  e  L

Equation (1), the first is the fault current steady-state component; it is the amplitude difference of
the steady capacitance current and steady inductance current. The rest is the transient component of
ground fault current; it is a sum of transient free oscillation component of the capacitance current and
transient DC component of the inductor current. Their amplitude not only can’t offset each other, but
also even may be superposed with each other, which leads to the amplitudes of transient grounding
current increasing obviously.
Based on the above analysis we can get following conclusion: after the single phase earth fault
occurs, the ground will flow the transient capacitance current with a very fast attenuation and the
transient inductance current with a very slow attenuation. No matter the neutral point of power grid
adopts grounded or via arc-suppression coil ungrounded. The transient capacitive current determines
the amplitude and frequency of the transient grounding current, their amplitude are related with initial
phase. Although the amplitude of transient grounding current is quite large, its duration is shorter,
about 0.5～1.0 power frequency period.
On the inductor current of the transient process, the initial value of the DC component has some
connection with the initial phase angle and the core saturation degree. Frequency of the transient
inductance current is equal to power frequency, its duration can be to about 2～3 power frequency as
usual. In order to balance the DC component, grounding current also produce a DC component which
is equal in size and opposite in direction. It only can raise the amplitude of transient grounding current.
If the arc can not be extinguished quickly for some reasons, it will be into the power state after the
attenuation of DC component is over. In this state, when the power frequency current is zero passage,
the grounding arc still has a opportunity to put out [4].
In general, the grounding arc extinction doest not affect the transient grounding current size directly.
But the reignition phenomena that exist in the process of extinction of arc will cause arc over voltage.
Then it can effectively reduce the grounding arc reignition phenomena through the arc suppression coil
grounding system, and has a significant inhibiting effect on the over voltage.
3. The simulation model of small current grounding system
Figure 1. Small current grounding system
1177
Fault Line Selection Method of Small Current Grounding System Based on Wavelet Packet and Multi Frequency Band Analysis
Wang Xiaowei, Lu Yongfang, Hou Yaxiao
According to small current grounding system as shown in Figure 1, it established a simulation
model by MATLAB toolbox, as shown in Figure 2.
The model adopts unlimited high-power source [5]. The source is 110kV, f=50Hz, x/r=7. The line 1,
2 and 5 are overhead lines, their length are 10km, 8km and 20km. The line parameters are
r1=0.55Ω/km, l1=1.254mh/km, c1=0.061µF/km, c0=0.038µF/km. The line 4 is cable line; its length is
10km. Its line parameters are r1=0.092Ω/km, l1=0.257mh/km, c1=0.160µF/km, c0=0.108µF/km. The
line 3 is the mix of overhead line and cable line. The length of cable line is 2km and the overhead line
is 6km. The total capacitance is 3c0=5.96µF, the over compensation degree of suppression coil is 10%
The inductance l of suppression coil can be calculated from the following equation:
I l  1  10%  I c
(2)
Figure 2. MATLAB simulation model
1
1

 1.574 H
1.1 3 2 c0
According to experience, the resistance of arc suppression coil is 10% the reactance value.
This paper adopts fixed step and discrete algorithm, the sampling time is Ts=1e-5s. The time of fault
occurring will be set in the process of the simulation.
Then U 0 / j l  1.1U 0 j c0 , So l 
4. Fault simulation
In the 20km of the overhead line 5, we can devise a faulty module on A phase to simulate
grounding short circuit. In 0.02s, namely the fault switching angle is 0°, the circuit will occurs
grounding fault until 0.04s. When the bus insulation monitoring device finds 3U0 rise, it will measure
the fault current and voltage by the bus bar connecting line protection unit [6]. The result is as Figure
2 and Figure 3.
Figure 3. Current waveform of overhead line 5 Figure 4. Voltage waveform of overhead line 5
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Fault Line Selection Method of Small Current Grounding System Based on Wavelet Packet and Multi Frequency Band Analysis
Wang Xiaowei, Lu Yongfang, Hou Yaxiao
From Figure 3 and Figure 4 , we can clearly see the three-phase voltage and current waveform
changes of the fault lines A, B, C. Therefore, using MATLAB/SIMLINK simulation toolbox, we can
get the changes rules of each correlative in detail in the small current grounding system. It gives a basis
to explore and establish the line selection algorithm.
In this paper, the zero-sequence current is no longer the zero sequence components of three
sequence currents in the traditional sense. It is the three-phase current instantaneous value of 1/3,
similarly the zero-sequence voltage is also the three-phase voltage instantaneous value of 1/3.
(3)
i  (i  i  i ) / 3
0
a
b
c
u0  (ua  ub  uc ) / 3
(4)
5. Wavelet packet and multi frequency band analysis
Wavelet packet analysis is a kind of more detailed analysis and reconstruction method to signal,
which is developed from the wavelet analysis. According to the need, it can do more detailed
descriptions on the high frequency part of the signal that have not been decomposed in the wavelet
decomposition process. Then it has a time-frequency analysis on the signal after the best wavelet
packet basis function decomposed. Its analysis ability is greater about signal, but the calculation
quantity will increase [7].
Advantages of the wavelet line selection method are as follows: first, the method is both suitable to
neutral point ungrounded and via arc suppression coil in the distribution systems. Second, the method
is particularly adapted to the complex fault status, fault waveform messy situation. This can form some
complementary advantages with the steady-state line selection method.
Wavelet packet analysis provides a more accurate signal analysis method. The method has a level
dividing on the band, which can improve the time-frequency resolution. Wavelet packet decomposition
structure diagram is shown in Figure 5.
Figure 5. Wavelet packet decomposition tree structure diagram
A shows low-frequency, D shows high- frequency. The number of the end expresses levels of the
wavelet packet decomposition (i.e., scale degree). The decomposition has the following equation:
(5)
S  AAA3  DAA3  ADA3  DDA3  AAD3  DAD3  ADD3  DDD3
So each frequency bands is energy of wavelet packet calculated as follows:
   [k( f ) (m)]
2
(6)
n
Where k( f ) is frequency band coefficient of the (f，k) node by wavelet packet, and each band is
composed by m coefficients [8].
According to the feature of the analyzed signal, wavelet packet analysis can choose the appropriate
frequency band adaptively to match with the signal spectrum. Thus, it can improve the time-frequency
resolution and has a broad prospect.
When the line is faulted，the fault line selection method of distribution networks based on the
transient zero sequence component can make use of the db10 wavelet packet to decompose the
transient zero sequence current flowing through each feeder [9-11]. Then the novel can find the max
and second-largest energy characteristic frequency band and have a correlation analysis of the wavelet
packet decomposition coefficient on the two frequency band to select the fault line [12-14]. Line
selection process is shown in Figure 6.
Step1: When the bus insulated monitoring device find 3U0 (zero-sequence voltage) increasing, it
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Fault Line Selection Method of Small Current Grounding System Based on Wavelet Packet and Multi Frequency Band Analysis
Wang Xiaowei, Lu Yongfang, Hou Yaxiao
will measure the zero-sequence current from the line protection unit connected by the bus. Then using
the db10 wavelet packet to have a five-layer decomposition on the transient zero-sequence current
flowing through each feeder without the lowest frequency band (5,0) of power frequency. Then
calculate the frequency band signal corresponding to the energy by (6) to find the max and
second-largest energy characteristic frequency band. The max energy frequency band is just the
frequency band of the feeder transient capacitance current having the most concentrated distribution
and the most obvious fault feature [15, 16].
Step2: After line is faulted, in turn to make correlation analysis operations about the wavelet packet
decomposition coefficients of the two frequency band of each line to calculate the correlation
coefficient matrix M1, M2.
Step3: According to M1, M2 to seek the correlation coefficient  s (i ) of each line relative to other
lines, where i=1, 2,…,n, n is the number of lines; s=1, 2, representing two characteristic frequency
band. As the line selection criterion, the integrated correlation coefficient  (i ) can take the mean of the
two frequency band correlation coefficient, as in (7) and (8):
n
1
(7)
 s (i ) 
i j

n  1 j 1, j  i
1
(8)
2
Step4: Comparing  (i ) of each line, when the difference  of the largest and the smallest  (i )
 (i )  [ 1 (i )   2 (i )]
Amp./A
is less than a certain threshold  set (the section take 0.2 in simulation test), it is determined that the
system is bus ground fault. Otherwise, the running lines should be sorted in ascending order of the
integrated correlation coefficient.
6
4
2
0
-2
-4
0.02
0.22
0.02
0.22
0.02
0.22
0.02
0.22
0.20
0.22
0.24
0.26
0.28
0.30
0.24
0.26
0.28
0.30
0.24
0.26
0.28
0.30
0.24
0.26
0.28
0.30
0.24
0.26
0.28
0.30
t/s
A m p./A
Amp./A
5
0
-5
A m p./A
10
5
0
Amp./A
10
0
-10
-20
Figure 6. Fault line selection process
t/s
时间
t/s
时间
t/s
时间
10
5
0
-5
t/s
Figure 7. Zero sequence current of each line
when cable is fault
Step5: According to the line selection result, the fault line selection device sends a jumping
command to the first possible grounding line selected and starts the reclosed. When the bus insulated
monitoring device find 3U0 (zero-sequence voltage) exist, line selection succeed. If not, the line is the
fault line. Then, it will treat possible grounding lines just as above on the basis of the line label
successively, until the ground line is selected. The bus insulated monitoring device can use the tripping
mode or the grounding alarm mode according to demand. If choosing the tripping, it needs to upload
the tripping line selection message to the main station and does not start the reclosing. If choosing the
grounding alarm, it should start the reclosed and upload the grounding alarm event message to the main
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Fault Line Selection Method of Small Current Grounding System Based on Wavelet Packet and Multi Frequency Band Analysis
Wang Xiaowei, Lu Yongfang, Hou Yaxiao
station.
According to the MATLAB model of Figure 2 to simulate, the result is as follows:
1) Installing a faulty module in the 4km away of the cable transmission L4 simulate the cable lines
ground fault. The ground fault will occur in the 0.02s when the fault close angle is 450. The fault will
disappear in 0.03s. When the bus insulated monitoring device find 3U0 increasing, it will measure the
zero-sequence current from the line protection unit connected by the bus. As shown in Figure 7.
Using the db10 wavelet packet to have a five-layer decomposition on the transient zero-sequence
current flowing through each feeder to find the max energy characteristic frequency band (5, 1) and the
second-largest energy frequency band (5,3). Making a correlation analysis about the wavelet packet
decomposition coefficients of the two characteristic frequency band acquire two correlation coefficient
matrix.
 1.0000 -0.1531 0.7879 -0.4903 -0.1805 
 -0.1531 1.0000 -0.0783 -0.7183 -0.1519


M1   0.7879 -0.0783 1.0000 -0.5066 -0.2207


 -0.4903 -0.7183 -0.5066 1.0000 -0.0462
 -0.1805 -0.1519 -0.2207 -0.0462 1.0000
 1.0000 0.4530 0.9436 -0.6406 -0.1176 
 0.4530 1.0000 0.5349 -0.8233 -0.2254 


M2   0.9436 0.5349 1.0000 -0.6824 -0.1547 


 -0.6406 -0.8233 -0.6824 1.0000 -0.2757
 -0.1176 -0.2254 -0.1547 -0.2757 1.0000
The integrated correlation coefficient of matrix M1 is [-0.0090 -0.2754 -0.0044 -0.4404 -0.1498]，
matrix M2 is [0.1596 -0.0152 0.1604 -0.6055 -0.1934], the comprehensive line selection result
is [0.0753 -0.1453 0.0780 -0.5229 -0.1716], the difference between the max integrated
correlation coefficient and the least correlation coefficient is 0.6009>0.2, so the line 4 is ground fault.
When the bus insulated monitoring device find 3U0 disappear, the selection result is correct. According
to the experimental data, the line selection device is very sensitive to the fault of the nonlinear element
as cable.
2) Installing a faulty module in the A phase to the end of the overhead lines L5 simulate the
overhead lines ground fault. The ground fault will occur in the 0.02s when the fault close angle is 0°.
The fault will disappear in 0.04s. When the bus insulated monitoring device find 3U0 increasing, it will
measure the zero-sequence current from the line protection unit connected by the bus. It is shown in
Figure 8.
10
10
5
5
0
0
-5
-5
-10
0.02
0.22
0.24
0.26
0.28
0.02
0.3
0.22
0.24
0.26
0.28
0.30
时间
时间
(a) Line 1
(b) Line 2
20
20
10
10
0
0
-10
-10
-20
0.02
0.22
0.24
0.26
0.28
0.30
0.02
0.22
0.24
0.26
0.28
0.30
时间
(c) Line 3
(d) Line 4
1181
Fault Line Selection Method of Small Current Grounding System Based on Wavelet Packet and Multi Frequency Band Analysis
Wang Xiaowei, Lu Yongfang, Hou Yaxiao
20
0
-20
-40
-60
0
0.02
0.22
0.24
0.26
0.28
0.30
(e) Line 5
Figure 8. Zero sequence current of each line when line 5 is fault
Using the db10 wavelet packet to have a five-layer decomposition on the transient zero-sequence
current flowing through each feeder without the lowest frequency band (5, 0) of power frequency. Then
calculate frequency band energy to find the max energy characteristic frequency band (5, 1) and the
second-largest energy frequency band (5, 6). Making a correlation analysis about the wavelet packet
decomposition coefficients of the two characteristic frequency band acquire two correlation coefficient
matrix.



M1  



1.0000 0.0255 -0.1116 -0.1320 -0.4658 
0.0255 1.0000 -0.2146 -0.3618 -0.5751 
-0.1116 -0.2146 1.0000 0.3394 -0.4603

-0.1320 -0.3618 0.3394 1.0000 -0.0858
-0.4658 -0.5751 -0.4603 -0.0858 1.0000



M2  



1.0000 0.0079 -0.0531 0.0461 -0.1230
0.0079 1.0000 -0.2426 0.0463 -0.4035
-0.0531 -0.2426 1.0000 -0.6554 0.4554

0.0461 0.0463 -0.6554 1.0000 -0.8849
-0.1230 -0.4035 0.4554 -0.8849 1.0000
According to the (7) and (8)，the correlation coefficient of matrix M1 is [-0.1710 -0.2815 -0.1118
-0.0601 -0.3968]，matrix M2 is [-0.0305 -0.1480 -0.1239 -0.3620 -0.2390]，the integrated
correlation coefficient is [-0.1008 -0.2148 -0.1179 -0.2110 -0.3197]，the difference between the
max integrated correlation coefficient and the least correlation coefficient is 0.2171>0.2，so the bus is
ground fault. And the ground possible lines are L5, L2, L4, L3 and L1 from big to small；Then give a
jump command to line 5, when the insulated monitoring device find 3U0 disappear, the line 5 is just
ground line.
In the experiment, if only to analysis the integrated correlation coefficient of matrix M2, the result is
that line 4 is faulted. This is simply because there are lots of nonlinear elements, which makes the 3
and 5 harmonic suffer the severe interference. While the 3 and 5 harmonic mainly exists in the low
frequency band of signal to lead to the line selection device malfunction. After line 4 is tripping, the
bus insulated monitoring device find 3U0 not disappeared, then send a special closing command to line
4. Besides, it also gives a jump command to line 5 on basis of the sorting. If 3U0 disappear or return to
normal after the line 5 is tripping, line 5 is faulted line.
All of the fault line, fault close angle, transition resistance and fault location are different; we can
make a simulation with the above method. The result is in the Table 1 as follows:
Table 1. Results of fault line detection
Fault
line
L5
L4
Bus
Fault
distance/(km)
Res./(Ω)
Angle/(°)
Integrated correlation coefficient
Result
18
20
0
[-0.0865 -0.1212
-0.2107 -0.3232 -0.3149]
10
100
30
[-0.2460 -0.0974
-0.0907 -0.1511 -0.3364]
Correct
Correct
-0.3114
4
20
0
[0.0368
0.0368]
Correct
3
0
100
20
30
0
[0.0298 -0.1771 -0.3334 -0.3584 0.0298]
[0.0992 -0.0994 -0.1970 -0.2356 0.0992]
Correct
Correct
0
100
30
[0.0702
Correct
-0.1826
-0.1273
-0.1718
-0.4531
-0.1742
0.0702]
This paper makes use of the transient of fault time as the line selection criterion and takes advantage
of the good time-frequency characteristics to find the information of fault time accurately. Combined
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Fault Line Selection Method of Small Current Grounding System Based on Wavelet Packet and Multi Frequency Band Analysis
Wang Xiaowei, Lu Yongfang, Hou Yaxiao
with the correlation analysis method of the digital signal processing, it can make a deal with data to
find the most likely fault line. Besides, using the existing bus insulated monitoring device to monitor,
the method has a good effect by using the automatic reclosing which can combine the traditional
manual pull road line selection and new method. The result shows that the method is accurate. Because
of the space, the article only makes experiments from the different lines, fault phase angle and distance
to simulate and prove. At last, the paper proves the selection line method is effective.
6. Conclusion
This paper presents a novel fault line selection method by multi frequency bands of wavelet packet,
by the simulation and calculation; we can acquire the following conclusions:
1) The high order wavelet packet db10 can have a quite good analysis about the transient zero
sequence current. Through the wavelet packet decomposition, we can render the high frequency
transient information. It provides more accurate frequency information to give a new fault line
selection criterion.
2) It adopts the method based on the wavelet multi-band correlation analysis to make use of the
characteristic information of two frequency bands, which improve the capability of characterizing
transient fault signal effectively and provide a guarantee to further improve the accuracy of fault line
selection. In addition, each characteristic frequency band employs correlation analysis method to
evaluate and can seize the essential difference between the fault line and healthy line when the line is
faulted, which provides a basis for the reliable line selection.
3) The method uses the line recluse to monitor the possible fault current sequence circularly, which
can improve the reliability of the select circuit results.
7. Acknowledgements
This work was supported by Science and Technology Research (12B470002) and Control
Engineering Lab Project (KG2011-15) of Henan Province, China, and Youth Foundation (Q2012-28)
of Henan Polytechnic University, China.
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