Journal of Power and Energy Engineering, 2014, 2, 586-593
Published Online April 2014 in SciRes. http://www.scirp.org/journal/jpee
http://dx.doi.org/10.4236/jpee.2014.24079
How to cite this paper: Wu, Y.C., Huang, D.C., Ruan, J.J., Chen, Y.D., Luo, H.W., Sun, X. and Chen, S.B. (2014) Study on
Influence of Trees around 10 kV Distribution Line. Journal of Power and Energy Engineering, 2, 586-593.
http://dx.doi.org/10.4236/jpee.2014.24079
Study on Influence of Trees around 10 kV
Distribution Line
Yongcong Wu1, Daochun Huang1, Jiangjun Ruan1, Yuandong Chen2, Hanwu Luo2,
Xin Sun2, Shubo Chen2
1School of Electrical Engineering, Wuhan University, Wuhan, China
2Eastern Inner Mongolia Power Ltd., Hohhot , China
Email: 362121393@qq.com
Received December 2013
Abstract
Considering the complexity of the geographical surroundings and the height of 10 kV distribution
line, the impact of trees on the lightning performance can not be ignored. A model of lightning po-
sition judgment and overvoltage calculation based on the concept of striking distance is built. With
the theory of orthogonal test, the main factors of trees' influence on lightning performance are
figured out. The results indicate that the location of trees is the main factor. In practical engineer-
ing, suitable management of vegetation can improve the lightning performance and reduce the
lightning failure of 10 kV distribution line.
Keywords
10 kV Distribution Line; Trees; Optimal Configuration ; Orthogonal Test
1. Introduction
There are trees around the area of 10 kV distribution corridors and some even grow just below the distribution
line. The height of trees can always reach 10 m - 20 m. Thus, trees may have influence on 10 kV distribution
line lightning performance. Researchers have discussed the influence on lightning overvoltage [1] [2]. And the
influence on 500 kV transmission line is studied. The results evidence that 10 m - 20 m trees can reduce 30% -
80% direct lightning strike. But the change of induced lightning overvoltage is not discussed and the results
dont apply to distribution. Researchers have performed many tests and theoretical studies on direct lightning
overvoltage and induced lightning overvoltage [3]-[6]. And striking distance is an important concept in EGM
which is used to find out the lightning strike location. In this paper, the model of lightning location judgment
based on the concept of striking distance is built. With the model, the lightning performance of 10 kV distribu-
tion line is quantitatively analyzed when trees are considered. The results can provide a reference for lightning
protection and vegetation management of 10 kV distribution line.
2. Model
2.1. Judgement of Lightning Location
According to [6], attracting range of line, ground and trees are combined arcs that centered on relevant object
Y. C. Wu et al.
587
and striking distance are radiuses. As it is shown in the Figure 1, B3 B2 C, A1 A2 C and DE are the correspond-
ing attracting surface. The location of lightning leader is O. ht and hl are height of tree and the line. Rt, Rl, Rg are
striking distance of tree, the line and the ground. L1 is the distance between the leader and the tree. And L2 is the
distance between the leader and the line.
When L1 < Rt, L2 < Rl the distance between the attracting surface and the ground H. The object which the max
Ht belongs to is the lightning striking target.
Trees:
2
1
()
tt t
HRL h= −+
(1 )
Linw:
2
2
()
tt l
HRL h= −+
. (2)
2.2. Lightning Performance Parameters
In this paper, the number of direct lightning flashover times (DLFT), induced lightning flashover times (ILFT)
and dangerous current times (DCT) serve as the characteristic parameters of the 10 kV distribution line lightning
performance.
Reference [7] concludes that direct lightning strike bounds to cause flashover. We define the number of direct
lightning flashover times as the times that a line span suffer in a year. The number of induced lightning flashov-
er times is defined as the times that insulators flashover caused by lightning induced overvoltage in a year. Ac-
cording to [8], the number of dangerous current times is defined as the sums of ILFT of a tower and the DLFT
on the two line span next to the tower in a year. These parameters can serve as the assessment of the lightning
performance.
2.3. Induced Lightning Overvoltage
When considering trees, lightning leader is not perpendicular to the ground as it is shown in Figure 2. S1 is the
horizontal distance between the vertical lightning leader and the line. S is the horizontal distance between the
tree and the line. ht, hl are the height of the tree and the line.
The resistivity of woods can reach
5
1.8 10m× Ω⋅
. Trees are regarded as dielectric with sharp tips in this paper.
Calculated datas of lightning induced-overvoltage are shown in Figu re 3. And the results of regulation method
is also given in Figure 3 for comparison.
2.4. Parameters
According to IEEE, the striking distance is expressed as:
0.8
6.72
l
RI
=
( 1)
t gl
R KR=
. ( 2)
Figure 1. Judgement of lightning strike location.
Y. C. Wu et al.
588
Figure 2. Lightning location and strikiing distance.
Figure 3. Results of induced-overvoltage (kV).
.
I: amplitude of lightning current, Rl, Rl are the striking distance of the line and the tree.
Reference [9] provides lightning current parameters:
lg/ 88PI
= −
. ( 3)
Thunderstorm day Td = 40. Average surface density of lightning is 0.07. Hl = 10 .2 m, impulse discharge vol-
tage of insulator U50% = 230 kV, line span L0 = 100 m.
3. Influence on Lightning Performance
In this section, simulations are carried out with trees that the height is between 5 m and 40 m. The Kg is set to be
0.95. we focus on the trees that located within 50 m from the line or the tower, Na, Nb, Nc are the simulation da-
tas of DLFT, ILFT and DCR without trees. If N is the relevant simulation value of DLFT, ILFT and DCR, rela-
tive value N/Na, N/Nb, N/Nc are used to describe the changes of lightning performance. In the diagram, the x-y
coordinate plane describe the location of the trees that is relative to the line or the tower.
10 20 30 40 50 60 70 80
0
200
400
600
800
1000
I/kA
Y. C. Wu et al.
589
3.1. Influence on DLFT
Firstly, we can get Na = 0.0314 without considering trees. It is equivalent to 31.4/(100 kma),which means the
direct lightning flashover times of 100 km distribution line reach 31.4 times in a year. The center of the diagram
is the middle of the line span. (0,0) is the location of the tower, and the y axis shows the result of N/Na. The di-
rection of the line is the same as the arrwo in Figure 4(a).
Simulation results ar e shown in Figure 4. When the height of trees ht > 5 m, trees can keep N/Na < 1. It indi-
cates that trees can reduce the DLFT. When the height of tree between 5 m and 12 m, the shape of the simula-
tion diagram is convex. It evidences that the closer to the line the poorer the protecting effect of the tree is. Tak-
ing 10.2 m trees for example, trees locating 25 m from the line can reduce 5% of the direct lightning strike but
only 2% when the distance is 10 m.
When ht > 20 m, the results are significantly different from that of 5 m - 12 m trees. Trees can best protect the
distribution line. The simulation datas show that the decrease of DLFT can reach 50% - 70% when ht = 20 m -
30 and the shielding effect is significant.
3.2. Influence on ILFT
We can get Nb = 0.0012/a without considering trees. It is equivalent to 1.2/(100 km·a),which is the ILFT of
(a) (b)
(c) (d)
Figure 4. Simulation results of N/Na. (a) ht = 5 m; (b) ht = 12 m; (c) ht = 20 m; (d) ht = 40 m.
-50
-40
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-10
0
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0
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60
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100
0. 975
0. 98
0. 985
0. 99
0. 995
1
沿线路方向坐标y
N/Na
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1
沿线路方向坐标y
N/Na
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0. 9
沿线路方向坐标y
N/Na
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0
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0
0. 2
0. 4
0. 6
0. 8
沿线路方向坐标y
N/Na
Y. C. Wu et al.
590
100 km distribution line.
The simulation results are shown in Figure 5. The center (0,0) of the result diagram is the location of the
tower and the y axis shows the simulation results of N/Nb. The direction of the line is the same as the arrow in
Figure 5(a).
The simulation results in Figure 5 shows that N/Nb > 1.They evidence that trees taller than 5 m can increase
the ILFT. There are many maxima scattered in the diagram. Comparing with the other location, trees locating at
these point may increase more threat to the insulation.
When ht > 30 m N/Nb is obviously segmented. The closer to the tower, the more significantly the induced
lightning flash over rate increase. Trees can increase the ILFT more than 10 times. It means that trees can in-
crease the threat of lightning induced overvoltage.
4. Orthogonal Test on Optimal Configuration of Greenbelts
According to the analysis above, trees have opposite influence on DLFT and ILFT. Thus different location and
ht of the tree may lead to different influence on the total flashover times of distribution line. Finding out the best
management of trees can protect the line from direct lightning strike and reduce the ILFT increase. In this sec-
(a) (b)
(c) (d)
Figure 5. Simulation result of N/Nb. (a) ht = 5 m; (b) ht = 12 m; (c) ht = 30 m; (d) ht = 40 m.
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0
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0
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1. 1
1. 2
1. 3
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1. 5
1. 6
沿线路方向坐标
N/Nb
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N/Nb
Y. C. Wu et al.
591
tion, orthogonal test is USED to study the influencing factors of the impact of trees. In the urban area, trees are
always appearing in greenbelt form. Thus, greenbelt serves as a proxy in the study.
Orthogonal test is a scientific method that is based on probability theory, mathematical statistics and practical
experience. Orthogonal test is USED to find out the best management of trees and 10 kV distribution line.
4.1. Factor and Level
According to the theory of orthogonal test, striking distance factor Kg, difference between ht and hl, location of
the greenbelts S, and the length of the greenbelts are regarded as 4 factors. Each factor includes 5 levels. Factors
and levels are shown in Table 1. The scheme is arranged according to
6
25
(5 )L
.
4.2. Results
The simulation and range analysis result are shown in Table 2. To DLFT, the range of Kg is the largest, which
indicates that Kg is main influence factor of DLFT. Meanwhile, the range of L reach 0.44 which means L is also
the factor that cannot be ignored. According to this analysis method, to ILFT, Kg is still the main factor. And
distance S becomes the second most important factor.
To DCT, Kg is not the main factor. And S becomes the main influence. It means that the increase of ILFT is
similar to decrease of DLFT when Kg changes. And the rational location of greenbelts can improve the lightning
performance of 10 kV distribution line.
Striking distance factor is not steerable in engineering and the height difference is not the main factor. The
optimal location of trees is figured out in different condition. The simulation data are shown in Figure 6.
The simulation results of Table 2 and Figure 6 indicate that the length of greenbelts and the location is the
main factors that influence the impact of trees. N/Nc should keep small enough so that the 10 kV distribution
Table 1. Orthogonal factor level.
Factor 1 2 3 4 5
A: Factor, Kg 0.92 0.94 0.96 0.98 1.00
B:height difference,
h
(m) 3 1.5 0 1.5 3
C: distance between trees and line, S (m) 5 15 25 35 45
D:Length of trees, L (m) 40 80 120 160 200
Table 2. Range analysis.
Factor I II III IV V R
A
N/Na 4.86 4.77 4.62 4.29 3.99 0.87
N/Nb 15.83 18.11 21.49 49.95 74.63 58.79
N/Nc 5.08 5.02 4.94 5.16 5.16 0.22
B
N/Na 4.62 4.53 4.56 4.30 4.52 0.31
N/Nb 31.32 28.31 30.31 48.14 41.92 19.83
N/Nc 5.13 4.99 5.05 5.14 5.24 0.24
C
N/Na 4.43 4.60 4.46 4.57 4.48 0.13
N/Nb 18.19 44.14 43.59 38.87 44.06 25.94
N/Nc 4.69 5.19 5.21 5.23 5.23 0.53
D
N/Na 4.73 4.52 4.58 4.42 4.29 0.44
N/Nb 38.10 42.25 38.24 27.71 33.71 14.53
N/Nc 5.37 5.24 5.23 4.86 4.85 0.52
Y. C. Wu et al.
592
(a) (b)
(c) (d)
Figure 6. Simulation datas of N/Nc (DCT). (a)
1 ,0.95,200
g
h mKLm∆= ==
; (b)
1 ,0.95,100
g
h mKLm
∆= ==
;
(c)
1 ,0.98,200
g
h mKLm∆= ==
; (d)
1 ,0.98,100
g
h mKLm∆= ==
.
face fewer failures. More simulation evidences that greenbelts can reduce N/Nc up to 20% if the location is suit-
able (N/N c < 0.8). To condition (a) in Figure 6, the best location distance S = 12 m - 38 m. To condition (b), the
best distance S = 12 m - 18 m. To condition (c) and (d), trees closer to the line may lead to better protecting ef-
fect.
5. Conclusion
In this paper, a feasible scheme of quantitative analysis about trees' influence on 10 kV distribution line light-
ning performance is proposed. The results can provide a reference for lightning protection and nearby vegetation
management of 10 kV distribution line.
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0510 15 20 25 30 35 40 45 50
1
1. 05
1. 1
1. 15
1. 2
水平距离
N/ Nc
0510 15 20 25 30 35 40 4550
1.1
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1.2
1.25
水平距离
N/ Nc
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