Journal of Power and Energy Engineering, 2014, 2, 680-686
Published Online April 2014 in SciRes. http://www.scirp.org/journal/jpee
http://dx.doi.org/10.4236/jpee.2014.24091
How to cite this paper: Luo, Y., Jiang, J.Z., Nong, Y. and Li, S.Z. (2014) Research on Evaluating Index of Lightning Protection
Safety Performance of High Voltage Overhead Transmission Line. Journal of Power and Energy Engineering, 2, 680-686.
http://dx.doi.org/10.4236/jpee.2014.24091
Research on Evaluating Index of Lightning
Protection Safety Performance of High
Voltage Overhead Transmission Line
Yi Luo1, Jingzhou Jiang1, Yu Nong1, Shizuo Li2
1Baise Power Supply Bureau Guangxi Power Grid Corporation, Nanning, China
2Institute of Electrical Engineering Guangxi University, Nanning, China
Received February 2014
Abstract
In order to improve the lightning protection performance of transmission lines, lightning protec-
tion management has been divided into every tower that lightning protection performance has
been evaluated respectively. According to factors such as landform, span, tower type, grounding
resistance, isolator type, and so on, relative ratio of tripping operation of every tower in the line
has been calculated to evaluate its lightning protection safety performance, it is beneficial to op-
eration maintenance and lightning reconstruction of transmission lines.
Keywords
Transmission Lines; Lightning Protection Safety Performance; Evaluating Index;
Ratio of Lightning Tripping Operation
1. Introduction
The ratio of lightning tripping operation of high voltage overhead transmission line is very high at all time, it
always exceeds 70% of total tripping operation, and lightning tripping operation becomes the main factor that
may endanger the safety of power system [1] [2].
Usually, there are few indexes to evaluate the lightning protection performance of high voltage overhead
transmission line, such as lightning withstand level and ratio of tripping operation, those indexes are rude and
unitary, and cannot reflect the influence of height, landform, span, tower type, grounding resistance, isolator
type, and so on, of every tower.
In order to improve the lightning protection performance of transmission lines, lightning protection manage-
ment has been divided into every tower that lightning protection performance has been evaluated respectively
according to different parameters of every tower [3].
2. Evaluating Index of Linghtning Protect
A. Relative Lightning Ratio

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681
Every tower of a transmission line has different parameters such as height above sea level, tower height, on-
ward and backward spans of conjoint towers, distance of two overhead ground wires, so lightning ratio of every
tower is different when there is thundercloud above transmission line. To reflect those differences, relative
lightning ratio k is introduced.
( )
MAX MaxMax Max
()
W HD
S
kSW HD
+
= =+
(1)
Here H is the height above sea level of overhead ground wires, W is the distance between two overhead
ground wires, D is half of sum of onward and backward spans, HMAX, WM AX, DMAX are maximums of those pa-
rameters of all towers in a transmission line. Obviously S is the area of an enlarged rectangle which length is
half of sum of onward and backward spans, and which width has been extended on account of the effect of
height above sea level of overhead ground wires. SMAX is the biggest area of those parameters of all towers. k
equals to ratio of the equivalent area of one tower to the biggest area.
B. Probability of Sustained Arc
Probability of sustained arc ν is:
0.75
2
[4.5 14]
3
U
l
ν
−

= −


(2)
Here U is the line voltage and l is the length of the isolator.
C. Withstand Level of Lightning Direct Stroke to Tower
Withstand level when lightning is striking to tower directly is:
50%
2
d
(1 )
2.6 2.6
U
Ih
L
Rq β
=

++ −




(3)
Here U50% is 50% impulse spark over voltage of isolator, β is the shunt coefficient of overhead ground wires,
R is the grounding resistance of tower, L is the inductance of tower, hd is the height of conductor to ground, q is
the coupling coefficient between conductor and overhead ground wire.
D. Withstand Level of Lightning Shielding Failure
Withstand level when lightning is striking to conductors directly is:
50%
2
100
U
I=
(4)
E. Direct Stroke Rate and Shielding Failure Rate
There is a relationship between striking distance rS and lightning current magnitude I:
0.75
7.1
S
rI
=
(5)
Geometrical model of direct stroke and shielding failure is illustrated in Figure 1, θ is the incline angle of
ground shown as line GH, GF is the centric line of a tower, B and D are overhead ground wire and conductor
respectively of one side.
Draw an arc PS which center is in the point B and radius is rS, and another arc ST which center is in the point
D and radius is rS, and a line UV which is paralleled to ground with a distance of rS.
Obviously, if imminent lightning leader gets to arc PS, lightning may hit to the overhead ground wire, on the
other hand, lightning may hit to the conductor when imminent lightning leader comes to arc ST. Direct stroke
rate and shielding failure rate can be calculated by angles α and γ corresponding to arc PS and ST.
Direct stroke rate η(rS) is:
( )
S
r
α
ηαγ =+
(6)
Shielding failure rate ξ(rS) is:
( )
S
r
γ
ξαγ =+
(7)

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682
Figure 1. Direct stroke and shielding failure.
Angles α and γ have a relationship with tower parameters and striking distance rS, according to the geometric-
al model in Figure 1, they can be given as:
222 2
2
22
11
()() ()
() 4()
4()( )
sinsin ()
22
db bdSdb
db bdd bbd
b
SS
ww hhrww
hh hhww hh
w
rr
π
α
−−
− +−−
−+−−− − +−

=+−


(8)
() ( )()( )
() ()
( )( )
( )
( )
22 2
2
2
22
1
22
1
2
44
sin ()
2
sin sin(θ)1 sin(sin)
sin ()
(1sin ())
db bdSdb
bd bd
d bbd
S
Sd dSSd d
S
ww hhrww
hh hhww hh
r
rhwr rhw
r
γ
θ θθ
θ
−
−

− +−−

−+−−−

− +−

=
−−−+−−−
−+
(9)
If γ < 0, then let η = 1 and ξ = 0, this indicates that shielding failure will not occur under that lightning current
magnitude Iand its striking distance rS.
Middle phase will be neglected. Direct stroke rate and shielding failure rate of another side of tower can be
computed by Formulas (6)-(9) in the same way, and will be added up.
For double lines on the same tower, angles α, γA, γB, γC, as illustrated in Figure 2, must be calculated, then,
( )
SABC
r
α
ηαγγγ =+++
(10)
( )
ABC
SABC
r
γγγ
ξαγγγ
++
=+++
(11)
F. Ratio of Direct Stroke Tripping Operation
Probability that lightning current magnitude exceeds I is:
( )
108
10 I PI − =
(12)
So, Probability of lightning current magnitude I is:

Y. Luo et al.
683
Figure 2. Double lines on the same tower.
( )
108
0.02132 10
I
fI
−
= ×
(13)
Ratio of direct stroke tripping operation is:
( ) ( )
1
1S
I
kfIrdI νη
∞
=
∫
(14)
G. Ratio of Shielding Failure Tripping Operation
Ratio of shielding failure tripping operation is:
( ) ( )
2
2S
I
kf IrdI νξ
∞
=∫
(15)
H. General Evaluating Index
After considering the effect of tower type, height over sea level, span, ground resistance, isolator, landform,
general evaluating index of lightning protection safety performance of every tower is:
12
()J kkk= +
(16)
By all appearances, the smaller general evaluating index of a tower is, the better lightning protection safety
performance of that tower is, on the other hand, the bigger general evaluating index of a tower is, the worse
lightning protection safety performance of that tower is.
Supposed that JMAX is the maximum of evaluating indexes of all towers in a transmission line, relative eva-
luating index can be defined as:
Max
100
r
J
JJ = ×
(17)
Relative evaluating index expressed by percentage is very intuitionistic, and it is easy to give a taxis to all
towers in a transmission line according to relative evaluating index.
3. Evaluating Software
Based on MS Visual Basic 6.0, evaluating software of lightning protection safety for high voltage overhead
transmission lines is developed, it includes six component: lines edit, tower edit, isolator edit, evaluating analy-
sis, graph show, and version information.
Line edit component inputs and manages lines information and all parameters of every line. Tower edit com-

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684
ponent manages tower type and its main parameter. Isolator edit component manages isolator type, save 50%
impulse spark overvoltage and length of every isolator (Figure 3).
Figure 4 shows the interface of the evaluating result. Result includes relative lightning ratio, ratio of direct
stroketripping operation, ratio of shielding failure tripping operation, general evaluating index, relative evaluat-
ing index and taxis. All parameters of a transmission line and evaluating result can be exported to an Excel
document.
Figure 5 shows height and span of atransmission line.
Figure 3. Tower main parameter.
Figure 4. Interface of evaluating result.

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685
Figure 5. Height and span of a transmission line.
4. Conclusions
By introduction of relative lightning ratio, the effect of tower parameters, such as height above sea level, tower
height, onward and backward spans of conjoint towers, distance of two overhead ground wires can be numerated,
and that is easy to reflect the difference of every tower.
Tower type and incline angle of ground have a distinct influence to direct stroke rate and shielding failure rate,
and are main parameters of the difference.
Relative evaluating index of of every tower is very intuitionistic and is beneficial to operation maintenance
and lightning reconstruction of transmission lines.
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