This document presents a novel stochastic approach for assessing the lightning performance of overhead transmission lines (OHLs). It combines systematic simulations using an accurate EMTP model of a 110 kV OHL with probability distribution functions obtained statistically. The probabilities of different outcomes, like the number of insulator string flashovers from a direct lightning strike, are calculated. These "stochastic lightning performance characteristics" provide a meaningful way to compare the lightning performance of different OHL configurations. The approach is demonstrated through simulations of a 110 kV line in Ireland that had experienced lightning issues.

1. Abstract-- An accurate EMTP model of a HV overhead line
under the influence of a direct lightning stroke is used in a novel
stochastic approach towards the assessment of the lightning
performance of OHLs. This approach combines systematic
simulations on our EMTP model with probability distribution
functions which were obtained from a statistical analysis of the
lightning performance of existing HV transmission networks and
from experimental data by other authors. Using this approach we
find the probability distributions for the number of flashovers
across insulator strings, or fault types, as a result of lightning
striking a line. We call these distributions ‘stochastic lightning
performance characteristics’ and use them as a convenient and
meaningful measure to describe, and to compare, the lightning
performance of overhead lines with different configurations.
Practical recommendations based on this approach are made for
the lightning performance enhancement of an actual unshielded
110 kV transmission line with wooden supports and non-earthed
metal cross-arms.
Index Terms—Lightning, Lightning performance, Power
transmission lines, Modeling, Simulation, and Pareto distribution.
I. INTRODUCTION
N earlier works [1-3] a concept was presented for the
accurate analysis of the lightning performance of a HV
transmission line using the ATP-EMTP program [4]. This
concept was applied to a study of 110 kV unshielded overhead
lines (OHLs) under the influence of a direct lightning stroke by
means of simulation on the digital model which we developed
within the ATP-EMTP program using its MODELS-feature.
The simulation includes a model of the transmission line whilst
also taking account of the frequency dependence of the line
parameters [5] and corona effect [3, 6]; models of wooden-
porcelain insulation with an adequate presentation of the
breakdown mechanism of the air-porcelain/glass insulation [6-
8]; wooden and metallic towers [8]; and grounding systems
including their impulse resistance characteristics [6, 7].
In this paper we introduce a novel stochastic approach
towards the assessment of the lightning performance of OHLs.
This work was supported by the Electricity Supply Board, Ireland,
through the award of a Newman Scholarship.
I. M. Dudurych is with EirGrid, Ireland, 27 Lower Fitzwilliam Street,
Dublin 2, Ireland (e-mail: idudur@ieee.org).
T. J. Gallagher is with the Department of Electronic and Electrical
Engineering, University College Dublin, Belfield, Dublin 4, Ireland (e-mail:
Tom.Gallagher@ucd.ie).
M. Holly is with the ESB National Grid, Ireland, 27 Lower Fitzwilliam
Street, Dublin 2, Ireland (e-mail: Maurice.Holly@ngrid.com).
This approach combines the outcomes of the previous
systematic simulations on our EMTP model with probability
distribution functions that were obtained from our statistical
analysis of the lightning performance of an existing HV
transmission network and from experimental data by other
authors [2, 9]. Through these simulations we vary parameters
such as the lightning current and the attachment point of the
stroke to the line. Then we apply known probability
distributions for the peak lightning current and attachment
point to obtain our ‘stochastic lightning performance
characteristics’ (SLPCs) for the overhead lines, which enables
a reliable comparison between the lightning performance of
different OHL configurations. Two types of SLPCs are
considered: firstly, the probability that the number N of
flashovers of insulator strings induced by a direct lightning
strike is N>n, where n=1,2,3…; and secondly, the probability
that a situation of ‘ no fault’, single-, two-, or three-phase fault
is produced on the line due to the lightning strike.
II. STUDIES OF LIGHTNING PERFORMANCE OF 110 KV LINES IN
TERMS OF PROBABILITY OF NUMBER OF INSULATOR
STRING FLASHOVERS CAUSED BY A DIRECT LIGHTNING
STRIKE
A. ATP-EMTP Model of 110 kV Line
Our ATP-EMTP model is applied to a typical 110 kV over-
head line with combined wooden poles and steel towers which
is located in the northwest region of Ireland. This line was
selected because it had been identified as a lightning ‘hot-spot’
on the system from another study of the lightning strike density
throughout this region. It has no shield wires and phase
conductors are supported on wood poles by 7/9 porcelain/glass
insulators attached to steel cross-arms, which are not earthed.
A sketch of a section of this line is shown in Fig. 1. The line
connects a sub-station from a hydro power plant with
customers in a location some 62 kilometers away. Steel anchor
towers 1, 6, 14, and 20 have a good earthing in the order of 35
Ohms and the wood poles comprise approximately 80% of all
line supports.
Some 19 spans were selected to include steel towers 1, 6, 14
& 20 in order to take into account the reflected voltage waves
from these towers. The models of the various elements of the
line in Fig. 1 have been described in [2]. They represent each
of the 19 spans of 200m length for the line. The rest of the line
A Novel Stochastic Approach to the Assessment
of the Lightning Performance of HV
Transmission Lines Using EMTP
Ivan M. Dudurych, Senior Member, IEEE, Tom J. Gallagher, and Maurice Holly
I
0-7803-7967-5/03/$17.00 ©2003 IEEE
Paper accepted for presentation at 2003 IEEE Bologna Power Tech Conference, June 23th-26th, Bologna, Italy

2. is terminated by their matching impedances.
Send. s/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Rec. s/s
Fig. 1. A sketch of the modeled 110 kV line section
B. Systematic Simulations
On a digital model of our 110 kV line we conduct
simulations of the application of a current surge of the Heidler-
type [4] τ/50 µs at 5 points along the line: at a cross-arm of
wood pole 10, at conductors A, B, and C in the mid-span
between poles 10-11, and at the top of metal tower 14 (see Fig.
1).
The instant on the wave of the system operating voltage
when the lightning strike occurred was also varied and 4
representative times were selected at 00
, 900
, 1800
, and 2700
.
TABLE I
RISE TIMES OF LIGHTNING CURRENT SURGES
Current,
kA
Rise time, µs Current,
kA
Rise time,
µs
1 3 0.2071 15. 10 0.5613
2 3.5 0.2350 16. 11 0.6074
3 4 0.2628 17. 12 0.6527
4 4.5 0.2896 18. 14 0.7416
5 5 0.3162 19. 17 0.8709
6 5.5 0.3421 20. 20 0.9964
7 6 0.3677 21. 25 1.1477
8 6.5 0.3929 22. 30 1.2860
9 7 0.4177 23. 40 1.5389
10 7.5 0.4423 24. 50 1.7688
11 8 0.4666 25. 60 1.9820
12 8.5 0.4906 26. 80 2.3716
13 9 0.5144 27. 100 2.7260
14 9.5 0.5379
Current magnitudes were selected starting from 3.0 kA
through to 100 kA. The lower limit was chosen as 3 kA
because below this value flashover of the line insulation does
not occur. The upper limit of 100 kA was selected from data
gathered by EA Technology, UK over a thirteen-year period
from 1989 to 2001. The current magnitudes and front times of
the current surges used are presented in Table 1. The small
increment of current was chosen in order to obtain accurately
the dynamics of developing types of faults in the lower range
from 3 to 10 kA. Thus, the total number of cases examined for
the same value of lightning current was 5×4=20 as shown in
Table 2. Consequently, the total number of simulations for the
same line configuration was 20×27=540. Each simulation gave
the number of string flashovers and the type of fault, if any, as
a result of a direct strike. The probability distribution of
numbers of flashovers was obtained by counting the number of
flashovers occurring when lightning strikes; a tower (nt); phase
A (nA); phase B (nB); phase C (nC); a pole (nP).
C. Statistical Treatment
Using the approach of finding separately the distributions
nt, nA, nB, nC and nP and combining these to calculate the
distribution of the number of flashovers N, we would ideally
compute the distribution of nj – the number of flashovers
resulting from a random strike of lightning hitting the section
j of the line- using [9]:
[ ] [ ]dInIfyIpnnP j ∫
∞
===
0
)()( , (1)
where n = 1, 2, 3,…; p(I) is the probability density function of
the cumulative distribution function P(I), that can be defined
as the probability that a random stroke of lightning has current
exceeding I and y(S) is an indicator function which takes the
value 1 if the statement S is true and 0 if S is false. f(I) is the
number of flashovers that result from a stroke of current i
hitting a section j of the line ( j = t, A, B, C, or p).
P[nj = n] is approximated by:
[ ] [ ]
[ ]dInifyIp
dInikifyIpnnP
I
IKI
K
k
IkI
IkI
j
∫
∑ ∫
−+
−
=
++
+
=+
+=+==
max
min
min
min
)1(
max
1
0
)1(
min
)()(
)()(
δ
δ
δ
δ
, (2)
where δI is the chosen lightning current increment and K is the
total number of increments used in simulations (in our case
K=27-1=26); Imin is the minimum current needed to produce
flashover when lightning hits the line (we took this current as 3
kA) and Imax. is the maximum current used in the simulations
(100 kA in our case).
The probability density function, p(I), can then be obtained
by differentiating the negative of the survival function, which
is also known as the cumulative probability distribution
function P(I). This function P(I) is the probability that the
lightning current IL will exceed the value I. This function was
obtained by authors earlier [1] from the EA Technology data.
Analyzing the shape of the probability function P(I) shown in
Figure 2, we have concluded that it can be represented as a
Pareto distribution [10]
b
aI
IP
)(1
1
)(
+
= . (3)
From Figure 2, for the land of Ireland, the parameters a =
0.128, and b = 1.6.
Thus the probability density function is
[ ]
[ ]
.
)(1
)(
)(1)( 2
1
b
b
dI
d
aI
aIab
IPIp
+
=−=
−
(4)

3. Provided the statements under the appropriate integrals in
equation (2) are true ( [ ] 1)( min ==+ nIkIfy δ ), these integrals
can be calculated after the substitution of p(I) from equation
(4) as:
[ ]
).()(
)(1
)(
)(1
)(
)( 2
1
IPaI
aI
aI
dI
aI
aIab
dIIp b
b
b
b
b
=
+
=
+
= ∫∫
−
(5)
Fig. 2. Cumulative probability distribution function
Thus equation (4) is very simple to calculate using the
expression for the integrals:
[ ]
[ ]
[ ]nIfyIPaIIPaI
nIkIfy
IPaIIPaInnP
III
b
II
b
K
k IkII
b
IkII
b
t
=⋅−+
+=+
×








−==
−==
−
= +=++=
∑
)()()()()(
)(
)()()()(
max
maxmax
min
1
0 min
)1(
min
δ
δδ
δ (6)
The probabilities of number of flashovers produced by a
random lightning strike to other parts of the line are calculated
in the same manner and then the total probability of number of
flashovers for a typical 110 kV line is calculated as
,)(
1
)(
1
∑ ∑
=






===
m
k j
ij nnPP
m
nNP (7)
where m is the number of points on the sinusoid of the
operating voltage (in our simulations we took m=4); j=t for the
steel tower, j=p for the wood pole, and j=A, B and C for the
midspan of phase A, B and C.
TABLE II
SIMULATION CASE NUMBERS
Stricken point on a line
Point on
voltage
curve Tower Pole Phase A Phase B Phase C
00
1 2 3 4 5
900
6 7 8 9 10
1800
11 12 13 14 15
2700
16 17 18 19 20
Fig. 3. Ratio of collected strikes between towers and phase conductors for
unshielded 110 kV lines
The following section outlines how the relative
probabilities of different parts of a typical 110 kV line being
hit by random lightning were estimated. Evidence from the
literature [9] indicates that the percentage of collected strikes
between towers and phase conductors for unshielded lines
varies from 25% and 75% to 40.6% and 59.4%, respectively.
Experiments on a 100:1 scale model of an unshielded 110 kV
line, conducted in the HV laboratory of UCD [11] also showed
that for lines, which were fitted with Franklin rods this
percentage was 35% and 65%, and for the same line with
unearthed cross-arms it changed to 25% and 75%,
respectively. A summary of the ratios measured by different
authors is presented in Fig. 3 that shows that the median ratio
is about 34% versus 66%. Our 110 kV line does not have
earthed cross-arms and therefore, for a comparison of this line
with other alternative configurations in the literature, we took
the percentage of strikes to towers and conductors to be 25%
and 75%, respectively, as against the median values from
Figure 3.
A common arrangement for a 110 kV line is that the total
number of metal towers comprises about 1/5 of all supports
that means that the distribution of lightning strikes between
metal towers and wood poles is 20% and 80% accordingly.
Thus, for our line configuration the relative probability that a
tower is hit by lightning is Pt = 0.25×0.2=0.05 whereas the
relative probability that a wood pole is hit is Pp =
0.25×0.8=0.2
Regarding the incidence of lightning on particular phase
conductors we used the data [10] shown in Fig. 4 to conclude
that the central conductor of a horizontal phase arrangement
was hit by approximately 10% of strikes compared with 45%
to the outer phases. In our modeled section of line the phase
sequence was BAC due to transposition, and therefore the
probabilities for lightning attachment to the conductors are; PA
= 0.1×0.75=0.075; PB = 0.45×0.75=0.3375; PC =
0.45×0.75=0.3375.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
IEEE
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D
,Fr.R
.U
C
D
,no
Fr.R
.
%offlashescollectedbyphaseconductors
Tower Phase
20 40 60 80 100
0.2
0.4
0.6
0.8
1
I,kA
p,pu

4. Fig. 4. Lightning Incidence to Phase Conductors on 110kV Lines
Having the probabilities of the numbers of flashovers
produced by a direct random lightning strike to the line now
we can now obtain their cumulative probability distribution, or
survival function. This function shows the probability that the
number of flashovers for the particular configuration of the
line is greater than or equal to n. In our practical
considerations we included all cases with the number of
flashovers over 30 to the last calculation column ‘30 and over’
due to very small possibility of those. To obtain the survival
function we add the possibilities of all flashover numbers,
greater than or equal to n:
,)()( ∑
=
==≥
m
Nk
nNPnNP (8)
where m=30 in our studies, because of the very low probability
of the number of flashovers exceeding 30 for the 110 kV line.
B. Example of Calculation of Probability of One Flashover
First we calculate the probabilities P[Ft =1]; P[Fp =1];
P[FA =1]; P[FB =1]; P[FC =1] using equation (6). Here nt =1
is the statement that the number of flashovers produced due to
strike of random lightning to a tower is equal to one. Further
indices correspond to strikes to a wood pole and to phases
A,B, C. For the tower this probability is:
[ ]
[ ]
[ ].1)()()128.0(
)()128.0(1)(
)()128.0(
)()128.0(
1
max
max
6.1
max
6.1
min
1
0
min
6.1
)1(min
6.1
=⋅−
−+=+×
×












−
−
==
−=
=
−
=
+=
++=
∑
IfyIPI
IPIIkIfy
IPI
IPI
nP
II
II
K
k
IkII
kII
t
δ
δ
δ
δ (9)
Doing this for all 5 possible strike locations, i.e. for P[np=1],
P[nA=1], P[nB=1], P[nC=1], we can now obtain the total
probability of just one flashover due to a random lightning
strike to a 110 kV line from equation (10) as:
[ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ]
[ ] [ ] [ ]).13375.013375.01075.0
12.0105.0(
4
1
)11
111(
4
1
1
4
1
4
1
=+=+=+
=+===+=
+=+=+===
∑
∑
=
=
CBA
p
k
tCCBB
AApp
k
tt
nPnPnP
nPnPnPPnPP
nPPnPPnPPNP
(10)
Repeating similar calculations for all the other possible
numbers of flashovers, i.e when P[N=2], P[N=3],…, P[N=m]
we obtain probabilities for each number of flashovers. The
results of these calculations as a probability distribution of
number of flashovers, or no flashovers when a 110 kV line is
struck by lightning are presented in Fig. 5. It is seen from the
figure that in 21.5% cases the random lightning strike to 110
kV line does not produce any fault, because the voltage surge
produced has lower magnitude than BIL of the line. The next
biggest probabilities are that 12 flashovers will be produced
(9.7%) or 14 flashovers (8.2%) will be produced. The lowest
probability is that 5 flashovers will be produced (0%). It is
also seen from the Fig. 5 that even number of flashovers is
more probable than odd number (the ratio of even number to
odd number of flashovers in about 3:2).
Fig. 5. Probability of number of flashovers on 110 kV line of original
configuration (with non-earthed cross-arms)
To obtain the cumulative probability (survival function) that
the number of flashovers produced due to random lightning
strike to 110 kV line is greater than or equal to n, we added
probabilities of all flashover numbers according to equation
(8). Result function is shown in Fig. 6.
Fig 6. Cumulative probability of number of flashovers
0
1 2
3
4 5
6
7 8
9
10 11
12
13
14
15
16
17
18
19 20 21
22
23
24 25 26
27
28 29
30 & more
0
0.05
0.1
0.15
0.2
0.25
Number of flashovers
Probability,pu
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
IEEE
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olde
%offlashescollectedbyphase
conductors
Central phase Left phase Right phase
0
0.2
0.4
0.6
0.8
1
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Number of flashovers
Cumulativeprobability,pu
calculated data
Apprx polynom of 6-th order

5. III. STUDIES OF LIGHTNING PERFORMANCE OF 110 KV LINES
IN TERMS OF PROBABILITY OF TYPES OF FAULT CAUSED BY A
DIRECT LIGHTNING STRIKE
In order to calculate the probability of fault type, occurring
due to a strike of a random lightning flash to a typical 110 kV
line we used an approach similar to that described in the
previous section. The only difference is that in this case
instead of counting the number of flashovers in each
simulation we note only what type of fault is produced: single-,
two-, or three-phase. Thus we can assess the probability
P(F=0) that no fault will occur, or a cumulative probability
that a single- P(F=1), two- P(F=2), or three-phase fault
P(F=3) will be produced.
For example, to calculate the probability that a single-phase
fault is produced we calculate first the probabilities P[Ft =1];
P[Fp =1]; P[FA =1]; P[FB =1]; P[FC =1] using equation(6)
with corresponding modifications. Here Ft =1 is the statement
that the worst type of fault, due to a strike to a tower is a
single-phase one, while the other indices correspond to strikes
to wood poles or to phases A, B, or C. Doing this for all 5
chosen strike locations we can now obtain the total probability
of a single-phase fault due to a random lightning strike to 110
kV line from formula (5). The results of these calculations as a
probability distribution of fault types are presented in Fig. 7.
Fig. 7. Probability distribution of fault types on 110 kV line
In Fig. 8 there is a comparison between the results, obtained
from available ESB National Grid statistics and calculated
results using our method. Only cases that produce faults on the
line are considered here with the total number to be 100%. The
average discrepancy between results is about 10%.
In terms of a cumulative probability we can obtain the
distribution of fault types as follows: the probability that any
fault will be produced when a line is hit by random lightning is
(see Fig. 8): P(1) = p(single-phase) + p(two-phase) + p(three-
phase) = 0.1129 +0.0925 + 0.5339 = 0.7397. The probability
of a two-phase fault is: P(2) = (two-phase) + p(three-phase) =
0.0925 + 0.5339 = 0.6264 while that for a three-phase fault is:
P(3) = p(three-phase) = 0.5339. The probability distributions
of fault types are shown in Fig. 9.
Fig. 8. Probability distribution of fault types triggered by lightning strike to
110 kV line: comparison of statistical and calculated data
Fig. 9. Probability Distributions for calculated and recorded types of faults
IV. SENSITIVITY ANALYSIS OF THE IMPACT OF THE LOCATION
OF THE STRUCK POINT ON THE LINE ON THE ACCURACY OF
CALCULATIONS
An analysis of the simulation data shows that these data are
most affected by those obtained when the midspan is struck by
lightning. If we try to build a probability distribution based
only on the simulation data of one stricken location point
conditions (from 20), we find that case 5, from Table 2, gives
the nearest conservative approximation to an actual cumulative
probability function. The other approximations based on the
conditions of the rest of the 19 chosen cases lie higher than
that for case 5, or lower than the curve representing all cases.
Fig. 10. All-case-, 1st
-case-, and 5th
-case based survival functions
As an illustration, probability distributions for cases 1, 5 and
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1 2 3
Fault type
Cumulativeprobability,pu
Calculated
Calculated 100%
Recorded 100%
Poly. (Calculated)
Poly. (Calculated 100%)
Poly. (Recorded 100%)
26.07%
11.29% 9.25%
53.39%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
Probabilitydistribution
No fault Single-phase Two-phase Three-phase
Type of fault
13.43% 15.27%
11.20% 12.51%
75.37%
72.22%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
Distributionoffaulttypes
Single-phase Two-phase Three-phase
Fault types
Statistical
Calculated
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Number of flashovers
Cumulativeprobability,pu
Based on all cases
Based on case 5
Based on case 1

6. all the cases in Table 2 are shown in Fig. 10. It is seen from
the figure that the distribution based on case 5 is higher by
almost 20% than the actual cumulative probability for the total
20 cases of the original configuration. This means that we can
consider the results derived from simulations of case 5 as
conservative, as it gives us an overestimate by about 20% of an
actual cumulative probability of number of flashovers.
Moreover this function is the nearest to the actual survival
function from all one-case survival functions that lie below the
actual one. The latter are not shown to avoid overlapping in
Figure 10. Therefore from this analysis we can conclude that
case 5 (strike to phase ‘C’ in a midspan) can be used for
comparative studies of different technologies to enhance the
lightning performance of a 110 kV line.
Fig. 11. Probability distribution of fault types triggered by lightning strike to
110 kV line: comparison of results based full statistical simulations data and
on data of case 5
Fig. 11 shows a comparison of fault type distributions due to
full statistical simulations and simulations of case 5 (see Table
2). As seen from this comparison, the average discrepancy
between the results in terms of single versus multiple faults is
less then 4 %.
From the foregoing results we can conclude that for rapid
assessment of the lightning performance of a 110 kV line we
need to use only one representative point of a lightning strike;
for our case this point is the phase of the outer conductor in
the midspan of the line when the sinusoid of operating voltage
passes through zero (case 5 in our studies). This assumption
allows us to decrease the analysis efforts by 20 times and we
use it in the next section for a comparative study of the
lightning performance of 110 kV lines with different
configurations.
V. COMPARATIVE STUDIES OF LIGHTNING PERFORMANCE OF
110 KV LINES WITH DIFFERENT CONFIGURATIONS
In order to assess the lightning performance of 110 kV lines
of different configurations in terms of the probability of
number of flashovers and types of faults following a direct
lightning strike we conducted a number of simulations for
seven lines with the following configurations:
• Original configuration (wooden poles with non-earthed
metal cross-arms as intermediate supports and steel towers
as an anchor supports. Arc horns are mounted across the
insulator strings)
• Metal cross-arms on wooden poles are earthed by two
downleads at each wooden support
• Metal cross-arms on wooden poles are earthed by two
downleads at every second wooden support
• Metal cross-arms on wooden poles are earthed by one
downlead at each wooden pole
• Metal cross-arms of wooden poles are replaced by
wooden ones
• Metal cross-arms of wooden poles are replaced by
wooden ones and metal towers are replaced with wooden
ones.
Fig. 12. . Cumulative probabilities of numbers of flashovers for the
original 110 kV line configuration, with all earthed cross-arms, and with
every second cross-arm earthed
A. Probabilities of Number of Flashovers
In Fig. 12 we show cumulative probability distributions of
number of flashovers for the original configuration of 110 kV
line without earthed cross-arms and for the same line with all
cross-arms earthed using two downleads (attached to each of
two wooden poles of a support), or every second cross-arm
earthed (with earthing resistances of 34 ohms). This figure
demonstrates a dramatic decrease in the probability of
numbers of flashovers for the configuration with earthed cross-
arms. For example, when original 110 kV line is stricken by
random lightning there is a 50% probability that 13 or 14
insulator strings will flash-over.
15.27%
14.26%
12.51%
8.76%
72.22%
76.99%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
Distributionoffaulttypes
Single-phase Two-phase Three-phase
Fault types
All cases Case 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Number of flashovers
Cumulativeprobability,pu
Median line
Original configuration
Earthed every 2-nd
cross-arm
Earthed cross-arms

7. Fig. 13. Cumulative probabilities of numbers of flashovers for the original
110 kV line configuration, with all cross-arms earthed by one lead, and by
two leads
On the other hand a line with all cross-arms earthed using
two downleads will have only 3 flashovers with 50%
probability, whereas a line with every second cross-arm
earthed will have 5 flashovers with the same probability.
Fig. 14. Cumulative probabilities of numbers of flashovers for the original
110 kV line configuration, with wooden cross-arms, and with all wooden
supports
To assess further the level of lightning performance
improvement of 110 kV lines using only one downlead on
each wooden support we conducted similar simulations as
those shown in Fig 12 and the results are presented in Fig. 13.
As seen from these two figures using only one downlead per
wooden support for earthing of metal cross-arms has almost
the same effect in terms of probability of number of flashovers
as earthing every second wooden support with two downleads.
As seen from Fig. 14 the configuration of the line with its
metal cross-arms replaced by wooden ones only slightly
improves the simulation with decreasing of 50% probability of
number of flashovers from 13 to 8. For the configuration with
all wooden supports 50% probability only decreases to 11. An
important note for these two configurations is that lightning
current flows through ionized path that may include wood, thus
causing permanent damage due to firing of the wood and the
density of probability of number of flashovers is higher then
for the line of original configuration.
B. Probabilities of Fault Types
Using the approach above we can assess the lightning
performance of different line configurations in terms of
probabilities of fault types as well. It is known that single-
phase faults are more tolerable and are effectively treated by
the operation of system protection compared to multi-phase
faults.
Fig. 15 demonstrates a very favorable redistribution of fault
types in favor of single-phase rather than multiphase flashovers
if the procedure of earthing the cross-arms on all the wood
poles is used. The number of multi-phase flashovers reduces
from 86% in original line configuration to 35% if one
downlead is used to earth metal cross-arms at each wooden
support, and to 15% if two downleads are used. Nevertheless,
if the cross-arms are earthed on every second pole (with two
downleads), the fault type distribution will be much like the
distribution for original configuration of the line despite the
fact that the total number of flashovers is much less then in
original configuration. Thus, as clearly seen from Fig. 15, a
substantial decreasing of multiphase faults can be reached if all
cross-arms of the line are properly earthed with two downleads
Fig. 15. Distribution of fault types for line configurations involving earthing
cross-arms
In case when metal cross-arms are replaced by wooden ones
the fault type distribution will be like in Fig. 16. A
hypothetical case when all supports of the line are wooden is
included in this figure too. As seen from this figure, no
substantial fault type re-distribution in favor of single-phase
ones can be achieved using these two approaches and using
all-wooden supports even worsen the results.
VI. CONCLUSIONS
Systematic simulations on our ATP-EMTP model of a 110
kV OHL combined with statistical data about lightning
behavior in Ireland and about the response of ESB’s 110 kV
lines allowed us to obtain stochastic characteristics of the
lightning performance of OH lines. These characteristics give
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Number of flashovers
Cumulativeprobability,pu
Median line
Original configuration
All wooden
Wooden cross-arms
0.14
0.23
0.65
0.85
0.09
0.11
0.13
0.04
0.77
0.65
0.22
0.11
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
Distributionoffaulttypes
Single-phase Two-phase Three-phase
Fault types
Original configuration Earthed every 2-nd cross-arm
Earthed by one lead Earthed by two leads
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Number of flashovers
Cumulativeprobability,pu Median line
Original configuration
Earthed with one lead
Earthed with two leads

8. a method to make reliable comparisons of different line
configurations in terms of their lightning performance.
Fig 16. Fault type distribution for the lines with wooden cross-arms versus the
line of original configuration with metal cross-arms
A novel stochastic approach shows that of all cheap
technologies considered in the paper the best lightning
performance of 110 kV OHL can be obtained using metal
cross-arm earthing technology.
Our ATP-EMTP model and model-based stochastic analysis
is not limited to simulations described in the paper. Other
simulations for overhead lines of different configuration can be
successfully conducted and our novel approach can be applied
to their lightning performance assessment.
VII. REFERENCES
[1] T. Gallagher , I. Dudurych, M. Holly, “Advanced Simulation of the
lightning Performance of a 110 kV Unshielded Overhead Line,”
European EMTP-ATP Conference proceedings, September 3-4, 2001,
UWE Bristol, UK, 2001, pp. 122-132.
[2] T. Gallagher, I. Dudurych, J. Corbett, M. Val Escudero, “Towards the
Improvement of the Lightning Performance of 110 kV Unshielded
Overhead Lines,” Proceedings of 26th
International Conference on
Lightning Protection, Cracow; September 2nd
– 6th
, 2002, pp. 458-463.
[3] T. Gallagher, I. Dudurych, “Modeling and Simulation of Fast Transients
in HV Overhead Lines Induced by Lightning Strokes,” Technical
Electrodynamics: Problems of Modern Electrical Engineering, v. 2,
Kyiv 2002, pp. 19-24.
[4] Alternative Transient program (ATP) Rule Book. K.U. Leuven EMTP
Centre, 1987.
[5] H.W. Dommel, Electromagnetic Transients program (EMTP Theory
Book), BPA, Portland, USA, 1986.
[6] CIGRE Working Group 33-01 (Lightning) of Study Committee 33
(Overvoltages and Insulation Co-ordination), Guide to procedures for
estimating the Lightning Performance of Transmission Line’, 1991.
[7] IEEE Working Group Report, “Modeling guidelines for fast front
transients,” IEEE Transactions on Power Delivery, Vol.1, No. 1, 1996,
pp. 493-506.
[8] M. Darveniza, M.A. Sargent et. al., “Modeling for Lightning Performance
Calculations,” IEEE Transactions on Power Apparatus and Systems,
Vol-98, No.6. 1979, pp. 1900-1908.
[9] J. Corbett, M. Val Escudero, T. Gallagher, I. Dudurych, “Statistical
Analysis and Modelling of Lightning Performance of 110kV and 220kV
Overhead Networks in Ireland,” Proceedings of SIGRE 2002 Symposium,
Paris; August 25th
– 30th,
2002, report 33-204.
[10] M. Evans, N. Hastings, B. Peacock, Statistical Distributions, John Wiley
& Sons, 2000.
[11] T. J. Gallagher, C.F. Huang, M. Holly, C. Kelliher, “A Comparison
Between Lightning Dissipaters and Franklin Rods on the Impulse
Response of a Scale Model of a 110 kV Transmission Line,” Proceedings
of ICLP 2000, Rodes, 18-22 September 2000, pp. 352-356.
VIII. BIOGRAPHIES
Ivan M. Dudurych (M’96, SM’02) received his
degree of electrical engineer from the Lviv
Polytechnical Institute in 1980 and was awarded
Ph D degree from Kyiv Polytechnical Institute in
1990 for his work on analysis of switching
transients of 1150 kV OHL. Associate Professor of
the National University “Lviv Polytechnic”,
Ukraine, he was awarded an ESB Newman
Scholarship at University College Dublin, Ireland.
He has published some 45 technical and 8 didactical
works. Now he is with the Ireland’s National
Transmission System Operator EirGrid, Plc as operation studies engineer. His
interests include modeling and simulation of electric power system transients
and steady-states, lightning performance and protection of power systems,
development of new methods and algorithms of power system analysis,
technological and economical issues of deregulation and privatization of
electric power industry.
T. J. Gallagher received the BE degree in
Electrical Engineering from University College
Cork in 1959 and was awarded the Ph D degree
from Queen Mary College, University of London
for his work on the electrical properties of
insulating liquids. He joined the Electrical
Engineering Department in UCD in 1965 and has
continued with his research interests into the
electrical behavior of materials under high
electrical stresses. He is a Fellow of the IEE, and has published some 35
technical articles and 3 books connected with his research. His current
research is focused on lightning effects on the transmission system in Ireland,
the behavior of bubbles in insulating liquids under high stress and the
development of a range of sensors utilizing the dielectric properties of
materials.
Maurice Holly received his B.Eng (Hons) degree in
electrical engineering from University College
Dublin in 1970. Following postgraduate research in
the area of diode braking of synchronous machines
he received a M.Eng.Sc. in 1972 and a Master of
Industrial Engineering in 1976. He has been
employed by Electricity Supply Board since 1971.
The majority of his time has been spent in National
Grid. His areas of work have included power system
planning, operation, control and protection. He has
been on consultancy assignments in Western
Australia and Dubai, UAE. His current responsibility is as Manager System
Studies Group in the Power System Operation area. He is a Member of the
IEI and the IEE. He has been appointed to the Board of EirGrid Plc. which
will shortly take over the operation of Ireland's electricity transmission system
from ESB National Grid (ESBNG).
0.14
0.31
0.44
0.09
0.03 0.03
0.77
0.65
0.53
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
Distributionoffaulttypes
Single-phase Two-phase Three-phase
Fault types
Original configuration All wooden Wooden cross-arms