CALCULATION OF LIGHTNING FLASHOVERS AND BACKFLASH LEVEL
ON 230kV TRANSMISSION LINES
Bander J. Al-Qahtani *
SAOO-NGPD-TSU
Saudi Aramco
Abqaiq, Saudi Arabia
Bander.qahtani@aramco.com
ABSTRACT
Lightning has been one of the important problems for
insulation design of power systems and it is still the
main cause of outages of transmission and distribution
lines. Lightning caused outages can be reduced by
lightning protection devices such as ground wires and
lightning arresters.
This paper presents a comparative studies used to
determine the lightning backflashovers level on 230kV
transmission lines utilized by Saudi Electric Company
(SEC) in Saudi Arabia, using two well known
approaches CIGRE, and the simplified method. The
studies include lightning flashovers, backflash
analysis, as dependent on the tower design parameters
which is considered the main parameters that reduce
the rate of lightning bachflashovers in the
transmission lines. The study results can be applied to
reduce the number lightning flashovers and therefore
reduce the transmission lines outages.
KEY WORDS
Lightning flashovers, backflashovers, simulation and
ground wires
1. Introduction
A complete awareness of the parameters of lightning
strokes is essential for the prediction of the severity of the
transient voltages generated across power apparatus either
by a direct stroke to the power line/apparatus, or by an
P.O.Box 66467, Dammam 31576, Kingdom of Saudi Arabia
M. H. Shwehdi
Electrical Engineering Department
King Fahd University of Petroleum & Minerals
Dhahran, Saudi Arabia
mshwehdi@kfupm.edu.sa
indirect stroke. However, no two lightning strokes are the
same. Therefore, the statistical variations of the lightningstroke parameters must be taken into account in assessing
the severity of lightning strokes on the specific design of a
power line or apparatus.
The lightning return-stroke current and the charge
delivered by the stroke are the most important parameters
to assess the severity of lightning strokes to power lines
and apparatus. The return-stroke current is characterized
by a rapid rise to the peak, Ip, within a few microseconds
and then a relatively slow decay, reaching half of the peak
value in tens of microseconds. The return-stroke current is
specified by its peak value and its waveshape. The
waveshape, in turn, is specified by the time from zero to
the peak value (tf, front time) and by the time to its
subsequent decay to its half value (th, tail time). The tail
time being several orders of magnitude longer than the
front time, its statistical variation is of lesser importance
in the computation of the generated voltage. The
generated voltage is a function of the peak current for
both the direct and indirect strokes.
For backflashes in direct strokes and for indirect strokes
the generated voltage is higher the shorter the front time
of the return-stroke current [1]. The front time (and the
tail time, to a lesser extent), influence the withstand
capability (volt-time characteristics) of the power
apparatus. The charge in a stroke signifies the energy
transferred to the struck object. The ancillary equipment
(e.g., surge protectors) connected near the struck point
will be damaged if the charge content of the stroke
2
exceeds the withstand capability of the equipment. The
return-stroke velocity will affect the component of the
voltage which is generated by the induction field of the
lightning stroke [1]. Field tests have shown that the
parameters of the first stroke are different from that of the
subsequent strokes.
2. Lightning Flashes
the system. Thus, assuming the lightning channel to be a
current source, the transient voltages across the insulator
of a phase conductor are generated in three ways: (i)
lightning striking the phase conductor (shielding failure),
(ii) lightning striking the tower or the shield wire
(backflash), and (iii) lightning striking the nearby ground
(indirect stroke). The severity of these three types of
transient voltages is influenced by different lightning
parameters [2, 3].
Lightning damages a power apparatus in two ways: (i) it
raises the voltage across an apparatus such that the
terminals across the struck apparatus spark over causing a
short circuit of the system or the voltage punctures
through the apparatus electrical insulation, causing
permanent damage. (ii) The energy of the lightning stroke
may exceed the energy handling capability of the
apparatus, causing meltdown or fracture.
The significance of lightning parameters on power
systems is gauged by the severity of the transient
overvoltages they create and the consequent damages to
the power system. As mentioned before, these
overvoltages are generated by three different ways.
A lightning flash generally consists of several strokes
which lower charges, negative or positive, from the cloud
to the ground. The first stroke is most often more severe
than the subsequent strokes. Low current continues to
flow between two strokes, thus increasing the total energy
injected to the struck object. The transient voltage from
the lightning strike is generated by: (i) direct stroke and
(ii) indirect stroke. For direct strike, it can strike an
apparatus. In that case, the apparatus will be permanently
damaged. Most often, lightning strikes the phase
conductor of the power line. In that case, a traveling
voltage wave is generated on the line; it travels along the
line and is impressed across the terminals of an apparatus
or most often the insulator between the phase conductor
and the cross-arm of the tower at the end of the span. If
the voltage is high enough, the insulator flashes over
causing a short circuit of the system.
The lightning return-stroke current is the most significant
parameter in the estimation of the response of electrical
apparatus and systems to lightning strikes. The return
stroke current rises to its peak in a few microseconds and
then decays to the half value in a few tens of
microseconds [4]. The return-stroke current is identified
by three parameters: peak value Ip, front time tf and time
to half value th. The difficulty with the exponential
function representing a return-stroke current is that it is
not easy to select the parameters of these analytical
expressions to fit the three parameters (Ip, tf and th).
However, this problem does not arise if the return-stroke
current is represented as linearly rising and linearly falling
functions [4]:
Many overhead power lines are equipped with shield
wires to shield the phase conductors. Even then, shielding
failures occur when lightning bypasses the shield wires
and strikes a phase conductor. When lightning strikes a
tower, a traveling voltage is generated which travels back
and forth along the tower, being reflected at the tower
footing and at the tower top, thus raising the voltages at
the cross-arms and stressing the insulators. The insulator
will flash over if this transient voltage exceeds its
withstand level (backflash). Even if lightning strikes a
shield wire, the generated traveling voltage wave will
travel to the nearest tower, produce multiple reflections
along the tower, causing backflash across an insulator.
When lightning hits the ground several hundred meters
away from the line (indirect stroke), the electric and
magnetic fields of the lightning channel can induce high
voltage on the line for the insulators of the low-voltage
distribution lines to spark over causing a short circuit of
3. Computation of Insulator Voltage
I (t )   1tu(t )   2 (t  t f )u (t  t f ) (1)
Where α1 = Ip/tf, and α2 = (2th–If)Ip/2tf (th–If). For short tf
in the order of a few microseconds, eqn. 1 seems to work
very well. With eqn. 1, the three parameters of the returnstroke current can be varied very easily. Starting with the
return-stroke current, the various voltage components
across the insulator were computed.
3.1 First and Second Voltage Components
To compute the first voltage component, i.e. the crossarm voltage Vca, the tower was assumed to be a vertical
transmission line of a fixed surge impedance Zt. The
voltage and current waves were assumed to travel along
the tower with a constant p.u. velocity of βt. The first
reflections from the adjacent towers for the shield-wire
voltages were also included in the computation. The
tower footing resistance was assumed to be constant, Rtf.
The tower-top was terminated by shield wire(s) and the
3
lightning channel of constant surge impedance Zch. The
cross-arm voltage due to the multiply reflected voltage
waves along the struck tower was computed by following
a previous method as shown in [4]. Although Zt, βt, Rtf
and Zch were assumed as constant, they were used as input
variables which could be changed for parametric analysis.
The second voltage component is the voltage induced on
the phase conductor due to electromagnetic coupling with
the shield wire. This voltage is equal to kcf Vt, where Vt is
the tower-top/shield-wire voltage and the coupling factor
kcf is equal to Zps/Zsh. Zps is the mutual surge impedance
between the phase conductor and the shield wire; Zsh is
the shield-wire surge impedance [4]. The tower-top
voltage was computed following the same procedure as
for Vca. The insulator-string voltage due to the first and
second voltage components is:
Vins  Vca  kcf Vt
(2)
3.2 Third Voltage Component
The third voltage component is the voltage induced on the
phase conductor due to the electromagnetic fields of the
lightning channel. The computation of the phaseconductor voltage followed previous analysis [4], with the
difference that, in the present case, the stroke hits the
tower top instead of the ground. This difference is
manifested in the inducing voltage Vi, which is the
voltage in space (in the absence of the phase conductor)
caused by the residual charge in the upper part and the
return-stroke current in the lower part of the lightning
channel. Vi is:
increases as a function of time and the return-stroke
velocity, with its lower and upper limits 0 and hc. For a
stroke to tower of height hc, the lower and the upper limits
of z‫ ׳‬are ht and hc. Thus, for a stroke to tower, the
voltages induced on the phase conductor were computed
for two different cloud heights (hc and ht), and then the
second induced voltage (for ht) was subtracted from the
first induced voltage (for hc).
4. Computation of Backflash Rate
The overhead ground wires or shield wires have been
located so as to minimize the number of lightning strokes
that terminate on the phase conductor. The remaining and
vast majority of strokes and flashes now terminate on the
overhead ground wires. A stroke that so terminate forces
current to flow down the tower and out on the ground
wires. Thus voltage are built up across the line insulation.
If these voltages equal or exceed the line CFO, flashover
occurs. This event is called a backflash. By referring to
figure 1, equations for the crest voltage, the voltage at the
tower top prior to any reflections from the footing
resistance, and the final voltage can be derived as follows
hp
A
(3)
) dz
t
0
Where Φ is the scalar potential due to the residual charge
in the upper part of the lightning channel, and A is the
vector potential due to the return-stroke current in the
lower part of the channel. For stroke to ground, Φ and A
are
Vi 
 ( 
r  r
hc q ( r , t 
)
0
1
c
 (r , t ) 
dr 

40 z 
r  r
A( r , t ) 
0
4
z

0
r  r
)
c
dr 
r  r
I ( r , t 
(4)
Figure 1. Surge voltages at the tower and across the insulation [5]
VTT  K sp K TT I
VTA  K sp K TA I
(4.1)
VF  Re I
And the current through the footing resistance is
(4.2)
Re
(5)
where r and r‫ ׳‬are field and source points, respectively: I
is the return-stroke current: q0 is the constant linear charge
density of the leader stroke: hc is the cloud height: and is
the instantaneous height of the upward-moving head of
the return stroke above ground. For a stroke to ground, z‫׳‬
IR 
Where
Ri
I
4
KTT  Re   T ZT
TT
tf
IC 
T
KTA  Re   T ZT A
tf
(4.3)
For these equations:
(4.9)
Since KTT is in many cases approximately equal to KTA,
then approximately,
CFO
(4.10)
I 
C
 T 
 T
 T 
2
K SP  1   R 1   T 1  2 S    R T 1  4 S    R T  1  6 S   .....
 t 
 t  
 t f 
f 
f 



CFO
KTA  CKTT K SP
1  C KTT K SP
The probability of a flashover is the probability that the
stroke current I equals or exceeds the critical current IC, or
Pr obI  I C   PI C  

 f I dI
(4.11)
IC
Re 
T
Z g Ri
Z g  2 Ri
R 
Z g  2 Ri
Z  Ri
 T

ZT  Ri
Z g  2 Ri
Zg
(4.4)
Z g  2 Ri
Also, the tail of the voltages can be conservatively
approximated by a time constant τ:
 
Zg
Ri
(4.5)
TS
That is, the equation for the tail of the surge is
eTT  VF e
(t t f ) / 
(4.6)
To be complete the definition of the variables are:
tf
= time to crest of the stroke current, μs
C
= coupling factor
ZT = surge impedance of the tower, ohms
Zg = surge impedance of the ground wires, ohms
TT = tower travel time, μs
TA = tower travel time to any location on the tower A,
μs
TS = travel time of a span, μs
I
= stroke current, KA
IR = current through footing of struck tower, KA
Ro = measured or low-current footing resistance, ohms
Ri
= impulse or high-current footing resistance, ohms
 = time constant of tail, μs
Now, to provide first estmate of the backflash rate, the
BFR, examine figure 6. The surge voltage on the ground
wires produces a surge voltage on the phase conductor
equal to the coupling factor C times the voltage on the
ground wires, or CVTT. Also note that the voltage VTA is
located on the tower opposite the phase conductor.
Therefore, the crest voltage across the insulation V1 is
V1  I KTA  CKTT K SP
(4.7)
Also, note that the crest voltage VIF across the insulation
caused by the footing resistance is
VIF  1  C Re I
(4.8)


For a flashover to occur, the voltage across the insulator
V1, must be equal to or greater than the CFO of the
insulation. Replacing V1 of Eq. (7) with CFO, the current
obtained is the critical current IC at and above which
flashover occur, i.e.,
The backflash rate BFR is this probability times the
number of strokes, NL, that terminate on the ground wires,
or
BFR= N L PI C 
(4.12)
Where
NL  Ng
28h
0.6
 Sg 
(4.13)
10
Where h is the tower height (meters), Sg is the horizontal
distance between the ground wires (meters), and Ng is the
ground flash density (flashes/km2-year), thus the BFR is
in terms of flashovers per 100 km-years.
The equations for KTT and KI show that the voltage across
the insulation increases as the time to crest of the stroke
current decreases. This is caused by the tower component
of voltage. Thus the critical current increases as the time
to crest increases. Therefore, theoretically, all fronts
should be considered. To do this, the equation for BFR
should be changed to the following:
BFR=0.6 NL P(IC)
(4.14)
5. Simulation & Results
The 230 kV HV line of figure 2 whose characteristics are
given in table I, are used to calculate the backflash rate
using different methods. Also, this case study will include
the following
1. The effect of decrease of resistance from Ro versus Ri
2. One versus two shield wires
3. The effect of underbuilt shield or ground wire
As shown in the figure 3 & 4 the backflash rate for the
above mentioned high voltage lines with span length of
300 meters and CFO of 1200kV has been calculated by
using CIGRE method software and simplified method.
The comparison appears acceptable for the line with
tower height of 35 meters, but for tower height of 70
meters the simplified method is inadequate. So, the
CIGRE method is always the proper tool.
5
10
BFR, Flashovers/100 km-yrs
Using the CIGRE method, the BFR of the single circuit
230 kV is shown in Fig. 5 as a function of RO with the
ratio ρ/RO as a parameter. To illustrate the effect of the
decrease of resistance with current, a curve labeled Ri=RO
for which the footing resistance is not decreased is also
presented.
9
8
7
CIGRE
Method
6
5
Simplified
Method
4
3
2
1
0
1
2
3
4
5
6
X10 Ro, ohms
Figure 3. Comparasion of BFRs for CIGRE method and simplified
method, 230kV double circuit towers with two ground wires and height
of 35 meters
BFR, Flashovers/100km-yrs
12
10
8
Simplified
Method
6
CIGRE
Method
4
2
0
1
2
3
4
5
6
X10 Ro, ohms
A ground wire located below the phase conductors cannot
truthfully be called a shield wire, since it has no shielding
function. Rather, its function is to increase the coupling
factor to the lower phases, those phases that are most
likely to flashover. For example, for the 230-kV doublecircuit, two-ground-wire line with a shield wire height of
35 meters and coupling factor to the top, middle, and
bottom phase of 0.350, 0.248, and 0.183, respectively,
installing a ground wire at 12 meters above ground at the
center of the tower increases these coupling factors to
0.441, 0.347, and 0.307, respectively. Thus all coupling
factors are increased and are more uniform. Figure 7
shows the dramatic decrease in BFR for this case.
12
BFR, Flashovers/100km-yrs
For some applications, where the cost of two shield wires
is not economically and technically justified, or where
there is low ground flash density, a single shield wire can
be used. The single wire increases the value of Re,
decreases the coupling factor, and thus increase the BFR.
To illustrate, the curves of Fig. 6 have been constructed to
compare one and two shield wires for a 230 kV doublecircuit line and two shield wires for a single-circuit 230
kV line. Using one shield wire on the double-circuit line
essentially doubles the BFR as compared to the twoshield-wire case.
Figure 4. Comparasion of BFRs for CIGRE method and simplified
method, 230kV double circuit towers with two ground wires and height
of 70 meters
10
8
p/Ro=40
6
p/Ro=20
p/Ro=10
4
2
0
1
2
3
4
5
6
7
8
X10 Ro, ohms
Figure 5. Effect of decrease to high-current footing resistance
9
BFR, Flashovers/100km-yrs
Figure 2. 230 kV Tower Dimensions
8
7
6
5
2 Grd Wire
4
1 Grd Wire
3
2
1
0
1
2
3
4
5
6
X10, ohms
Figure 6. Tow shield wires for the 230kV double circuit line with height
of 35 m decrease the BFR, p/Ro=20
6
BFR, Flashovers/100km-yrs
10
9
8
7
2 Grd Wires
6
5
2 Grd
Wires+under
built grd wire
4
3
2
[1] P. Chowdhuri, J. G. Anderson, W. A. Chisholm, T. E.
Field, M. Ishii, J. A. Martinez, M. B. Marz, J.
McDaniel, T. R. McDermott, A. M. Mousa,T. Narita,
D. K. Nichols, & T. A. Short, Parameters of
Lightning Strokes: A Review, IEEE Transactions
and Power delivery, March 28, 2003.
1
0
1
2
3
4
5
6
7
8
X10 Ro, ohms
Figure 7. An underbuilt ground wire decreases the BFR, 230kV double
circuit line with height of 35 m, p/Ro=20.
6. Conclusion
The most significant parameters of the lightning return
stroke to estimate the severity on the power system are: (i)
peak current, (ii) current front time, (iii) velocity and (iv)
total charge of the flash.
The electromagnetic fields of the lightning channel and
the magnetic fields of the traveling current waves along
the power-line tower will significantly affect the
insulator-string voltage, and hence the outage rate due to
backflash. Analytical methods to estimate the backflash
outage rate have been proposed, which should result in
better prediction of the lightning performance of overhead
power lines.
In this report, equations were developed to estimate the
BFR that include the tower component of voltage; their
use is called CIGRE method. This method is suffiently
complex so that the use of the computer program is
suggested. The effect of decrease of the concentrated
grounds value on the BFR was addressed. Also, the effect
of the number of shield wires as well as adding underbuilt
shield or ground wire were highlighted.
The 230 kV line design from SEC is considered very
highly engineered, using two ground shield wires with 7.3
meter span at each side made almost a full cover for both
circuits. This tower can be considered as lightning proof.
7. Acknowledgment
The authors express appreciation to Saudi Electric
Company engineers for thier time and support also their
gratitude to KFUPM for educational, studies facilities and
support.
References:
[2] P. Chowdhuri, A.K. Mishra & B.W. McConnell,
Volt-time characteristics of short air gaps under
nonstandard lightning voltage waves, ibid., Vol. 12,
No. 1, pp. 470-476, 1997.
[3] P. Chowdhuri, A.K., Parameters of Lighting Strokes
and Their effect on Power Systems, Vol. 12, No. 1,
pp. 1047-1051, 2001
[4] P. Chowdhuri, A.K., S. Li & P. Yan Rigorous
analysis of back-flashover outages caused by direct
lightning strokes to overhead power lines, IEEE
Proceedings, 2002
[5] Andrew R. Hileman, Insulation Coordination for
Power Systems, (Eastern Hemisphere Distribution,
New York, 1999)
[6] R. Thottappillil & M. A. Uman, Comparison of
lightning return stroke models, J. Geophys. Res., vol.
98, pp. 22 903–22 914, 1993.
[7] V. Cooray & R. E. Orville, The effect of the variation
of current amplitude, current rise time and return
stroke velocity along the return stroke channel on the
electromagnetic fields generated by the return stroke,
J. Geophys. Res., vol. 95, pp. 18 617–18 630, 1990.
[8] Dennis W. Lenk, F. Richard Stockum & David E.
Grimes,A new approach to distribution arrester
design, IEEE Transactions on power delivery, vol. 3,
No. 2, April 1988.
[9] P. Pinceti & M. Giannettoni, A simplified model for
zinc oxide surge arrester, IEEE Transactions on
power delivery, Vol. 14, No. 2, April 1999.
Biographies
Bander J. Qahtani; Born in Al-Khobar 1979. He obtained his
B.Sc. degree in electrical engineering with honors from King
Fahd University of Petroleum & Minerals (KFUPM) in 2002. In
the year 2000 he was selected as distinguished student for Saudi
Aramco Scholarship program. During his studies at KFUPM he
has conducted several term projects and studies dealing with
Industrial power systems. Upon graduation, Bandar was
employed by Aramco as instrument engineer with Southern
Area Producing Engineering Department (SAPED) in Abqaiq.
He is enrolled in the Msc. Program at KFUPM. Bandar has
7
published and presented many technical papers and reports to
region, and international conferences.
includes, power system analysis, Power Quality & Harmonics,
overvoltages analysis on Power Systems, Transmission and
Distribution Systems. Dr. Shwehdi is active in IEEE activities.
He is listed as a distinguished lecturer with the DLP of the
IEEE/PES DLP upon the Board selection, was named and
awarded the 2001 IEEE/PES outstanding chapter engineer,. He
was named and awarded the 1999 IEEE WG for standard award,
the GCC-CIGRE 1998 best applied research award, IEEE/IAS
Outstanding Supervisor for Student Research 1989, 1990, and
the IEEE outstanding student advisor in 1990.
M. H. Shwehdi (S'74, M'85, SM 90) received the B. SC. degree
from University of Tripoli, Libya in 1972. He obtained the M.
Sc. Degree from the University of Southern California and Ph.D.
degree from Mississippi State University in 1975 and 1985
respectively all in electrical engineering. He was a consultant to
A.B. Chance Company, and Flood Engineering. Dr. Shwehdi
held teaching positions with the University of MissouriColumbia, Texas A & I University, University of Florida and
Penn. State University from 1991-1993. At present he is
associate professor with the King Fahd University of Petroleum
& Minerals (KFUPM), Saudi Arabia. His research interest
Table I Characteristics of Lines, Distances in meters
System
Voltage
h
yA
yB
yC
Sg
Sa
Sb
Zg
ZT
CA
CB
CC
230
35
29
24
18
5
8
11
379
190
.35
.25
.18
a230
35
29
24
18
0
8
11
600
190
.22
.16
.12
230
70
64
59
53
5
8
11
421
210
.42
.34
.28
35
29
24
18
5
8
11
239
190
.44
.35
.31
b230
a
b
Single ground wire. Underbuilt ground wire at h=12 m at center of tower