Volume 56, Number 1-2, 2015
9
Investigation into Tower Model Effect
on Fast-Front Overvoltages in
Transmission Lines
Levente Czumbil, Dan D. Micu, Denisa Şteţ, Andrei Ceclan
Dept. of Electrotechnics and Measurements, Technical University of Cluj-Napoca, Romania
Abstract: The proper modelling of transmission line towers and conductors plays an essential part in the travelling-wave analysis
of fast front overvoltages due to lightning surges in overhead power lines. This paper investigates the effect of different simulation
component models like power line towers, lightning current or tower footing resistance on the transient overvoltages produced by
back flashover phenomena. A new combined tower model that takes into consideration both the bracings and the damping effect of
each tower section is proposed.
keywords: fast front overvoltages, tower models, lightning current models, transmission lines, back flashover.
1.
INTRODUCTION
One of the principal causes of Fast Front
Overvoltages (FFO) in power systems is lightning
stroke to transmission lines. Lightning overvoltages
have a wave head of several microseconds and are an
important factor in determining the insulation design of
substation equipment [1, 2].
Lightning overvoltages could be produced by
direct lightning strokes to phase wires or by back
flashover, when the lightning stroke hits the tower or
the ground wire and the voltage across the phase wire
insulator string exceeds its withstanding capability.
A direct strike to a power line is very rare, and
most of the lightning strikes the top of the transmission
tower. The lightning back flashover effects are
recognized as one of the major causes of transmission
line (TLine) outages and may also result in substation
outages, caused by incoming surges with amplitude
exceeding the insulation level of the substation
equipment [2].
It is very difficult to observe the lightning
overvoltage experimentally, thus a numerical
simulation is adopted in order to investigate it [3]. This
paper studies the effect of different simulation
component implementation (e.g. tower model, footing
resistance, lightning current model and waveform, etc.)
on the transient overvoltages produced by back
flashover phenomena in case of overhead power lines.
2.
TRANSMISSION LINE TOWER
MODELLING
One of the most important steps in the evaluation
of fast front overvoltages produced by lightning strikes
to overhead power lines, is the accurate modelling of
transmission line towers. Although the lightning
response of a transmission line tower is an
electromagnetic phenomenon, the representation of a
tower is usually made in circuit terms.
Fig. 1. a) Single lossless transmission line model; b) Multi-Story
transmission line model;
2.1. Single lossless transmission line models
The simplest representation of power line tower is
a lossless distributed-parameter transmission line,
characterized by its surge impedance and travel time.
Table I shows the different tower surge impedance
formulas presented in the literature, based on an
electromagnetic theory approach or on experimental
measurements. Due the multiple paths through
© 2015 – Mediamira Science Publisher. All rights reserved
ACTA ELECTROTEHNICA
10
crossarms and the lattice structure of the tower, the
propagation velocity of the lightning current and
voltage waves across the tower is reduced to 290 ∙ 106
m/s.
TABLE I
DIFFERENT TOWER SURGE IMPEDANCE FORMULAS
Author
Proposed Formula
Wagner
[4]

H
Z S = 60 ⋅ ln 2 2 ⋅
RB

Sargent [4]

RB 2 + H 2

Z S = 60 ⋅ ln 2 ⋅
RB


 H
Z S = 60 ⋅ ln
 RB
Jordan [4]
ZT =
TABLE III.
OBTAINED EVALUATION ERRORS






 − 60


 1
 R Avg
Z S = 60 ⋅ ln cot ⋅ arctan
 H
 2

 
CIGRE [2]
IEEE [5]
Corrected
CIGRE [4]
Baba &
Ishii




  
 Ravg
1

⋅ 60 ⋅  ln cot ⋅ arctan
4
   2
 H
 
π
  




  
  − ln 2 




TABLE I (CONTINUES)
DIFFERENT TOWER SURGE IMPEDANCE FORMULAS
Author
Ametani [6]
Hara [7]
The evaluation error produced by each of the
above presented tower surge impedance formula are
presented in Table III. It can be observed that the most
accurate results are provided by Ametani’s formula.
However, due the fact that the tower response to a
lightning strike is directly dependent on its surge
impedance value one could also use the corrected
CIGRE formula in order to obtain a higher margin on
the evaluated overvoltage values at GIS entrance.
Proposed Formula
2



2
2

 R Eq + H + H 



+
ln


2
2
Z S = 60 ⋅  R Eq ⋅  R Eq + 4 H + 2 H 




 3R Eq + R Eq 2 + 4 H 2 − 4 R Eq 2 + H 2
+
2H











2.2. Ishii Multi-Story Tower Model
For a more realistic representation of transmission
line towers, Ishii proposed a multi-story tower model
where, in order to take into account the attenuation of
the traveling wave long tower height, each tower
section is represented by a lossless TLine in series with
a parallel R–L circuit (see Fig. 2).
 2 2 ⋅H

Z S = 60 ⋅  ln
− 2


REq


where: H is tower height; RB, RAvg and REq are
tower base, average and equivalent radius by
considering the tower as system of multiple vertical
parallel conductors, respectively.
Due the fact that most of the tower surge
impedance equations are empirical ones or have been
developed by imposing a set of simplifying conditions,
in order to determine the most accurate evaluation
formula the authors have developed MathCad algorithm
which implement and test the above presented
equations for different tower geometries. Obtained
results have been compared to measured surge
impedance values presented in literature [6, 8]. Table II
contains details regarding the investigate tower
geometries:
TABLE II.
INVESTIGATED TOWER GEOMETRIES [6, 8]
Fig. 2. Ishii Multi-Story Tower Model [4].
The values of the parameters, and the model itself,
have been revised in more recent years by Ametani [9].
Thus, the damping resistances and inductances could be
evaluated based on tower section surge impedance,
according to the following equations:
hi
1
Ri = 2 ⋅ Z T 1 ⋅ ln  ⋅
 γ  l1 + l 2 + l 3
(i = 1, 2, 3)
1
H
R 4 = 2 ⋅ Z T 2 ⋅ ln  , Li = 2 ⋅ Ri ⋅ τ , τ =
υT
γ 
(1)
(2)
where: ZT1 and ZT2 are the surge impedance of the
three upper tower sections, and of the tower foot
section respectively, hi is the height of each tower
section, γ is an attenuation coefficient (γ = 0.8944) and
τ is the wave travel time across the tower.
Volume 56, Number 1-2, 2015
2.3. Hara Multi-Story Tower Model
Measurements on scaled and real size
transmission line towers showed that the surge
impedance of conductors is reduced about 10% by
adding the bracings to the main legs. To take into
account this reduction in the real value of tower surge
impedance, Hara proposed [7] a multi-story tower
model (see Fig. 3) where introduced for each tower
section an additional parallel surge impedance:
Z Lk = 9 ⋅ Z Tk , k = (1,2,3,4)
(3)
where: ZT is the surge impedance of each tower
section.
11
In order to eliminate unwanted wave reflections
the authors propose to use the same surge impedance
value considering one single section for the upper part
of the tower. To obtain accurately the surge impedance
of each tower section the Ametani formula, should to
be used.
2.5. Tower Footing Impedance
In order to take into account soil ionization
phenomena, tower footing could be represented by a
current dependent variable resistance driven by
equation (5) proposed by CIGRE [2] and IEEE [5]:
RT =
R0
1+
; IC =
I
IC
1 E0 ⋅ ρ
⋅
2π R0 2
(5)
where: RT is the current dependent tower footing
resistance, R0 is the low current and low frequency
footing resistance, IC is the limiting current to initiate
soil ionization, I is the strike current, ρ is the soil
resistivity and E0 is the soil ionization gradient.
3.
Fig. 3. Hara Multi-Story Tower Model.
Also, for each tower crossarm, Hara introduced an
equivalent transmission line component based on the
surge impedance expression for a conventional
horizontal conductor:
Z Ak = 60 ⋅ ln
l
2 ⋅ hk
, rAk = Ak
rAk
4
LIGHTNING CURRENT MODELLING
The lightning current produced by a lightning
stroke to an overhead transmission line could be model
using a variable current source in parallel with a 400 Ω
resistance representing the air path between the clouds
and the transmission line. To describe the lightning
impulse current, usually manufactures use a Ramp, eq.
(6), or a Double Exponential, eq. (7), function which
are easier to implement in test equipment.
(4)
where: hAk and rAk are respectively the height and
the equivalent radius of the kth crossarm (¼ of the
crossarm length)
2.4. Proposed Multi-Story Tower Model
In order to take into account both the presence of
tower crossarms, the damping effect of each tower
section and the surge impedance values reduction
produced by bracings, a new combined tower model
has been implemented by the authors based on the
previously presented two multi-story tower models, see
Fig. 4.
I LC

⋅t

tf

I Ramp (t ) = 
I LC

⋅ 2th − t f − t
⋅
t
2

h −tf

(
(
)(
I DExp (t ) = I LC ⋅ e − A⋅t − e − B ⋅t
t ≤ tf
)
,
t > tf
)
(7)
where: ILC is the amplitude of the lightning
current, tf is the time to front, th is the time to half,
while A and B are exponential coefficients for the
double exponential model.
In 1991, based on statistical analysis of recorder
lightning strikes around the world, CIGRE [2] proposed
a more complex formulation of lightning current which
to take into account the concave form of the rise up
part:

A1 ⋅ t + A2 ⋅ t n
t ≤ tc

 t − tc 
 t − tc 
I CIGRE (t ) = 




 B1 ⋅ exp − t  − B2 ⋅ exp − t  t > tc
1 
2 



Fig. 4. Proposed Multi-Story Tower Model.
(6)
(8)
ACTA ELECTROTEHNICA
12
TABLE V
CONDUCTORS POSITION ON TOWER
where: tc is the time to crest, t1 and t2 are time
parameters and A1, A2, B1, B2 are coefficient
parameters which describe the front and the tail part of
lightning current waveform [2].
Recently, in literature, the Heilder lightning
current function [10] is used for the study of fast front
overvoltages produced by lightning strikes to overhead
power lines:
n
 t 
 
 t 
I LC  t f 
⋅
⋅ exp − 
I Heidler (t ) =
n
h
 t 
 th 
1+  
 tf 
 
(9)
where: n is the order of the implemented Heidler
function and η is a scaling coefficient.
Conductor
Phase Wire A1
Phase Wire B1
Phase Wire C1
Phase Wire A2
Phase Wire B2
Phase Wire C2
Sky Wire
4.
CASE STUDY
In order to determine the effect of the different
simulation component models presented above on the
produced fast-front overvoltages a 110 kV double
circuit power line connecting two distribution
substations is considered (see Fig. 5). The overhead
power line consists in one sky wire and six phase wires
placed in an anti-symmetrical phase arrangement on
ITSn110.256 type transmission line towers. Table V
presents the geometry of the power line tower, while in
Table VI the position of each transmission line
conductor on the tower is presented.
Height [m]
34.4
28.2
23.2
23.2
28.2
34.4
39.5
The 110 kV power line has a total length of 50 km
and an average 35 MVA power load (approximately
160 A on each phase wire). The produced fast-front
overvoltages due to back flashover are analysed
considering different tower models, different lightning
currents and different tower footing resistance values.
5.
SIMULATION RESULTS
Due the fact that the insulator string may
withstand a high transient voltage for a short duration,
but it could fail to withstand a lower transient voltage
with a longer duration, the volt-time characteristic
proposed by CIGRE [2] has been implemented for the
back flashover simulations.
VWIns = K 1 +
Fig. 5. 10 kA, 8/20 µs lightning current implementation with different
mathematical functions.
Position [m]
-3.2
-5.3
-3.2
3.2
5.3
3.2
0
K2
t 0.75
(10)
where: VWIns is the insulator string withstand
voltage in (kV), K 1 = 400 ⋅ L , K 2 = 710 ⋅ L , L is the
length of the insulator string in (1.5 m for the
investigated power line), and t is the elapsed time in
(µs) from the lighting strike occurring.
Fig. 7. Lightning current flowing through the tower.
Fig. 6. Investigate 380 kV overhead power line.
TABLE IV
POWER LINE TOWER STRUCTURE GEOMETRY
Section Width
Conductor Radius
Section Height
DT
[m]
0.4
DM
[m]
1.28
DB
[m]
4.78
rT
[mm]
30
rM
[mm]
50
rB
[mm]
85
H1
[m]
23.2
H2
[m]
16.3
Considering the worst case scenario, when a 200
kA lightning hits the sky wire next to a tower, the
produced FFO waveforms, due to back flashover on left
side upper phase wire (Phase A1), are evaluated along
the power line length are evaluated by modeling the
first five tower in both direction from the lightning
discharge location.
From Fig. 6 it can be observed that most of the
lightning stroke current flows directly to the ground
through footing resistance of the tower that has been
hit. However, a part of the lightning current flows
through the insulator string air gap to left side upper
phase as a result of the back flashover phenomena, and
another part flows through the sky wire to the nearest
towers and that way to the ground. (see Fig. 7).
Volume 56, Number 1-2, 2015
Fig. 8. Current flowing through insulator string air gap and nearby
towers.
Due to electromagnetic coupling, the amount of
current flowing into the faulted phase wire and through
the sky wire, will not only produce overvoltages on the
upper left side conductor but in all of them. The
produced FFO waveforms propagate over the
transmission line towards the distribution substation.
Fig. 8 presents the evaluated FFO waveforms on Phase
A1 (faulted phase) and Phase A2 (symmetrically
opposite on power line towers) at different locations
along transmission line length considering no surge
arresters connected at substation entrance. In this case
even if the lightning hits at the middle of the power line
length the overvoltage value that reaches the
distribution substations is far over their basic insulation
level.
13
considering
a
200 kA, 8/20 µs lightning current and the back
flashover appears on the left side upper conductor (A1)
when the phase voltage riches its negative peak value.
It can be observed that, by neglecting the different
overvoltage levels produced at tower crossarms, the
single TLine model provides an overestimation of the
produced FFO. On the other hand, by taking into
consideration the presence of tower crossarms and
bracings, the Hara multi-story model introduces a small
delay when the FFO waveform reaches its peak values.
The proposed tower model makes o good correlation
between the evaluated overvoltage levels and the
introduced oscillations by crossarm reflections.
5.2. Effect of different lightning current
implementations
To determine the effect of using different
mathematical function implementation of the lightning
stroke current, the produced FFO waveform at
flashover location has been analyzed for a 200 kA, 8/20
µs lightning current waveform.
Fig. 11. Produced black flash FFO for different lightning current
functions.
Fig. 9. Produced FFO waveform along power line length.
5.1. Influence of Different Tower Models
To identify the effect of using different tower
models in the simulations of a back flashover on the
110 kV power line, the transmission line tower are
model using the equivalent circuit configuration
proposed by the authors. Obtained FFO values and
waveforms are compared with the situation when the
towers were modeled using the single and multi-story
transmission line models presented in section II: the
simple multi-story model, the Ishii and respectively
Hara multi-story model.
From Fig. 10 it can be observed that for the
investigated power line geometry the Ramp and GIGRE
lightning current function implementations provide
higher overvoltage values. However, due their
exponential rise up curve the Double Exponential and
the Heidler function implementations provide an earlier
overvoltage peak value.
Fig. 12 presents the obtained FFO waveforms, at
fault location, in case of a 200 kA lightning current,
with different waveforms using a Heidler function
implementation.
Fig. 12 Produced black flash FFO at fault location for different
lightning current waveforms.
Fig. 10. Produced back flashover FFO at GIS entrance considering
different tower models and no surge arresters connected.
Fig. 9 presents the evaluated FFO waveform at
fault location for each implemented tower model
5.3. Effect of different tower footing resistance
values
To show the effect of different tower footing
impedance values, the produced FFO waveforms have
ACTA ELECTROTEHNICA
14
been evaluated considering for each transmission line
tower footing resistance a fixed 20 Ω, 10 Ω, and 5 Ω
value, respectively the CIGRE soil ionization model
with a 20 Ω low frequency footing resistance and a 300
kV/m soil ionization gradient. Obtained simulation
results are presented in Fig. 11. It can be observed that
the value of tower footing resistance plays an important
role in the produced maximum FFO values during
black flashover phenomena.
oscillations by crossarm reflections, has been proposed
by the authors. Obtained FFO waveforms have been
compared to other existing tower models.
Based on obtained results, the authors conclude
that besides tower modeling, the proper tower footing
resistance and possible soil ionization processes
representation consists in one of the most important
steps regarding the evaluation of fast front overvoltages
produced by lightning strikes to overhead power lines.
Also, it is recommended that in frequent thunder storm
areas to provide a low grounding resistance to
transmission line tower in order to protect the line
against back flashover phenomena.
ACKNOWLEDGEMENTS
Fig. 13. Produced back flashover FFO at GIS entrance for tower
footing impedance values.
Taking into consideration the proper soil
ionization process could prevent overestimations of the
produced overvoltage values and an overdesign of
power line and substation protection equipment.
5.4. Effect of surge arrester on FFO
Finally the effect of surge arresters on the
produced back flashover FFO is analyzed. Usually
surge arresters are connected at substation entrance in
order to protect substation equipment. However, in
frequent thunder storms area could be placed also along
the transmission line in order to protect it Fig. 12
presents the FFO waveform at substation entrance with
and without surge arresters connected and respectively
at the third tower from fault location if additional surge
arresters would be placed there:
Fig. 14. Produced black flash FFO at substation entrance without and
with surge arresters connected to power line.
6.
CONCLUSIONS
The influence of different simulation component
models (like transmission line towers, footing
impedance or lightning current) on fast front transient
overvoltage evaluation, in case of lighting strokes to
overhead power lines has been investigated.
A new more realistic transmission line tower
model that makes o good correlation between the
evaluated overvoltage levels and the produced
This paper was supported by the Post‐Doctoral
Programme POSDRU/159/1.5/S/137516, project cofunded from European Social Fund, through the Human
Resources Sectorial Operational Program 2007‐2013.
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Levente Czumbil
Department of Electrotechnics and Measurements
Faculty of Electrical Engineering, Technical University of
Cluj-Napoca
Cluj-Napoca, Romania
levente.czumbil@ethm.utcluj.ro