2013 Electrical Insulation Conference, Ottawa, Ontario, Canada, 2 to 5 June 2013
Computation of Tower Surge Impedance in Transmission
Line
1
Truong X. Cao1, Thinh Pham1, Steven Boggs2
Department of Power Systems, Hanoi University of Science and Technology
1 Dai Co Viet Street, Hanoi, Vietnam
2
Institute of Materials Science, University of Connecticut
97 N Eagleville Road, Storrs, CT 06369, USA
Abstract:
This paper deals with computation of
transmission line tower surge impedance of a twin circuit
220kV transmission line using Finite Element Analysis
(FEA). The capacitance method was used, but two
different ways of computing capacitance were investigated.
Computation results were compared with experimental
data and other numerical methods. It was shown that the
capacitance computed by FEA provides a better estimation
of the tower surge impedance than any other methods and
also can accommodate complexities such as the presence of
guy wires.
II.
METHODOLOGIES
A. Analytical method
In this method, any type tower of Ht height can be
considered as consisting of two parts, h1 and h2 as shown in
Figure 1. The tower surge impedance is calculated as follows
[1-3]:
⎡ ⎛1
−1 ⎛ ravg ⎞
⎞⎤
Zt = 60ln ⎢cot ⎜ tan ⎜⎜
⎟⎟ ⎟⎥
⎝ Ht ⎠ ⎠⎦
⎣ ⎝2
(1)
where:
Keywords—Finite Element Method (FEM), tower surge
impedance, guy wire
I.
ravg =
INTRODUCTION
Ht
is the average geometric radius of the tower, and r1, r2 and r3
are the actual radius of the tower. Ht is the tower height.
The tower surge impedance is one of the main parameters
to determine the lightning-induced outage rate of a
transmission line. The tower surge impedance can be
determined in several ways including analytical methods [1-4],
experimental measurement [9], numerical computation based
on the electromagnetic field theory [5-7, 13], or a combination
of field computation and transmission line theory [14]. The
analytical method considers a tower as simple cylinder, cone,
or combination thereof. By this method, the surge impedance is
estimated through many approximations. Experimental
determination is valid only for a specific tower on which the
measurement was carried out [9]. The electromagnetic field
method has recently been applied to compute the tower surge
impedance. The basic idea behind this method is to inject a
current surge at the tower top and compute the voltage
waveform developed in the tower [5–7]. Another approach to
compute tower surge impedance is to work in electric field by
computing the capacitance of the tower and then infer the surge
impedance thereof [8].
Figure 1. A simple shape of tower in analytical approach
B. CIGRE method
The surge impedance of tower can be computed from the
total tower capacitance Ct and the travel time Tt [10] as the
following equation:
In the present contribution, we compute the surge
impedance of a twin circuit 220kV transmission line using a
Finite Element Method. The surge impedance of tower was
estimated through the equivalent capacitance. The influence of
guy wires on surge impedance is also computed and compared
with existing data in literature.
978-978-1-4673-4744-0/13/$31.00 ©2013 IEEE
r1h2 + r2 H t + r3 h1
Zt = Tt/Ct
(1)
If the speed of surge is ν, which is assumed to be the speed
of light, and the tower height is Ht, the equation (1) becomes:
Zt =
77
Ht
νCt
(2)
In this method the capacitance of a tower is computed as
suggested by Chow and Yovanovich [11], and also
recommended by CIGRE [4]:
1
Ct = ε 0c f (4π S ) 2
(3)
where:
cf =
2Y
ln(4Y )
Figure 2. Cone tower in the simulation
where Y is the ratio between maximum height and maximum
width, ε0=8,85x10-12 F/m and S is the surface area of the
tower in m2
Table I. Tower impedance, in Ω, of a tower in cone shape
Analytical
CIGRE
Our FEM
FEMM in FLUX3D
method
method [4]
simulation
[8]
in[8]
149.5
C. Computation procedure with a finite element method
(FEM) based software
The module AC/DC in COMSOL multiphysics was used to
compute the electric field energy stored between the tower or a
part of the tower and earth, from which one can infer the
capacitance of the tower or any part of the tower. The Poisson
partial differential equation (PDE) was chosen with
Electrostatic interface. Given the tower capacitance, the surge
impedance as defined in the eq(2). The FEA simulation was
performed in three-dimensions for a tower used in a 220kV
transmission line in Vietnam and which is of similar geometry
to that measured in [9]. The tower under consideration is put in
a box with the boundary conditions are set on the surfaces
thereof (Figure 2). The outer boundary of the box is placed in
order to get its distance from to the center of the tower should
be at least 5 times the distance between the most remote outer
surface of the tower and the center of the tower [12]. The
boundary conditions are set on the base plane and other
surfaces of the box, which are assumed to have zero potential.
The footing resistance is ignored and the base plane is set to be
zero charge, which means the potential is symmetric with
respect to the boundary. The tower is assumed to have a
potential of 1V. This procedure is adopted throughout
simulations performed in this work. The capacitance of the
tower is inferred from the electric field energy stored in the
system by:
Ct =
2We
U2
136.9
155.8
125.9
B. Comparison with experiment
Figure 3. UHV tower in [9]
The simulation was also performed with UHV tower
configuration in Figure 3, and the results were compared with
the experiments from [9].
In our FEM analysis, 3D model was selected to simulate
such a complex structure. The influence of the presence of the
lattice girder on the tower surge impedance is insignificant and
therefore it was neglected as suggested in [8]. In this model,
the mesh is “free tetrahedral”. The boundary limit is a
hexahedron with the distance from the “convex point” to
boundary which depends on the tower shape as described in
the section II.C. The results obtained from our simulations are
shown in Table II.
(4)
where U is the potential set on the tower (1V) and We is the
computed energy.
III.
142.4
SIMULATON RESULTS
A. Comparison with another simulation
First, the simulation was performed with a tower in the shape
of a cone. Figure 2 shows the representation of a cone 30
meters high and 10 meters diameter at its base. Table I shows
the surge impedance obtained by various methods [8]
compared with that obtained in our analysis. As can be seen in
the Table I, the computed impedance from our analysis is
close to that from other simulations.
Figure 4. UHV tower representation in our FEM simulation
78
200
Table II. Comparison of different methods of tower surge impedance
calculation
CIGRE
Our FEM
Experiment
Analytical
method [4]
simulation
[9]
FEM simulation
CIGRE method
Tower surge impedance (Ohm)
180
184.4
150
146.52
130
The result obtained from the analytical method
differs from experiments because it does not consider the
tower crossarms. The CIGRE method takes into account the
crossarms but approximates the tower capacitance based on
the surface area of the tower [11]. That might be a reason why
the result obtained from our FEM simulation provides a tower
surge impedance which is closer to experiment than that
estimated from CIGRE method. The simulation is also
performed for various towers used in a twin circuit 220kV
transmission line in Vietnam as shown in Figure 5 (see
Appendix).
sFigure 5. Tower surge impedance computed for various towers used in a
Zt(Ω)
160
140
120
100
80
60
40
0
1
2
3
4
5
6
7
8
9
Number of guy-wire
Figure 7. Tower surge impedance as a function of number of guy wire
Tower surge impedance (Ohm)
180
FEM simulation
CIGRE method
160
220kV transmission line in Vietnam (see appendix)
C. Surge impedance in presence of guy wires
This section examines the use of guy wires to reduce the
total tower surge impedance of a transmission line in order to
improve its lightning performance. This case study used the
tower D52 as specified in the appendix. The guy wires are
connected to the tower at the height of Hb above the base. The
guy wire radius is 20mm, and the guy wires hang at 45
degrees to the tower (Figure 6). In our FEM simulation, the
boundary condition is a box having width and length of 103m
and height of 66.8m for the tower D52. The boundary
conditions are set as described in the section 2C.
140
120
100
80
60
5
10
15
20
25
30
35
Distance from the top "attach" to the base (m)
Figure 8. Tower surge impedance as a function of the height of guy wire
attachment above tower base of the tower D 52
180
Tower surge impedance (Ohm)
before extending guy-wires
after extending guy-wires
160
140
120
100
80
ND39
N34
ND40
D52
D33
D38
D44.5
Type of tower
Figure 9. The tower surge impedance before and after extending 4 guy wires
for various tower types used in 220kV transmission line (see appendix), height
of guy wire, Hb, is 31 m.
Figure 6. Tower D 52 with guy-wires. (a)- 2 guy wires. (b)- 3 guy wires.
(c)- 4 guy wires. (d)- 8 guy wires
Figure 8 show the tower surge impedance as a function of
the distance from the “top attach” to the base Hb. The tower
surge impedance decreased when Hb is increased. Thus, the
utility should make a trade-off when they want to decide the
position to hang the guy wire. The tower surge impedance are
also computed for various tower type in a 220kV transmission
line which results from using 4 guy wires (Figure 9)
As can be seen in Figures 7, the tower surge impedance
computed by our FEM simulation get closer to that estimated
by CIGRE method as the number of guy wire increases. This
Figure 7 shows the tower surge impedance as a function of
number of guy wires for tower D52 tower with Hb of 31m.
Changing the number of guy wire from 2 to 8 does not
decrease the surge impedance much. Therefore, 2 guy wires
attached to a tower would be an optimal solution in term of
decreasing tower surge impedance.
79
[12] Qiushi Chen and Adalbert Konrad. “A Review of Finite Element Open
Boundary Techniques for Static and Quasi-Static Electromagnetic Field
Problems. ” IEEE Trans on Magnetics, Vol. 33, No 1, January 1997, pp
663-676
difference comes from the fact the CIGRE method considers a
tower surface area greater than that used in FEM analysis in
presence of guy wires. Therefore, the equivalent capacitance
in CIGRE estimation become close to that calculated from the
FEM simulation when many guy wires seem to form a surface.
IV.
[13] Shoory, Abdolhamid, Felix Vega, Peerawut Yutthagowith, Farhad
Rachidi, Marcos Rubinstein, Yoshihiro Baba, Vladimir A. Rakov,
Keyhan Sheshyekani, and Akihiro Ametani. "On the Mechanism of
Current Pulse Propagation Along Conical Structures: Application to Tall
Towers Struck by Lightning." IEEE Transactions on Electromagnetic
Compatibility, vol. 54, no. 2 (2012), pp. 332-342.
CONCLUSION
The tower surge impedance of various types of
towers used in 220kV transmission line in Vietnam was
computed by capacitance method, with the capacitance
estimated by the CIGRE method and using FEM simulation.
The results from FEM analysis indicate that it may provide a
better agreement with experiments than other methods.
Furthermore, it is more flexible when computing tower surge
impedance in presence of guy wires. From the agreement with
experiment, FEM simulation can be used to compute the surge
impedance of any part of the tower, which is very convenient
to implement to into electromagnetic transient analysis of the
transmission line.
[14] Harid, Noureddine, Huw Griffiths, and Abderrahmane Haddad. "A new
frequency-dependent surge impedance calculation method for highvoltage towers." IEEE Transactions on Power Delivery vol. 21(3)
(2006), pp. 1430-1437.
APPENDIX
REFERENCES
[1]
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[2]
General Electric Company and Electric Power Research Institute,
"Transmission line reference book, 345KV and above" pp. 555–556
[3]
Chisholm, W. A. , Chow, Y. L. and Srivastava, K. D. , “Lightning surge
response of transmission towers.” IEEE Trans. PAS. Vol. 88 No. 9,
September 1983, pp 3232-3242
[4]
CIGRE, “Guide to procedures for estimating the lightning performance
of transmission lines.” CIGRE Brochure 63, 1991
[5]
F. P. Dawalibi, W. Ruan, S. Fortin, J. Ma, J. Ma, and W. K. Daily,
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Ditribution Conference and Exposition, Atlanta, Oct. 28-Nov. 2, 2001.
[6]
[7]
[8]
[9]
Name in
the
simulation
N34
Type of tower
H(m)
h1(m)
h2(m)
NP220-4+5
34
15.5
18.5
N36
N222A+DP
36
19.5
20.5
N38
38
19.5
18.5
39
19.5
19.5
N40
NP220-4+9
N222AY;BY;C;D
+9
N222A+9DP
40
19.5
20.5
ND40
N222A+9DP
40
19.5
20.5
ND36
N222A+5DP
36
15.5
20.5
D33
DP220-4-5
33
17,5
15.5
D38
38
22.5
15.5
44.5
29
15.5
D46,5
DP220-2
D222AY;BY;CY
+6.5
DP220-46
46.5
21
15.5
D52
DP220-52
52
36.5
15.5
V58
V22-58
58
38
20
V68
V222Y-68
68
48
20
N39
Leonid Grcev, Farhad Rachidi, “On tower impedances for transient
analysis.” IEEE Trans. on Power Delivery, Vol. 19, No. 3, July 2004,
pp. 1238-1244.
Changzeng Gao, Lin Li, Bing Li, and Zhibin Zhao “ Computation of
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P.C.A. Mota , M. L. R. Chaves, “Power Line Tower Lightning Surge
Impedance Computation, a Comparison of Analytical and Finite
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and Power Quality (ICREPQ’12), Santiago de Compostela (Spain),
March, 2012
D44,5
Yamada, T.; Mochizuki, A.; Sawada, J.; Zaima, E.; Kawamura, T.;
Ametani, A.; Ishii, M.; Kato, S., “Experimental Evaluation of A UHV
tower model for lightning surge analysis.” IEEE Trans Power Delivery,
Vol 10, No 1, Jan 1995, pp 393-402
[10] W.A. Chisholm and Y.L.Chow, “Travel time of transmission towers.”
IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104,
No. 10, October 1985, pp. 2922-2928
[11] Y. L. Chow, M. M. Yovanovich, “The shape factor of the capacitance of
a conductor.” J Appl. Phys. 53(12), December 1982
80